entropy & energy

[gsax]

Hi

Entropy is defined as:
" A measure of the disorder or randomness in a closed system"

Alternatively it is also defined as
:"For a closed thermodynamic system, a quantitative measure of the
amount of thermal energy not available to do work."

I am not sure how one definition follows from the other & how are they
equivalent.

If Heat is "Disordered form of Energy" , then what are the "Ordered
forms".
You may say ...light.

But then any hot body also radiates EM waves & then could be said to be
producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...

Alternatively what is the Entropy of a collection of Light Quanta?

Hope this makes sense. I would appreciate any lucid responses that can
reduce my confusion about what is Ordered form of Energy & what is not.

thanks
Gsax

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[Igor Khavkine]

On 2005-09-03, gsax <gaurav_iitg@yahoo.com> wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
>:"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

It's a very good question. This equivalence is far from obvious. It is
the great achievement of Boltzmann and other founders of statistical
mechanics.

> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.

Actually, I was going to say mechanical energy. Examples include
kinetic energy, the potential energy of a pendulum, the compression
energy or a spring, or the work that can be done by a gas exerting a
pressure on a piston. These are forms of energy that we can directly
exploit. If a source of such energy is available, it is a simple matter
to rig up some pulleys and gears to use this energy to, say, make an
elevator work.

From the experiments of Joule and others, we know that this kind of
mechanical work can be turned into heat. But, can heat be turned back
into mechanical work? Intuitively, it's clear that that's not so easy.
It's kind of hard to power an elevator with a hot piece of rock. One has
to use a medium that can convert thermal energy into mechanical energy,
such as a gas which expands when heated, or a thermoelectric device that
produces a current under a temperature gradient.

The empirical study of such "converter" media has resulted in the
formulation of thermodynamics and the identification of entropy, which
quantifies how much thermal energy cannot be extracted as mechanical
work. The great achievement of Boltzmann was to calculate this quantity
based on a microscopic theory of the material in question. He calculated
it precisely as the "amount of disorder" in the microscopic
configuration of the material.

> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?

Radiation, just like matter, can be treated thermodynamically. Also,
contrary to what you seem to be thinking, radiation is not energy, it
can store energy. Just like an ideal gas of molecules, a bunch of
photons bouncing around in a box behave like an ideal gas. It has the
same equation of state, pV = NT (Boltzmann's constant set to 1), but a
different internal energy, U = 3NT, as opposed to U = (3/2)NT for a
non-relativistic monatomic gas. Just like a regular gas, it has pressure
that can do mechanical work as well as entropy, which quantifies the
amount of work that can be extracted from it, as you said above.

> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.

The short answer is mechanical energy (available to do mechanical work),
and sometimes chemical energy (available to change the number of
molecules of a particular species). There are other examples, of various
degrees of sophistication, but these are the most common ones. The rest
is heat, or so-called disordered energy.

Hope this helps.

Igor

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[gsax]

Hi Igor

Thanks for your mail. It helps clarify the concepts.

Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Mike]

gsax wrote:
> Hi
>
> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."
>
> I am not sure how one definition follows from the other & how are they
> equivalent.

Boltzmann defined entrophy as

S = k * (ln omega)

k is Boltzmann's constant
omega is the number of states that the components (say gas molecules)
can be in so that whole has the following bulk properties: energy=E,
pressure=P, temperature=T, and volume=V.

A bulk gas consists of a truely large number of molecules/atoms, each
with its own momentum and position values. The number of unique
configurations of these individual states is what omega captures.

OK, listen up. Omega is a measure of the order of a system. Systems
with low entropy have very few possible states. The suite of hearts in
a deck of cards fresh from the factory consists of 13 ordered cards.
When so ordered they have low entrophy, i.e. there is only one
configuration of 13 cards that describes this ordering. However when
shuffled there are many possible disordered states as many a card
player hoping for a royal flush have found.

So Boltzmann's equation relates the energy, temperature, pressure, and
volume of a system to the degree of disorder in that system.

See, for example:
http://en.wikipedia.org/wiki/Thermodynamic_entropy

--Mike Jr.

>
> If Heat is "Disordered form of Energy" , then what are the "Ordered
> forms".
> You may say ...light.
>
> But then any hot body also radiates EM waves & then could be said to be
> producing "Ordered Energy" (Light) from "Disordered Energy" (Heat)...
>
> Alternatively what is the Entropy of a collection of Light Quanta?
>
> Hope this makes sense. I would appreciate any lucid responses that can
> reduce my confusion about what is Ordered form of Energy & what is not.
>
> thanks
> Gsax

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Andy Resnick]

Igor Khavkine wrote:

<snip>
>
> Hope this helps.
>
> Igor

Igor,

Thanks for the masterly exposition- well put! For those interested in
another extremely clear (for me, at least) discussion of the study of
energy 'converters', especially the work of Kelvin, Carnot, and
Clausius, I recommend:

Truesdell, C. The Tragicomical History of Thermodynamics, 1822-1854

If you can find it.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Edward Green]

gsax wrote:

> Entropy is defined as:
> " A measure of the disorder or randomness in a closed system"
>
> Alternatively it is also defined as
> :"For a closed thermodynamic system, a quantitative measure of the
> amount of thermal energy not available to do work."

Your "definitions" can be made slightly more quantitative. The first
description is based on the law:

S = k ln W (I)

where S is the entropy, k Boltzmann's constant, and W a measure of the
number of microscopic states compatible with the macroscopic state,
whereas the second description is based on:

TdS = dQ_rev (II)

where T is the absolute temperature, dQ the heat into the system
(dQ_rev the heat in a reversible change of state), and the principle
that for any real process

dQ < dQ_rev

Given that the change in internal energy

dE = dQ - dW

(where dW is the work done by the system) is fixed for a given change
of state, it follows that entropy change, by putting a upper bound on
dQ, puts an upper bound on dW.

I don't know how one moves quantitatively from (I) to (II), but since
your question was submitted to sci.physics.research, and apparently
accepted, maybe somebody there will be kind enough to at least sketch
the outline of the precis of an argument to that effect!

[Given that we have written out the relations I & II, and that entropy,
temperature and energy are related by

1/T == @S/@E_V (III)

(i.e., reciprocal temperature is defined by the partial derivative of
entropy w.r.t energy at constant volume) it doesn't seem impossible
that we will get both these ideas on the same page. Maybe we need some
other principle, like equipartition of energy.]

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY

[Daryl McCullough]

Edward Green says...

>Your "definitions" can be made slightly more quantitative. The first
>description is based on the law:
>
> S = k ln W (I)
>
>where S is the entropy, k Boltzmann's constant, and W a measure of the
>number of microscopic states compatible with the macroscopic state,
>whereas the second description is based on:
>
> TdS = dQ_rev (II)
>I don't know how one moves quantitatively from (I) to (II)

Okay, imagine that we have two systems that are in thermal
contact, so that they can exchange energy. (For example, two boxes
touching each other, each filled with some substance like air.)

Let E1 be the amount of energy in system 1, and let E2 be
the amount of energy in system 2. When we put the two systems
in contact, is energy more likely to flow from system 1 to
system 2, or the other way around?

We can work it out as follows:

Let W1(E1) be the number of states of the first system with
energy E1.

Let W2(E2) be the number of states of the second system with
energy E2.

Then W(E1,E2) = W1(E1)W2(E2) is the number of states of the
combined system with the given energies in the two subsystems.

Now, look at the quantity

dW = W(E1-dE, E2+dE) - W(E1,E2)

where dE is some tiny quantity of energy. If dW is positive,
then that means that are more ways for the subsystems to have
energies E1-dE and E2+dE than there are ways for the subsystems
to have energies E1 and E2. That means that energy is more likely
to move from system 1 to system 2. If dW is negative, energy
is more likely to go in the opposite direction.

We'll assume that W1(E1) and W2(E2) can be approximated by
differentiable functions. In that case, we can approximate
dW as follows: (using @f/@x to mean the partial derivative
of f with respect to x)

dW = - @W/@E1 dE + @W/@E2 dE
= (- W2(E2) d/dE1 W1(E1) + W1(E1) d/dE2 W2(E2)) dE
= W1(E1) W2(E2) ((dW2/dE2)/W2 - (dW1/dE1)/W1)
= W1(E1) W2(E2) ( d log(W2)/dE2 - d log(W1)/dE1 )

So, if we let S2 = k log(W2) and S1 = k log(W1), then energy
will flow from system 1 to system 2 if

dS2/dE2 > dS1/dE1

or

1/(dS1/dE1) > 1/(dS2/dE2)

So the quantity T = 1/(dS/dE) is a measure of how "hot" a system is;
energy is most likely to flow from a system with a larger value of T
to a system with a smaller value of T.

By the definition of T, it follows that

T dS = dE

so this statistical measure works just like the thermodynamic
temperature, and we can identify the two concepts.

--
Daryl McCullough
Ithaca, NY