What rules, energy or entropy?

1. May 10, 2012

sugeet

what rules, energy or entropy??

any physical system goes to a state of maximum entropy or minimum energy,

they don`t imply each other, by my understanding

1>third law
s->0 as e->0
2>system tends to be in a state of least energy

how??

2. May 10, 2012

Andrew Mason

Re: what rules, energy or entropy??

This is not really true, since there is no "maximum" to a system's entropy. The statement "any physical system experiences an increase in entropy in any thermodynamic process" would be true only for an isolated physical system. The entropy of the universe is always increasing but little parts of the universe, like the inside of a refrigerator, can experience decreases in entropy.

Again, this is true only of a system that is not isolated. If the system is losing energy, the energy has to be accounted for somewhere else.

I am having difficulty understanding your question.
AM

3. May 10, 2012

Cleonis

Re: what rules, energy or entropy??

The text of your message is very unclear, so I limit myself to the content of the subject line.

I remember the following classroom demonstration: a glass was put on the table and with some chemistry Iodine gas was produced. Iodine molecules are very heavy. Pure Iodine gas is much heavier than air. It also has a distinct brownish color. A piece of paper covered the glass, so that the Iodine gas wouldn't escape. A second glass was placed on top, inverted, so that when the piece of paper was pulled away the two compartments became one compartment.

Then we watched the brownish color climb up, and gradually it developed to an even distribution.

(I think it was Iodine gas, but maybe I don't remember correctly. Anyway, that detail is not important for the point I'm making.)

That was a demonstration of entropy overpowering energy. The gas mixture tends to develop towards the most probable state, and a uniform distribution is more probable. Iodine molecules migrated upward, against the gravitational potential.

The gain in gravitational potential energy is at the expense of thermal energy. If perfecly insulated from the environment the gas mixture will drop in temperature.

There are also circumnstances where energy overrules entropy. Example, spinning a tube containing blood in a centrifuge results in separation of constituent parts of the blood. Under normal gravity the proteins in the blood remain in suspension (entropy stronger than energy)
The centrifuge is pulling G's, far more than normal gravity. Now inside the blood containing tube there is a far steeper gradient in gravitational potential. Now energy overpowers entropy, and the proteins in the blood go out of suspension.

So, energy and entropy are independent, and there are lots of circumstances where the two have opposing influences. Depending on the precise circumstances one or the other is strongest.

4. May 10, 2012

sugeet

Re: what rules, energy or entropy??

Yes I understand, that I did not put the question well...
I think last night I have got the concept as I was pondering.
Let me try to put it in a proper way,
any system has max prob to be in a state of maximized entropy(considering sys + surr), that is in a state having maximum number of microstates..., does this state always correspond to a state of least energy?........ it this the state which is most probable, even energetically.

I have confused a bit, but I think, u all will understand.

5. May 10, 2012

sugeet

Re: what rules, energy or entropy??

Andrew thanks for addressing my question, yah! I got it, I am talking in one place about a closed system, and then about an open system, energy is always conserved, so there is nothing like least energy also. But I want to understand the equivalence, in the fact(I think, it must be so, just a feeling) that any process, described energetically, that is this happened , because, the system wants to be in a state of lesser energy, is also the most probable state, If I am still wrong, please tell me!!!!!!!!

Last edited by a moderator: May 18, 2012
6. May 11, 2012

Andrew Mason

Re: what rules, energy or entropy??

It depends on what is happening with the system. If the system is the Sun, would you say this?

The first and second laws say that 1. energy will always be conserved in some form but 2. it will not flow on its own from a state of high entropy to a state of low entropy. 2. since entropy is defined as dQrev/T, this is just another way of saying that heat flow will not occur on its own from a colder to a hotter body.

You can answer your questions by simply applying those 2 principles. You have to be careful to distinguish between closed and open systems. You cannot make general statements about open systems, since it depends on how it is interacting with its surroundings.

For closed systems, entropy cannot decrease but energy will always be conserved. How much entropy will increase or how rapidly it will increase depends on what the system consists of.

AM

7. May 11, 2012

Whovian

Re: what rules, energy or entropy??

Let's first determine what you mean by a closed system tending to "lower energy." By The First Law of Thermodynamics (aka Conservation of Energy), this energy can't be destroyed. So what you probably mean is the amount of usable energy is decreasing in a closed system. There are a few ways to think of Entropy. One's a well-defined measure of disorder. Another's a measure of the amount of information in a system. But another's a measure of the amount of unusable energy in a system.

So when the amount of usable energy is decreasing, entropy is necessarily increasing, and so they're equivalent.

Oh, and double-posting isn't ideal, there's an edit button there for a reason ...

8. May 11, 2012

Andrew Mason

Re: what rules, energy or entropy??

I am not sure whose post you are referring to. The quote button is there for a reason ...

In any event, a closed system does not and cannot tend to lower energy. Total energy is always conserved: first law.
How is it a measure of the unuseable energy in a system?

First of all, the entropy of a closed system is inversely related to the amount of useful work that the system is capable of doing.

Furthermore, entropy is not directly related to the capacity to do useful work. A system with high entropy can easily have more capacity to do useful work than a system with much lower entropy. For example a system consisting of a tank of steam and a block of ice has much more entropy than a system consisting of just a block of ice. But the former can do a lot more work than the latter. What is material is the change in entropy, and that depends on how the energy in the system is distributed and in what form it is in.

What you can say about entropy is that the universe tends toward ever increasing entropy and that a closed system will not experience a decrease in entropy.

They are not equivalent unless the decrease in energy is equal to the increase in entropy. Are they?

Not sure who this is directed to.

AM

9. May 11, 2012

Studiot

Re: what rules, energy or entropy??

Do you guys not think this reference to a closed system is a tad disingenuous?

How is energy preserved within a closed system?
By definition a closed system is one in which energy can pass across the system boundary between the surroundings and the system.
A thermometer is a closed system. Place one in a refrigerator and you remove energy.

With respect to the original question:

A system is said to be in equilibrium when no further spontaneous change occurs. The entropy of an isolated system tends to increase until no further spontaneous change can occur.

So in an isolated system in equilibrium at constant energy and volume the entropy is a maximum.

S → max at const E (U) and V

If instead we have constant entropy and volume then the equilibrium criterion is that the energy is a minimum.

S → min at const S and V

So the drive to max S and min E compete and only if E is held constant can S achieve its max or if S is held constant can E achieve its min.
In order to calculate what happens in the intermediate stages you need to consider one of the free energy or work functions.

does this help?

10. May 11, 2012

Andrew Mason

Re: what rules, energy or entropy??

Technically, you are correct. We are using "closed system" to mean "isolated system", one that is, by definition, thermodynamically isolated from the rest of the universe ie: it cannot exchange matter or energy with the rest of the universe. Energy is preserved in an isolated system.

How about an isolated system consisting of a Carnot engine, operating between hot and cold finite reservoirs, compressing a ratcheted spring. Can any further spontaneous change occur? When the temperature difference becomes arbitrarily small, the engine cannot do any more work and the spring remains compressed. Has entropy increased? Is it at a maximum?

If it is an isolated system, where does the energy go?

AM

11. May 11, 2012

Studiot

Re: what rules, energy or entropy??

How is the spring (gaseous?) compressed at constant volume in an isolated system?

Good question to a poorly worded statement.
In a system at constant entropy there can be no heat change so the only energy change is mechanical work. So this is the statement of ordinary mechanical least action.

12. May 11, 2012

Andrew Mason

Re: what rules, energy or entropy??

It doesn't really matter. Lets just say that the engine through a system of gears compresses the spring or lifts a weight - just something that stores mechanical energy indefinitely.

Since the Carnot engine is doing work, heat is flowing out of the hotter reservoir and into the colder reservoir. So there is a conversion of heat energy into mechanical work and all of this is kept within the isolated system. But there is no increase in entropy.

AM

13. May 11, 2012

Studiot

Re: what rules, energy or entropy??

How does this machine do work without expansion, since constant volume means no expansion.

Whether you raise your weight by placing it on a piston or by heating a gas or raising steam and turning a turbine or whatever you are not operating at constant volume.

14. May 11, 2012

Andrew Mason

Re: what rules, energy or entropy??

It does work over many cycles and returns to its original volume. It is a Carnot engine operating between two finite reservoirs using a working volume of a gas that goes through many, many cycles.

15. May 12, 2012

sugeet

Re: what rules, energy or entropy??

AM, I guess it is the maximum, consider two metal containers of water at diff temp, in contact
isolated, from everything else, at equilibrium, both have same temp , and yes, this is a state of maximised entropy!!!
but i cannot explain it in energetics...

16. May 12, 2012

Andrew Mason

Re: what rules, energy or entropy??

But what if you operate a Carnot engine between them and extract work that you store in a mechanical or electrical device (eg. a spring or battery). There is no increase in entropy but the two reservoirs end up at the same temperature. Can you say that the entropy is maximized?

17. May 12, 2012

Studiot

Re: what rules, energy or entropy??

I'm sorry I still don't see how your engine meets the stated criteria.

18. May 12, 2012

Andrew Mason

Re: what rules, energy or entropy??

The engine keeps running until the two reservoirs are arbitrarily close to the same temperature. Think of the engine and reservoirs being in a insulated container of fixed volume. The total energy is the same, it is just distributed over both reservoirs and in the spring or battery. The total entropy has not changed because the engine operated on a Carnot cycle.

AM

19. May 12, 2012

Studiot

Re: what rules, energy or entropy??

Oh dear, I fear this thread is wandering off topic and sugeet is still interested in it.

Never mind I think that discussing Andrew’s system is bringing out some related fundamental issues.

For someone making their way in Thermodynamics there are a lot of formulae and definitions to find their way round. It is easy to apply the wrong one or the right one in the wrong way. So easy that even the most experienced sometimes slip up and do it.

The key to a good analysis is the proper definition of the system.

To be complete a proper system definition must define

1) The system components
2) The system boundary
3) The system process.

In each case the definition should specify what is included and what is not included. This applies both to the physical participants such as 'bucket of water' and to the mathematical considerations such as 'quantity of heat', boundary conditions, location etc. By changing one or more of these we can convert between isolated, open and closed systems.

Andrew, I see nothing in your system contrary to what I said. However your system initially is not in equilibrium so does not conform to the conditions of my statement until the reservoirs have equilibrated. At this time the heat flow has ceased and, as you say the entropy is constant, since no further change occurs.

I do have two reservations, however.
Firstly you have yet to describe a mechanism for doing work at constant volume.
Any change to mechanical energy at constant volume involves the product VdP rather than PdV. Unlike PdV, VdP is not work.

Secondly you are misapplying the first law. The first law connects a property of the system components (internal energy) to a property of the system boundary the (energy flows across it). By including both the carnot engine and the mechanism within your system and making it isolated (as specified) you exclude applying the first law across the boundary. In order to do this you must divide the system into subsystems.

20. May 12, 2012

Andrew Mason

Re: what rules, energy or entropy??

It is an ENGINE!!. The whole point of a thermodynamic engine is to do ∫ PdV work, of course. The engine does work using a complete thermodynamic cycle. The gas expands doing work and is then compressed (but using less work to compress than was performed during the expansion). The gas ends up back in its initial state after having done net work.

Who says that you cannot include the reservoirs in the system? I am defining the system as an isolated container composed of two reservoirs that are thermally isolated from each other that are initially at different temperatures plus a Carnot engine operating between them. Nothing is preventing you from applying the first law anywhere. It always applies between states of thermodynamic equilibrium. Since it is a Carnot engine, the working substance in the engine is in thermodynamic equilibrium with the reservoir that it is in thermal contact with at any given time.

AM