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Entropy Confusion

by gadje
Tags: confusion, entropy
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Andy Resnick
#19
Apr14-10, 11:58 AM
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Quote Quote by mr. vodka View Post
<snip>E,V,S are always well-defined and in SM you can then define pressure and temperature as partial derivatives of these quantities, so they also always exist. A fact is that when a real system goes to equilibrium, P and T are in that process not well-defined, but the partial derivates stay well-defined and as soon as the system has reached equilibrium, the experimental P and T and the partial derivate definitions coincide.

<snip> The partial derivatives play the role of these complex numbers in the way they have no meaning in the system you are concerned about as it is in non-equilibrium state, but that it's correct to use them since the end result gives you the experimental P and T.

Am I wrong in that view, according to you?
I believe you are wrong, and your statements above are inconsistent with each other. One example:

You claim that in nonequilibrium systems, one cannot define a P or T, but I (me, my person) have a well-measurable temperature in spite of existing far from equilibrium.
nonequilibrium
#20
Apr14-10, 12:14 PM
P: 1,416
If they appear inconsistent, then that is purely by my bad explaining, which of course would be my fault.

About your example: do you? I don't know a lot of biology, but in a strict sense I suppose your temperature is not exactly defined and fluctuates throughout your body. But that is not what I was really getting at. I was trying to say that there can be situations where very obviously you can't say what the temperature is and I thought you were thinking of those situations when you said SM fails, because you presumed that when T is non-defined, SM breaks down because it uses dT for example. My point was that indeed, in a physical sense dT makes no sense if T is not well defined, but SM does not have that problem because it defines T as a partial derivate of a quantity that is always well-defined.

Does this clear things up? Still in disagreement? I'm not trying to get you convinced about my point so much as to see where you think SM breaks down.

EDIT: gadje, about your problem, I wouldn't really know how to solve that. I do know however you can't just make up your own definition by replacing temperature with height and such (if you do, you'd have to show that it is compatible with the general definition). More about your problem: I find it interesting, but I think I'm missing something. Don't forget the formula you're thinking of , dS = dQ/T, is for gasses...
gadje
#21
Apr14-10, 12:20 PM
P: 23
I think I've got it, actually. It's not what I have up there, upon thinking about it.
nonequilibrium
#22
Apr14-10, 12:25 PM
P: 1,416
What is your solution/method then?
gadje
#23
Apr14-10, 12:32 PM
P: 23
There's an earlier part of the question which talks about the lake being at 10 Celsius and being of a high specific heat. Dropping the block into the lake introduces mgh of energy into it, changing the entropy of the universe by mgh/T = 10*g*100/(10+273).

I think.
Count Iblis
#24
Apr14-10, 12:38 PM
P: 2,157
I agree with Mr. Vodka.

You can also consider Maxwell's Demon though experiment and the resolution of the paradox by Landauer to see that Classical Thermodynamics is incomplete. Of course that doesn't mean that statistical mechanics as it is used in practice doesn't have limitation due to the assumptions made there, but it is more fundamental.


This is a bit similar to discussing whether quantum mechanics is more fundamental that classical mechanics. One could easily argue along the same lines that Andy does here to argue that Classical Mechanics can be applied to certain areas where quantum mechechanics as we know it cannot, because of issues such as the measurement problem.
nonequilibrium
#25
Apr14-10, 12:53 PM
P: 1,416
gadje - that is indeed the entropy increase of the environment, (EDIT, first had something else following this) but I wonder if the entropy of the stone decreased. Should you see it as if there is a heat flow from the stone to the water? Maybe not, not sure...

Count Iblis - I wonder, does SM presume you are working with a reservoir as an environment? In the sense that the Tenv and Penv are constant. Anyway, the part of SM I have worked with always presumed this to derive free energy laws and such, but this does seem like one of the restrictions, unless I'm just wrong on the fact that it's an assumption in SM.
Andy Resnick
#26
Apr14-10, 02:18 PM
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I am confused as to what is meant by 'classical' thermodynamics, as opposed to thermodynamics. Is there quantum thermodynamics, as a distinct field?

I would be surprised if someone here claimed there is any process in the universe that does not obey the Clausius-Duhem inequality. By contrast, I can list of a long list of things not covered by statistical mechanics. Again, statistical mechanics is in no way more fundamental than thermodynamics. Simplified models do not elucidate the range of theory.

As for my original objection (body temperature- the fact that my core body temperature fluctuates is not germane. I'm not sure what you mean by dT in the context of statistical mechanics.

My central point is that statistical mechanics is not equipped to handle nonequilibrium systems. Onsager's relations are a linearization, and do not hold in general.

By contrast, thermodynamics covers *everything physically allowed*.
Andy Resnick
#27
Apr14-10, 05:25 PM
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Quote Quote by mr. vodka View Post
<snip>
Does this clear things up? Still in disagreement? I'm not trying to get you convinced about my point so much as to see where you think SM breaks down.
<snip>
I haven't given anyone a chance to respond, but I feel like I have been having this argument for over a month and not getting anywhere.

So, here's a simple challenge: solve this, and I will reconsider my earlier claims.

Using SM, solve either Q(t) or T(t) in the OP's question. If SM is truly a more fundamental theory than thermodynamics, this should be trivial.
Count Iblis
#28
Apr14-10, 05:40 PM
P: 2,157
In many textbooks, thermodynamics and statistical mechanics are treated in a unified way. There is an introduction in which the fundamental postulate of equal prior probabilities is introduced. Then both thermodynamics and statistical mechanics are developed.

This is done in the book by F. Reif. He distinguishes this from classical thermodynamics; he points out that classical thermodynamics has more postulates than "statistical thermodynamics". Classical thermodynamics is basically early 19th century theory about Heat, temperature, work etc. developed by Carnot. Statistical thermodynamics is the modern version of this developed by Boltzmann, Gibbs etc.
SpectraCat
#29
Apr14-10, 05:49 PM
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Quote Quote by Count Iblis View Post
In many textbooks, thermodynamics and statistical mechanics are treated in a unified way. There is an introduction in which the fundamental postulate of equal prior probabilities is introduced. Then both thermodynamics and statistical mechanics are developed.

This is done in the book by F. Reif. He distinguishes this from classical thermodynamics; he points out that classical thermodynamics has more postulates than "statistical thermodynamics". Classical thermodynamics is basically early 19th century theory about Heat, temperature, work etc. developed by Carnot. Statistical thermodynamics is the modern version of this developed by Boltzmann, Gibbs etc.
Ok .. from the point of view of an objective observer, one thing that would help clear this up is to get clear definitions of what folks mean by the following terms, what distinctions (if any) are drawn between them, and what fundamental limitations they may have.

Statistical Mechanics:

Statistical Thermodynamics:

Classical Thermodynamics (or just Thermodynamics, as per Andy's usage):


This would help me to better understand what y'all are discussing here.
Andy Resnick
#30
Apr14-10, 05:57 PM
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Quote Quote by Count Iblis View Post
In many textbooks, thermodynamics and statistical mechanics are treated in a unified way. There is an introduction in which the fundamental postulate of equal prior probabilities is introduced. Then both thermodynamics and statistical mechanics are developed.

This is done in the book by F. Reif. He distinguishes this from classical thermodynamics; he points out that classical thermodynamics has more postulates than "statistical thermodynamics". Classical thermodynamics is basically early 19th century theory about Heat, temperature, work etc. developed by Carnot. Statistical thermodynamics is the modern version of this developed by Boltzmann, Gibbs etc.
I'm not letting you off the hook that easily, since you accused me of

"...Andy does here to argue that Classical Mechanics can be applied to certain areas where quantum mechechanics as we know it cannot"

Statistical mechanics is *not* a modern version of thermodynamics. Anyone that seriously tries to argue that knows little about either.

Hiding behind a bad textbook is poor form.
Andy Resnick
#31
Apr14-10, 06:10 PM
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Quote Quote by SpectraCat View Post
Ok .. from the point of view of an objective observer, one thing that would help clear this up is to get clear definitions of what folks mean by the following terms, what distinctions (if any) are drawn between them, and what fundamental limitations they may have.

Statistical Mechanics:

Statistical Thermodynamics:

Classical Thermodynamics (or just Thermodynamics, as per Andy's usage):


This would help me to better understand what y'all are discussing here.
Fair enough- here's mine:

Statistical Mechanics: (classical or quantum) mechanics of a large number of discrete particles.

Classical Thermodynamics: theory of heat and mass transfer

Statistical Thermodynamics: A misguided amalgamation of the two.

Distinctions:
Statistical mechanics is a discretized approach, thermodynamics is a continuum approach.

Statistical mechanics postulates 'states' and defines 'equilibrium' and is based on distribution functions and the existence of a partition function. Thermodynamics postulates 'temperature' and 'heat', and has been largely axiomatized (along with continuum mechanics). Thermodynamics also postulates the conservation of energy and second law.

Statistical mechanics is a linear theory, thermodynamics is a nonlinear theory. Whether this is good or bad depends on your perspective.

Limitations: statistical mechanics cannot calculate time-dependent behavior except in a very limited sense (involving equilibrium concepts). Thermodynamics requires constitutive relations that do not have a basis in physical theory.


There's more, I'm sure...
Studiot
#32
Apr14-10, 06:43 PM
P: 5,462
I have to say that I think the whole SM v CT issue rather like the big endian v little endian argument in Gulliver's Travels.
They are both aspects of the same egg, each useful in their own way. In cases where they overlap they predict the same thing, unlike wave v corpuscular theory of light.

Isn't that glorious corroberation?

I can't let this pass however.

Statistical mechanics is a linear theory..............................Limitations: statistical mechanics cannot calculate time-dependent behavior except in a very limited sense (involving equilibrium concepts).
The whole of chemical reaction dynamics, and therefore chemical engineering, is built on statistical mechanics. Only the simplest reactions have linear dynamics.
nonequilibrium
#33
Apr14-10, 07:19 PM
P: 1,416
Hm, I've come to the realization I probably know too little to have enough insight for decent arguments.

But Andy Resnick, let me ask you one thing. SM has a rigid definition of entropy that in essence allows you to calculate the entropy of any situation (in practice, one might be lacking knowledge/skill to actually do it). But more importantly, and basically my question, how is entropy defined in classical thermodynamics? I was taught that dS = dQ/T viewed from a reversible process, but this definition is incredibly limited, so I assume there is a more general one out there that everybody has neglected to teach me. Could you tell me?

EDIT: re-reading my post, it may sound as though I am sniping, but that wasn't meant that way, it was/is an honest question
Andy Resnick
#34
Apr14-10, 09:04 PM
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Quote Quote by Studiot View Post
<snip>

I can't let this pass however.

[...]

The whole of chemical reaction dynamics, and therefore chemical engineering, is built on statistical mechanics. Only the simplest reactions have linear dynamics.
You should have, because you are completely wrong. Find me *any* discussion of statistical mechanics in this:

http://www.amazon.com/Perrys-Chemica...1296782&sr=1-1

or this:

http://www.amazon.com/Basic-Principl...1296623&sr=8-6

or this:

http://www.amazon.com/Introductory-C...1296623&sr=8-1

Attitudes like the one you express here are a reason why Physicists are taken less and less seriously by other technical folks.
Count Iblis
#35
Apr14-10, 09:38 PM
P: 2,157
Quote Quote by Andy Resnick View Post
I'm not letting you off the hook that easily, since you accused me of

"...Andy does here to argue that Classical Mechanics can be applied to certain areas where quantum mechechanics as we know it cannot"

Statistical mechanics is *not* a modern version of thermodynamics. Anyone that seriously tries to argue that knows little about either.

Hiding behind a bad textbook is poor form.
Statistical mechanics as used in practice (like evaluating partition functions or doing monte carlo simulations), may not be all that useful to engineers who use thermodynamics. But that doesn't mean that the foundations of thermodynamics lie firmly within the realm of what we in theoretical physics call "statistical mechanics".

Note that statistical mechanics can also be the study of chaos theory, far out of equilibrium phenomena etc. etc.
Studiot
#36
Apr15-10, 06:44 AM
P: 5,462
You should have, because you are completely wrong. Find me *any* discussion of statistical mechanics in this:
In what way?

True chemical engineers also need/use mechanical engineering theory of pipes pumps and fittings, structural engineering theory of pressure vessels and structures, and so on and so forth. So there is much of this in chem eng literature.

This just proves my point about how much overlap there is between disciplines.

But all this would be at nought without the theory of the chemicals and their reactions that go into these plants.

It is often said in textbooks on physical chemistry that thermodynamics (read classical here) define what reactions are possible, but tell us nothing about the rates of these reactions. The reaction may be thermodynamically feasible, but so slow as to be unusable.

For instance glass is soluble in pure water.
The catch is that the rate of solution is measured on the geological timescale.

The mathematics of these rates is definitely the province of statistical mechanics. I amsure you will find lots of reaction rate information in the references you mention amongst others.

Physical Chemists also use a slightly different notation when they discuss classical thermodynamics - it has much to commend it.

This is simply labelling some of the variables with subscripts to indicate the conditions, so for instance rather than using

[tex]\Delta Q\quad or\quad q[/tex]

[tex]\Delta {Q_v}\quad or\quad {q_v}[/tex] or [tex]\Delta {Q_p}\quad or\quad {q_p}[/tex]

are used to indicate conditions of constant volume or pressure.
This helps ensure the appropriate equations are used in calculating quantities such as enthalpy, entropy, free energy etc.

There is another entropy thread concurrent with this one where we are working through rather better without all this squabbling.

I had though my " attitude" one of evenhandedness to both CT and SM as both have their place, both supply answers unavailable to the other and both concur where they overlap.


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