Entropy and Heat Capacity have the same units. Connection? Redundancy?

In summary, the conversation discusses the relationship between heat capacity and entropy, and whether energy flows from media with low heat capacity to those with high heat capacity. It is also mentioned that heat energy transferred during phase changes does not affect heat capacity. The concept of entropy flowing from one place to another is also debated, with one participant suggesting that entropy increases in both the system and surroundings during a process. The conversation ends with a discussion on the definition of energy and whether it can be thought of as having a temperature.
  • #1
kmarinas86
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1
Given that heat capacity is a ratio of change of energy over change of temperature, while entropy is a change of energy over absolute temperature...

I was wondering if there is any basis for the idea that energy will tend to flow from media having low heat capacity to media having high heat capacity, such that the imported energy becomes colder as a result of the higher heat capacity of the destination medium relative the medium departed.

See a table of specific heat capacities for different materials:
http://en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities

In other words, energy of an object could be thought of as getting hotter or colder due to heat capacity variations. As a result of such a energy transfer (=ΔE), the entropy would increase as result of ΔE/t increasing (i.e. 0 < ΔE/t_(cold, final) - ΔE/t_(hot, initial)), where ΔE specifically would refer to the energy that is transferred. In this sense, entropy is not so much a flow, but rather an intensity like heat capacity. And what if, in the end, if we account for entropy changes by such transfers of energy, couldn't that concept of pinning thermodynamic state variables to energy as opposed to pinning them to boundary-defined systems, as is almost always assumed in traditional teaching, make entropy and heat capacity one-and-the-same-thing?

It is also known that there are different heat capacities for a given substance based on:
* constant volume, as in an isochoric process
* constant pressure, as in an isobaric process

So depending on the present process occurring in a given thermodynamic cycle, the direction of energy flow that would increase entropy could change - or even reverse.

Conversely, one could flip the perception around and imagine that entropy itself flows from systems of low heat capacity to those of high heat capacity, causing the heat capacity of the systems which they flow into to increase, while causing the heat capacity of systems they are leaving to decrease.

Certain materials have different effects on the flow of heat, so couldn't understanding of that be aided by the idea that entropy and heat capacity are intimately connected? Could the ability to engineer extreme differences in heat capacity facilitate extraction of ambient thermal energy? If there can be a heat capacity for constant pressure and a heat capacity for constant volume, wouldn't the concept of pinning thermodynamic state variables to energy as opposed to pinning them to boundary-defined systems, as is almost always assumed in traditional teaching, suggest the existence of a temperature for constant pressure [dynamics] and a temperature for constant volume [statics], so maybe it is related to the relation between dynamic pressure vs. static pressure: https://www.physicsforums.com/showthread.php?t=169660?
 
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  • #2
Entropy and Heat capacity are, indeed, related concepts.
I think you want the statistical mechanics description of these things to understand your questions.

What you don't want to do is think of the energy as having a temperature. An object may have thermal energy as well as temperature... two properties which are related.
 
  • #3
Simon Bridge said:
What you don't want to do is think of the energy as having a temperature.

Why not?
 
  • #4
Why not?

Well it is estimated that the average temperature of the world ocean is about 4°C whereas the average temperature the average temperature of the water in my kettle is 100°C. But which has more energy and entropy?

I was wondering if there is any basis for the idea that energy will tend to flow from media having low heat capacity to media having high heat capacity, such that the imported energy becomes colder as a result of the higher heat capacity of the destination medium relative the medium departed.

Heat energy transferred in the process of phase change has nothing to do with heat capacity.

Entropy (unlike energy) does not 'flow from one place to another'. In the above example the take up of latent heat on say melting goes into a rearrangement of the melting system such that it has greater entropy. The heat supplied to cause the melting may also result in greater entropy of the surroundings if it is the result of a say a chemical reaction such as burning a fuel.
So the entropy does not flow from surroundings to system but increases in both. The overall entropy of the universe may increase by such a process.
 
  • #5
Studiot said:
Well it is estimated that the average temperature of the world ocean is about 4°C whereas the average temperature the average temperature of the water in my kettle is 100°C. But which has more energy and entropy?


The ocean has more entropy because of two things:

1: There is more heat energy in the ocean (Joules)

2: The heat energy in the ocean is at lower temperature (Kelvins)
 
  • #6
Studiot said:
kmarinas86 said:
Simon Bridge said:
What you don't want to do is think of the energy as having a temperature. An object may have thermal energy as well as temperature... two properties which are related.

Why not?

Well it is estimated that the average temperature of the world ocean is about 4°C whereas the average temperature the average temperature of the water in my kettle is 100°C. But which has more energy and entropy?

Is that really a good reason why we should not think of energy as having a temperature?

I can think of a van as having 1 passenger. Such a concept makes sense. I can state that, "A van has 1 passenger." That statement is not made incomprehensible or meaningless by the notion of a Mini Cooper which has three passengers on board. It means something, and that meaning makes sense. It is not unreasonable to think of such a case.

Studiot said:
Heat energy transferred in the process of phase change has nothing to do with heat capacity.

How can you be so sure of that? Doesn't adding enough energy to 99 degree Celsius water at atmospheric pressure cause it to change its heat capacity as it transitions to the gaseous phase?

http://chemistry.about.com/od/worke...eat-Capacity-Phase-Change-Example-Problem.htm

Studiot said:
Entropy (unlike energy) does not 'flow from one place to another'. In the above example the take up of latent heat on say melting goes into a rearrangement of the melting system such that it has greater entropy. The heat supplied to cause the melting may also result in greater entropy of the surroundings if it is the result of a say a chemical reaction such as burning a fuel.
So the entropy does not flow from surroundings to system but increases in both. The overall entropy of the universe may increase by such a process.

How do you know that the entropy didn't already exist and that it didn't come from some atoms, causing the entropy within the atoms to fall and the entropy outside the atoms to increase?
 
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  • #7
jartsa said:
The ocean has more entropy because of two things:

1: There is more heat energy in the ocean (Joules)

2: The heat energy in the ocean is at lower temperature (Kelvins)

Do you think it makes sense for energy to have an entropy?

If so, why is the same not the case for temperature?

If not, then why does it make sense for a system to have entropy, while the same is not true for energy. Also, why does it make sense to talk about the temperature of a system, and the temperature of an object, but not the temperature of an energy?
 
  • #8
I will try one more time.

Energy, entropy and temperature are different physical quantities or properties or variables.

Temperature is an intensive property.

Entropy and energy are extensive properties.

(Pressure, temperature , molar volume, specific heat, refractive index are examples of intensive properties.

Mass, volume, enthalpy, entropy, heat capacity, pressure_volume product are extensive examples.)

The physical dimensions (units) of energy or entropy preclude them "having a temperature".
An example property that does have a temperature is boiling point.

The same goes for "energy having an entropy"

Both are nonsensical notions.
 
  • #9
Studiot said:
I will try one more time.

Energy, entropy and temperature are different physical quantities or properties or variables.

Temperature is an intensive property.

Entropy and energy are extensive properties.

(Pressure, temperature , molar volume, specific heat, refractive index are examples of intensive properties.

Mass, volume, enthalpy, entropy, heat capacity, pressure_volume product are extensive examples.)

The physical dimensions (units) of energy or entropy preclude them "having a temperature".
An example property that does have a temperature is boiling point.

The same goes for "energy having an entropy"

Both are nonsensical notions.

Like units of temperature, units of velocity "m/s" constitute an intensive property. Using the same logic that you just gave here, you would then say that the idea that a mass (kg) could have both velocity (m/s) and momentum (kg*m/s) would also be nonsensical. That does not follow, because mass with velocity and momentum is imaginable, and in fact I'm looking at one right now. So it's not imaginary.

Using your contrived argument, you would also conclude that: "1 kg of water doesn't have a boiling point, because 1 kg of water is 1 kg of mass, 1 kg of mass is an extensive property, and an extensive property cannot have an intensive property such as a boiling point." That to me sounds a bit ludicrous.
 
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  • #10
I was wondering if there is any basis for the idea that energy will tend to flow from media having low heat capacity to media having high heat capacity

This is also not true.

Take soldering iron (specific heat about 0.5) heat it and apply to solid solder (specific heat about 0.15).
Heat flows from the iron to the solder and the solder melts, although the heat capacity of the iron is more than 3 times that of the solder.
 
  • #11
Studiot said:
kmarinas86 said:
I was wondering if there is any basis for the idea that energy will tend to flow from media having low heat capacity to media having high heat capacity

This is also not true.

Take soldering iron (specific heat about 0.5) heat it and apply to solid solder (specific heat about 0.15).
Heat flows from the iron to the solder and the solder melts, although the heat capacity of the iron is more than 3 times that of the solder.

I'm not saying that heat cannot flow from media of high heat capacity to media of low heat capacity. I'm ask about the tendency for heat to flow from a material of low heat capacity to another of high heat capacity, versus the other way around.
 
  • #12
Heat flows (spontaneously) from a body with a higher temperature to one with a lower temperature.

That is one version of the second law of thermodynamics, due to Clausius.
 
  • #13
Let's take another simple example.

Liquid water has about 10 times the specific heat (5) of the iron in the previous example.

Heat the iron to 180°C and dip it into the water at 25°C.
Yes the heat will flow from the iron to the water, as you said.

Now cool the iron to 5°C and again dip it into the water.

Heat will now flow from the water to the iron.

What's changed other than the direction of heat flow?

Thermodynamics is quite clear about this. Temperature (difference) is the property which determines the direction of the heat flow.
Nothing else.
 
  • #14
Studiot said:
Heat flows (spontaneously) from a body with a higher temperature to one with a lower temperature.

That is one version of the second law of thermodynamics, due to Clausius.

Studiot said:
Thermodynamics is quite clear about this. Temperature (difference) is the property which determines the direction of the heat flow.
Nothing else.

What I'm suggesting is that the temperature itself could be affected by the heat capacity. The temperature could be a secondary result. Think about iron, it has a high heat capacity, but compared to what? Many solids tend to have low heat capacity as a result of many factors, including their density for example. It takes less energy to increase the temperature of most solids relative to gases. Cause and effect could work like this:

Energy -> Various heat capacities -> Temperature differences -> Heat flows
 
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  • #15
What I'm suggesting is that the temperature itself could be affected by the heat capacity.

No, it's the other way round.

Heat capacity varies with temperature.

When you have a better understanding of thermodynamics fundamentals you will be able to explore the reasons for this variation.

But you need to come to terms with the basics first, rather than argue with the second law.
 
  • #16
Studiot said:
No, it's the other way round.

Heat capacity varies with temperature.

"Vary" does not mean the same as "caused by".

"Heat capacity varies with temperature" is equivalent to saying "temperature varies with heat capacity". "Varies" is an associative term.

What explains the difference of heat capacity between lead and gold (i.e. what is it caused by)? It's obviously not the temperature.
 
  • #17
Heat capacity is actually an extrapolation of a more general statistical expression. From Hill's statistical thermodynamics I derived this expression for CV. If you have the book I used eqns [2-5], [2-1], and [1-11]. Of course, there are probably better definitions but this is as far as I've gotten in the text so far.

[itex] C_V = ( E- (\sum_j E_{j}e^{-E_{j}/{kT}} /{ \sum_j e^{-E_{j}/{kT}} }) )^{2}/{kT^{2}} [/itex]

where E is the energy of the system
k is the Boltzmann constant
T is temperature
Ej is the energy of an individual molecule in the system (a function of N,V for the canonical ensemble)

So if you really wanted to you could sum over the energy this way, knowing the temperature distribution to solve for the heat capacity. DISCLAIMER: I am a novice at stat-thermo!
 
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  • #18
Vary" does not mean the same as "caused by".

"Heat capacity varies with temperature" is equivalent to saying "temperature varies with heat capacity". "Varies" is an associative term.

Indeed correlation does not prove causation.

But what I can do is take a block of material and set its temperature.
Nature does not force a temperature on me.
Nature, however does force a heat capacity on me, I cannot set a heat capacity, which is why I looked up the values I posted earlier in Kaye and Laby.
 
  • #19
Also, note that the entropy can be expressed statistically as:
[itex] kT ({\partial Q} /{\partial T})_{V,N} + k ln{Q} [/itex]
where Q is a partition function expressed by
[itex]Q = \sum e^{ -E_{j}/kT }[/itex]

equations [1-33] and [1-29] in Hill. Also note that this is for the canonical ensemble. I forgot to mention this earlier, but a canonical ensemble is a 'closed' thermodynamic system governed by the number of molecules, N, volume, V and temperature, T.

So to answer your question, yes they are very much related and dependent on each other!
 
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  • #20
What explains the difference of heat capacity between lead and gold (i.e. what is it caused by)? It's obviously not the temperature.

It's no use asking questions if you are not willing to listen to the answer, as you have done several times in this thread.

So I will leave you for tonight with the suggestion that you get a good hold of the basics so that you do not come out with more ideas that contradict the basic laws as when you suggested that something other than temperature determines the direction of heat flow.

It is useful and perhaps important to be able to have a good idea of what is happening in a simple example system such as my iron dipped in the water or solder before you delve into the statmech that Simon and Aero are offering. Otherwise it is easy to go hoplessly astray. You need to be aware that their approach has yielded some real successes but also some spectacular failures in explaining the behaviour and properties of real materials.
 
  • #21
Studiot said:
Indeed correlation does not prove causation.

But what I can do is take a block of material and set its temperature.
Nature does not force a temperature on me.
Nature, however does force a heat capacity on me, I cannot set a heat capacity, which is why I looked up the values I posted earlier in Kaye and Laby.

It appears that when the association between object and "region" is made, not much is said, if anything at all, about the heat capacity of the imported thermal energy itself (e.g. thermal phonons). Perhaps the "heat capacity of a solid" is actually the "heat capacity of a solid plus any imported energies". This would appear to correspond to the fact that adding heat to a mass will tend to increase the (total) heat capacity. So maybe that increase can be thought of as an imported heat capacity coinciding with the import of energy (i.e. heat capacity and thermal energy could be cotransported).
 
  • #22
kmarinas86 said:
Using your contrived argument, you would also conclude that: "1 kg of water doesn't have a boiling point, because 1 kg of water is 1 kg of mass, 1 kg of mass is an extensive property, and an extensive property cannot have an intensive property such as a boiling point." That to me sounds a bit ludicrous.
One kilogram doesn't have a boiling point. I.e. mass does not have a boiling point. Water can have mass and water can have a boiling point, so there is nothing wrong with saying that 1 kg of water boils at 100°C, but there is something wrong with saying that 1 kg boils at 100°C
 
  • #23
DaleSpam said:
One kilogram doesn't have a boiling point. I.e. mass does not have a boiling point. Water can have mass and water can have a boiling point, so there is nothing wrong with saying that 1 kg of water boils at 100°C, but there is something wrong with saying that 1 kg boils at 100°C

Right, and the reason has nothing to do with extensive vs. intensive properties, as was being claimed earlier. 1 kg of water is as "extensive" as 1 kg of mass itself. The former implies a boiling point (given that pressures are not extreme), while the latter does not.

It is in this sense where I was suggesting that an energy could "have a temperature". Some people expressed some disagreement regarding that claim, saying that it makes no sense for an energy to have a temperature. However, if a mass can have a temperature, why not energy itself (whether in the form of large numbers of particles, quasiparticles, or waves)?

What I'm questioning is the necessity of having a boundary-defined thermodynamic system be attributed with thermodynamic variables to explain thermodynamic phenomenon. I'm also questioning how such attribution could be distorting the relationship between entropy, energy, temperature, and other thermodynamic variables, and I'm thinking that these thermodynamic variables are better attributed to each other mutually, without regard to heat and mass flow to and from boundary-defined "systems". Such a change could lead to more accurate models, where no one talks about a "reservoir" having a temperature or about any such approach which seems to ignore inhomogeneities and anisotropies in thermodynamic systems.

My concern is for systems in non-equilibrium thermodynamics, where a simple temperature function seems unobtainable, which might be due to the fact that the "heat reservoir" concept still sticks to some minds and which also manifests itself in the equations assumed by equilibrium thermodynamics, which might be shown to be inadequate.
 
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  • #24
Temperature can be thought of as energy per state. Doubling the mass, at the same temperature, doubles the energy and the number of states. In a gas mixture, monatomic gases have three states for storing energy (x, y, and z velocities) while diatomic gases have 5. Hence diatomic gases have a higher specific heat.
If we add heat to a body mass M, raising its temperature from T0 to T1, and it has constant specific heat H, its gain in entropy is M H log(T1/T0). So you could think of s.h. as an entropy gain factor.
One of the posts (considering oceans versus a kettle) implied that a colder body has more entropy than warmer one of the same mass etc. This is wrong. Its rate of increase of entropy as heat is added will be higher, but its total entropy will be lower.

The whole discussion about intensive versus extensive can be resolved fairly simply: instead of suggesting that "energy has a temperature", try "energy per unit mass has a temperature". I'm not saying that's valid either, but it has a better chance.
 
  • #25
kmarinas86 said:
However, if a mass can have a temperature, why not energy itself (whether in the form of large numbers of particles, quasiparticles, or waves)?
A mass cannot have a temperature. If you believe otherwise then what is the temperature of a mass of 1 kg?

Similarly energy cannot have a temperature. If you believe otherwise, then what is the temperature of an energy of 1 J?

kmarinas86 said:
My concern is for systems in non-equilibrium thermodynamics, where a simple temperature function seems unobtainable, which might be due to the fact that the "heat reservoir" concept still sticks to some minds and which also manifests itself in the equations assumed by equilibrium thermodynamics, which might be shown to be inadequate.
I share your frustration with respect to non-equilibrium thermo, but I think this approach is a non-starter. I would look elsewhere.
 
  • #26
DaleSpam said:
A mass cannot have a temperature. If you believe otherwise then what is the temperature of a mass of 1 kg?

Similarly energy cannot have a temperature. If you believe otherwise, then what is the temperature of an energy of 1 J?

I share your frustration with respect to non-equilibrium thermo, but I think this approach is a non-starter. I would look elsewhere.

It depends on what J or kg you are dealing with.

What do you call a thermal mass? Something that does not have a temperature??!
 
  • #27
It is not a good idea to think of energy as being the thing that has the temperature because it will lead you into all kinds of confusions. For one thing you risk confusing different models. If you try to express your original question without referring to the temperature of the energy you should be able to see the answer.

Generally, entropy, heat, and temperature are all properties of some object or fluid system. It also has color and weight ... but we don't normally want to talk about it's weight having a color. We can argue that it makes a kind of a sense to do so - just not a helpful kind.

In your case, for the kind of question you are asking, it is unhelpful to think of (heat) energy having a temperature. Temperature is an emergent property from the random motions of small bits of the object ... the temperature of energy would involve random motions of small bits of the energy not the bits of the object.

It looks to me that you have made a mistake that comes from your unconventional use of technical terms in thermodynamics.
Humour me.
 
  • #28
A mass cannot have a temperature. If you believe otherwise then what is the temperature of a mass of 1 kg?
A mass can have whatever temperature the thermometer says it has ;)

You will find examples stating "a mass of 1kg is moving at speed 5m/s ..." so apparently a mass can have a speed: why not a temperature?

I thought of that example but didn't use it because there are two uses of the word "mass" in physics. We talk about mass as the inertia of an object, but also to refer to the object itself. So the word "mass" here, has two roles. Such is English.

However, where it is important to distinguish, we do use different words - just to avoid confusion - like I did above by saying "object". So, properly, "an object has a mass of 1kg and a speed of..."

Confusion on this point is not uncommon amongst students and can take quite a long time to stamp out. We need to be able to articulate the distinction better.

In thermodynamics, it is important to distinguish what it is that has the temperature.

Using OPs own example of passengers in a car: myself, my wife, and my dog are all passengers in my car. My car has three people in it, I have a wife and a dog. But my car does not have my wife, nor does my dog. I may say "I have two passengers" but not in the same sense that I say "my car has two passengers".
 
  • #29
kmarinas86 said:
It depends on what J or kg you are dealing with.
Then the temperature is a property of that "what" that "you are dealing with", not the energy or the mass. If energy itself has temperature then there must be an unambiguous answer to the question "what is the temperature of 1 J".

For example, energy has mass. There is an unambiguous answer to the question "what is the mass of 1 J". That is given by the formula E=mc², so the mass of 1 J is 1.1E-17 kg.
 
  • #30
Simon Bridge said:
A mass can have whatever temperature the thermometer says it has ;)
No, the system has a temperature and a mass. If you believe otherwise then please provide the equation that relates the temperature to the mass.
 
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  • #31
It should be remembered that temperature is a variable of macroscopic thermodynamics.

As such it performs well in use and is fit for purpose.

When you get to microscopic thermodynamics (which roughly equates to statistical thermodynamics) the concept of temperature becomes less and less useful the smaller you get, as does heat capacity and entropy. This comment also applies to thermodynamics of very sparsely populated systems.

What, for instance, is the temperature, entropy etc of a universe that consists of a single particle?

Associating a temperature with an energy is not possible even in macroscopic thermodynamics. If I move a brick from the floor to the table top in my room there is an energy change but no corresponding temperature change as a result.
 

1. What is the unit of measurement for entropy and heat capacity?

The unit of measurement for both entropy and heat capacity is joules per kelvin (J/K).

2. Why do entropy and heat capacity have the same units?

Entropy and heat capacity are both thermodynamic properties that describe the amount of energy in a system. They are related to each other through the equation: ΔS = ΔQ/T, where ΔS is the change in entropy, ΔQ is the change in heat, and T is the temperature. Therefore, since both entropy and heat capacity involve energy and temperature, they have the same units.

3. Is there a connection between entropy and heat capacity?

Yes, there is a connection between entropy and heat capacity. As mentioned in the previous answer, they are related through the equation ΔS = ΔQ/T. Additionally, both entropy and heat capacity are important concepts in thermodynamics and are used to understand the behavior of systems.

4. Are entropy and heat capacity redundant?

No, entropy and heat capacity are not redundant. While they have the same units and are related to each other, they describe different aspects of a system. Entropy measures the disorder or randomness of a system, while heat capacity measures the amount of heat required to raise the temperature of a system by one degree. Both are important in understanding the behavior of a system.

5. How do entropy and heat capacity affect each other?

Entropy and heat capacity affect each other in the sense that changes in one can cause changes in the other. For example, an increase in temperature (which affects heat capacity) can lead to an increase in entropy. Additionally, changes in entropy can affect the heat capacity of a system. Understanding the relationship between these two properties is crucial in studying thermodynamics.

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