# Youtube says the 2nd Law is Broken.

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3 minutes ago, swansont said:

You added a partition, where there was none. You added a piston earlier, and talked about changing variables that were fixed, and doing work.

You’ve done little but change the conditions.

I'm sorry that the standard engineering techniques for analysing thermodynamic systems cause you such consternation. Better engineers than me have approved my approach and given me repeat contracts to lead the detailing out their power design projects since I turned thirty, and that was a very long time ago. Your pride blinds you. I'm out of here.

6 minutes ago, studiot said:

Wow, what a lot of invective just to dodge answering a question, similar to the one you asked in the OP.

The joke is that it is based on one from a textbook entitled

Thermodynamics for Chemical Engineers

written by three professors from the Dept of Chem Eng at Imperial College.

Just stick a heat engine between T2 and T1 heat reservoirs and you've got free energy. Well done! You've solved the worlds energy problems! Have a ball!

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4 minutes ago, sethoflagos said:

Just stick a heat engine between T2 and T1 heat reservoirs and you've got free energy. Well done! You've solved the worlds energy problems! Have a ball!

What a pity you are preventing yourself from seeing the answer to your original question, which is contained in the answer to my question.

I have never claimed it breaks any laws, (quite the reverse in fact if you read my post properly) or that it will provide a supply of free energy.

All I asked was how it fits with the second law (which is what you did).

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Posted (edited)
24 minutes ago, studiot said:

What a pity you are preventing yourself from seeing the answer to your original question, which is contained in the answer to my question.

I have never claimed it breaks any laws, (quite the reverse in fact if you read my post properly) or that it will provide a supply of free energy.

All I asked was how it fits with the second law (which is what you did).

It's late and a combination of your obscurantism and swansont's bloody-minded negativity has exhausted my patience (which to be frank, I've never had in great excess).

It must be obvious to you by now that I've been clear in my own mind since way back on page 1 of this thread where the Youtube presentations break down. The key lies in conservation of angular momentum which is a topic I usually shy away from. Turns out, it can be quite useful on occasion.

Do we have anything more to discuss?

If your earlier posting was a joke, then I'm sorry I didn't get it and took its meaning at face value.

Edited by sethoflagos

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8 hours ago, sethoflagos said:

You're in the same trap as swansont. At each bounce, there is an interchange of momentum with the box. The box is actively participating in the thermodynamic process, so you now have to consider it's inertia, thermal capacity, temperature and entropy.

The simplifying to an idealization "trap"? (allowing focus on what is actually significant)

An infinite mass box can (obviously) exchange all the momentum any particle requires, while allowing the particle to maintain the same energy it had without exchanging any at all. You can ignore the box's temperature in an idealization, or add more assumptions to your model. (just be clear when you do this to be fair to other posters)

Your beef seems to be with standard/accepted idealizations (and perhaps Youtube...), the limits of which are generally well known.

13 minutes ago, sethoflagos said:

It's late and a combination of your obscurantism and swansont's bloody-minded negativity has exhausted my patience (which to be frank, I've never had in great excess).

It must be obvious to you by now that I've been clear in my own mind since way back on page 1 of this thread where the Youtube presentations break down. The key lies in conservation of angular momentum which is a topic I usually shy away from. Turns out, it can be quite useful on occasion.

Do we have anything more to discuss?

If your earlier posting was a joke, then I'm sorry I didn't get it and took its meaning at face value.

+1 for admitting that, but let's be fair with one another.

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9 minutes ago, J.C.MacSwell said:

Your beef seems to be with standard/accepted idealizations (and perhaps Youtube...), the limits of which are generally well known.

My understanding is that the difficulties of applying the microcanonical ensemble to the real world are pretty well documented. Following this thread has highlighted to me some of the more blatant pitfalls that people can fall into. I didn't name and shame the Youtube channels concerned in the OP since actually, some of them are pretty well-informed - their message doesn't crumble under research, but in this instance ...

18 minutes ago, J.C.MacSwell said:

+1 for admitting that, but let's be fair with one another.

I'm 61. I'm not blind to my own limitations. Those I forget, my better half reminds me of quickly enough.

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Posted (edited)
1 hour ago, sethoflagos said:

My understanding is that the difficulties of applying the microcanonical ensemble to the real world are pretty well documented. Following this thread has highlighted to me some of the more blatant pitfalls that people can fall into. I didn't name and shame the Youtube channels concerned in the OP since actually, some of them are pretty well-informed - their message doesn't crumble under research, but in this instance ...

I'm 61. I'm not blind to my own limitations. Those I forget, my better half reminds me of quickly enough.

Me too. (still somewhat blinded though...and honestly not sure what my better half is on about half the time...)

Edited by J.C.MacSwell

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I don't even have a better half...
Just my own worse half.

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Posted (edited)
12 hours ago, sethoflagos said:

It must be obvious to you by now that I've been clear in my own mind since way back on page 1 of this thread where the Youtube presentations break down. The key lies in conservation of angular momentum which is a topic I usually shy away from. Turns out, it can be quite useful on occasion.

Do we have anything more to discuss?

To continue.

Quote

Clausius

It is impossible by a cyclic process to transfer heat from colder to a warmer reservoir without net changes in other bodies

Quote

Thomson, Lord Kelvin

It is impossible by a cyclic process to take heat from a reservoir and convert it into work without, in the same operation, transferring heat from a hot to a cold reservoir.

So how does my process stack up against classical statements ?

Well since the process does take transfer heat from a colder body to a warmer one it is a good job that it is not a cyclic process so does not satisfy all the conditions of the classical second law. In other words the Second Law (classical formulation) should not be applied.
That example is exactly why the originators included the cyclic requirement.

But of course it is unsatisfactory not to be able to apply the Second Law to non cyclic processes, there are many such in Chemistry.
This is where the Chemists' version comes in useful.
The key to this is now to consider the system and surroundings together as one 'Universe'.

Quote

Warn

There exists a state function called entropy, S. The entropy and its surroundings taken together increases during all natural or irreversible processes.
For reversible processes the total entropy is unchanged.

Quote

Keeler and Wothers

In a spontaneous process the entropy of the Universe increases.

This may be applied to my one shot reversible process.

The process considering the reordering of particles in a box is also a one shot process.

Considering my example the particle track is entirely reversible so there is no change of entropy.

However you are wrong to say that the box must be included as part of the system.

The system can be anything I want it to be so long as I can draw (define) a boundary round it.

Of course an injudicious choice of system and boundary can make calculations difficult or even impossible, as you are finding out with the box.

A System is whatever is inside the boundary. The boundary is not part of the system.

In the box case I choose the box as the boundary.

Thermodynamics provides the exchange variables of work and heat which are not state variables to connect the system to its surrounding across the boundary.

I would recommend comparing a thermodynamic discussion of the latent heat of fusion of a pure substance with the multiparticle case for the box.

Edited by studiot

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Posted (edited)
2 hours ago, studiot said:

So how does my process stack up against classical statements ?

Well since the process does take transfer heat from a colder body to a warmer one it is a good job that it is not a cyclic process so does not satisfy all the conditions of the classical second law. In other words the Second Law (classical formulation) should not be applied.
That example is exactly why the originators included the cyclic requirement.

But of course it is unsatisfactory not to be able to apply the Second Law to non cyclic processes, there are many such in Chemistry.
This is where the Chemists' version comes in useful.
The key to this is now to consider the system and surroundings together as one 'Universe'.

Some unnecessary complications in here aren't there? The 2nd Law is the 2nd Law.

Your process extracts a certain amount of work from a pressurised gas in a W=Q process so W = Q1 and dS1 = W/T1 ( - W/T1 to reservoir  1)

Let us say half this shaftwork is used to isentropically compress the gas in stage 2 where dS = 0 by definition

The remaining W/2 is spent in a further W=Q process at T2 so Q2 = W/2 and dS2 = - W/2T2 ( +W/2T2 to reservoir 2)

So what's happened to the gas overall? We've heated it increasing it's internal energy by W/2 and increasing its entropy by W(T2-T1/2)/T1T2

So okay, you've moved W/2 worth of heat from T1 to T2 but where is the nett change in entropy? There isn't one. 2nd Law is good.

2 hours ago, studiot said:

This may be applied to my one shot reversible process.

The process considering the reordering of particles in a box is also a one shot process.

Considering my example the particle track is entirely reversible so there is no change of entropy.

dS = dQrev/T by definition. Your process may be ideally reversible, but it absolutely is not isentropic other than the stage you call 'adiabatic compression'. If you also called this stage 'isentropic compression' it may help alert you to the fact that isothermal compression processes are very far from isentropic.

So if you've drawn inferences from this line of thinking that you believe will help me with my box problem (I no longer have one), I fear that you have managed to confuse yourself.

2 hours ago, studiot said:

In passing, I would strongly recommend sketching out thermodynamic processes on HS diagrams rather than PV.

On an HS diagram ideal isothermal processes are horizontal lines, ideal isentropic processes are vertical. With practice, you can see at a glance whether there's a 2nd Law infringement. Invariably, such infringements arise from human error.

Edited by sethoflagos
sp

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Posted (edited)
55 minutes ago, sethoflagos said:
3 hours ago, studiot said:

This may be applied to my one shot reversible process.

The process considering the reordering of particles in a box is also a one shot process.

Considering my example the particle track is entirely reversible so there is no change of entropy.

dS = dQrev/T by definition. Your process may be ideally reversible, but it absolutely is not isentropic other than the stage you call 'adiabatic compression'. If you also called this stage 'isentropic compression' it may help alert you to the fact that isothermal compression processes are very far from isentropic.

So if you've drawn inferences from this line of thinking that you believe will help me with my box problem (I no longer have one), I fear that you have managed to confuse yourself.

Read it again properly and post the extract where I also called this stage isentropic

If I did that why do you think I allocated q1,2 to stage 1 - 2 and q3,4 to stage 3 - 4 resulting in a net heat change?

So the system entropy  changes are

$\Delta {S_{3,4}} = \frac{{{q_{3,4}}}}{{{T_2}}}$

and

$\Delta {S_{1,2}} = \frac{{{q_{1,2}}}}{{{T_1}}}$

What I said was the that net w = 0

Quote

Studiot

Thus exactly zero external work is performed, but a quantity of heat is transferred from a lower temperature reservoir to a higher temperature heat reservoir.

So can you explain why this does not contravene the Second Law  ?

Edited by studiot

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12 minutes ago, studiot said:

Read it again properly and post the extract where I also called this stage isentropic

Both in the text and on the associated sketch you refer to Stage 2-3 as 'adiabatic compression'. Adiabatic processes may be isentropic but not necessarily so.

19 minutes ago, studiot said:

If I did that why do you think I allocated q1,2 to stage 1 - 2 and q3,4 to stage 3 - 4 resulting in a net heat change?

Because that's how you defined those two isothermal stages.

33 minutes ago, studiot said:

So the system entropy  changes are

So you do acknowledge that the entropy changes are precisely as I defined them in my last post. You had not mentioned them previously. This appears to be in direct conflict with your earlier statement:

3 hours ago, studiot said:

Considering my example the particle track is entirely reversible so there is no change of entropy.

... which I think you need to gracefully withdraw. No shame. Just own the error.

43 minutes ago, studiot said:

ΔS1,2=q1,2T1 What I said was the that net w = 0

Not in dispute.

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Posted (edited)
58 minutes ago, sethoflagos said:

So you do acknowledge that the entropy changes are precisely as I defined them in my last post

Only if we accept your changing my post to the specific value of work you introduced.

If you can only work with that particular figure, rather than the general one I introduced, then we can use your w/2.

However that leads to what appears to me to be a self conflicting pair of statements.

2 hours ago, sethoflagos said:

So what's happened to the gas overall? We've heated it increasing it's internal energy by W/2 and increasing its entropy by W(T2-T1/2)/T1T2

So okay, you've moved W/2 worth of heat from T1 to T2 but where is the nett change in entropy? There isn't one. 2nd Law is good.

How can we have "increased its entropy overall by W(T2-T1/2)/T1T2 and also have "there isn't a change in entropy" ?

58 minutes ago, sethoflagos said:

You had not mentioned them previously. This appears to be in direct conflict with your earlier statement:

4 hours ago, studiot said:

Considering my example the particle track is entirely reversible so there is no change of entropy.

... which I think you need to gracefully withdraw. No shame. Just own the error.

I can't see the connection between this and the first example designed specifically to show why the process needs to be cyclic to obey the second law ( as stated by its originators as I have already posted) and the second example which might have been put better, but was designed to show something else. A particle bouncing back and for in a perfectly elastic manner along a predifined track suffers no change in entropy.

You have still not stated the version of the second law you wish to employ, despite several requests.

That is pretty rude in my opinion.

Edited by studiot

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Posted (edited)
43 minutes ago, studiot said:

Only if we accept your changing my post to the specific value of work you introduced.

If you can only work with that particular figure, rather than the general one I introduced, then we can use your w/2.

However that leads to what appears to me to be a self conflicting pair of statements.

How can we have "increased its entropy overall by W(T2-T1/2)/T1T2 and also have "there isn't a change in entropy" ?

The gas has increased in entropy by W(T2-T1/2)/T1T2 (= W/T1 - W/2T2)

Reservoir 1 has decreased in entropy by W/T1

Reservoir 2 has increased in entropy by W/2T2

W/T1 - W/2T2 - W/T1 + W/2T2 = 0 Hence no nett change in entropy.

43 minutes ago, studiot said:

I can't see the connection between this and the first example designed specifically to show why the process needs to be cyclic to obey the second law ( as stated by its originators) and the second example which might have been put better, but was designed to show something else. A particle bouncing back and for in a perfectly elastic manner along a predifined track suffers no change in entropy.

Your examples don't come into it. Your assertion (paraphrasing) "it is reversible therefore it is isentropic" is a clearly flawed assumption.

43 minutes ago, studiot said:

You have still not stated the version of the second law you wish to employ, despite several requests.

That is pretty rude in my opinion.

My version of the 2nd Law is that there are no versions. On more than one occasion I've answered your question quite fully with the statement that "The 2nd Law is the 2nd Law". If you're unhappy with that answer then I'm afraid that's your problem.

If there is an alternative version to consider, then either it yields precisely the same results (and is therefore identical in all but name and is therefore superfluous), or it is wrong.

It's not rude to evade semantic entrapment. Simply prudent.

Edited by sethoflagos
sp

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26 minutes ago, sethoflagos said:
1 hour ago, studiot said:

Only if we accept your changing my post to the specific value of work you introduced.

If you can only work with that particular figure, rather than the general one I introduced, then we can use your w/2.

However that leads to what appears to me to be a self conflicting pair of statements.

How can we have "increased its entropy overall by W(T2-T1/2)/T1T2 and also have "there isn't a change in entropy" ?

The gas has increased in entropy by W(T2-T1/2)/T1T2 (= W/T1 - W/2T2)

Reservoir 1 has decreased in entropy by W/T1

Reservoir 2 has increased in entropy by W/2T2

W/T1 - W/2T2 - W/T1 + W/2T2 = 0 Hence no nett change in entropy.

So you have used (confirmed) the Chemists' version of the second law as I suggest for a non cyclic process.

Congratulations.

28 minutes ago, sethoflagos said:
1 hour ago, studiot said:

I can't see the connection between this and the first example designed specifically to show why the process needs to be cyclic to obey the second law ( as stated by its originators) and the second example which might have been put better, but was designed to show something else. A particle bouncing back and for in a perfectly elastic manner along a predifined track suffers no change in entropy.

Your examples don't come into it. Your assertion (paraphrasing) "it is reversible therefore it is isentropic" is a clearly flawed assumption.

Please post accurately the text you claim to be paraphrasing.

33 minutes ago, sethoflagos said:

My version of the 2nd Law is that there are no versions. On more than one occasion I've answered your question quite fully with the statement that "The 2nd Law is the 2nd Law". If you're unhappy with that answer then I'm afraid that's your problem.

If there is an alternative version to consider, then either it yields precisely the same results (and is therefore identical in all but name and is therefore superfluous), or it is wrong.

It's not rude to evade semantic entrapment. Simply prudent

This must be arrant nonsense. You must have at least one version.

No one is trying to 'entrap you' , although you did earlier suggest you had trapped both swansont and myself.

Such colourful language is not conducive to cooperative discussion.

I asked for your version or statement of the second law and gave the reason that it was to enable us (all) to compare the OP offending process (and any other) with this statement.

Why is that trying to trap you  or in any way unreasonable?

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Posted (edited)
1 hour ago, studiot said:

So you have used (confirmed) the Chemists' version of the second law as I suggest for a non cyclic process.

Congratulations.

The congratulations really aren't necessary, sincere or otherwise. I provided you with a standard 1st year BSc thermodynamic calculation and in return you provide some ontological classification of my methodology? What's the point?

1 hour ago, studiot said:

Please post accurately the text you claim to be paraphrasing.

7 hours ago, studiot said:

Considering my example the particle track is entirely reversible so there is no change of entropy.

This is a non sequitur.

1 hour ago, studiot said:

This must be arrant nonsense. You must have at least one version.

How many versions of the truth can there be?

1 hour ago, studiot said:

No one is trying to 'entrap you' , although you did earlier suggest you had trapped both swansont and myself.

Neither of you need any help from me in that. IMHO you both ensnare yourselves in petty formalistic rituals that simply obscure.

1 hour ago, studiot said:

I asked for your version or statement of the second law and gave the reason that it was to enable us (all) to compare the OP offending process (and any other) with this statement.

You're no nearer to answering the OP paradox now than you were when you first posted at 9.51 pm on Friday. If you don't know then just say so. Frankly, with so many of you stumbling over the 1st Law constraints, there seems little point in discussing the 2nd.

Edited by sethoflagos

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1 hour ago, sethoflagos said:
2 hours ago, studiot said:

This must be arrant nonsense. You must have at least one version.

How many versions of the truth can there be?

You are the one who stated plainly that there are zero versions.

3 hours ago, sethoflagos said:

My version of the 2nd Law is that there are no versions.

I simply pointed out that there must be at least one version.

1 hour ago, sethoflagos said:
2 hours ago, studiot said:

Please post accurately the text you claim to be paraphrasing.

8 hours ago, studiot said:

Considering my example the particle track is entirely reversible so there is no change of entropy.

This is a non sequitur.

I have no idea what you are trying to say here.

A particle that is following a specific track, with no opportunity to change its kinetic energy and therefore its 'temperature' and no opportunity to receive or distribute heat is a purely mechanical system.

How is that not a constant entropy system ?

Since I only drew one single solitary particle and one single solitary track, surely you cannot have mixed them up.

1 hour ago, sethoflagos said:
2 hours ago, studiot said:

I asked for your version or statement of the second law and gave the reason that it was to enable us (all) to compare the OP offending process (and any other) with this statement.

You're no nearer to answering the OP paradox now than you were when you first posted at 9.51 pm on Friday. If you don't know then just say so. Frankly, with so many of you stumbling over the 1st Law constraints, there seems little point in discussing the 2nd.

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21 hours ago, studiot said:

What a pity you are preventing yourself from seeing the answer to your original question, which is contained in the answer to my question.

I've provided an analysis of your heat pump system and have thus answered your question. However, I need you to explain to me why this provides a solution to the OP.

You could perhaps help by providing me with a simple expression for T2 in my worked example. After all, you do understand your pet a lot better than I do (plus you have the textbook it came from).

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Posted (edited)

24 hours has passed which I guess is enough.  For what it's worth, T2 = T1 + W/2nCv which defines the maximum value of Q2*(T2-T1) for the system, but that's now by the by.

On 7/6/2020 at 10:46 PM, studiot said:

Certainly there was no ad hominem intended (and many sincere apologies if it appeared otherwise). I was simply the stating that the heat pump example you asked me to consider seemed to shed no light at all on the  OP paradox. I present three main grounds in support of this assertion.

Firstly, in the OP case, the Youtube presentations claim that the 2nd Law has been broken by 'statistics'. ie that some quantity of system entropy has somehow vanished. I think I've demonstrated clearly enough that the heat pump at least preserves initial total system entropy. So here, it seems uninformative.

Secondly, the presentations claim that the gas has somehow contracted from some initial equilibrium state to occupy half of its original volume purely through its own internal mechanics. ie that the contraction happens without any external nett energy exchange with the environment. Again, for the heat pump case I've demonstated that all volumetric changes have exactly matching Q and W terms, so again, it seems uninformative.

Lastly, as stated earlier, it dawned on me on Saturday that there seemed to be a strong conservation of occupied volume arising from the conservation of angular momentum. I don't see how the heat pump example was leading us toward such a conclusion. In hindsight, perhaps a centrifuge would have been a more effective guiding light - the volume restoring forces here are quite explicit and macroscopically large.

In conclusion, it's become clear that the Youtube proposal of a broken 2nd Law is nothing but a red herring. Their real stumbling block arises from overlooking fundamental 1st Law constraints. Their loss of control of the 1st Law simply results in entropy being undefined, even in qualitative terms. Lies, damned lies and statistics again.

Anyway many thanks to you all for your assistance in clarifying and solving the OP paradox so completely. I'm most grateful for your time and patience.

Edited by sethoflagos
missing words

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Posted (edited)
10 hours ago, sethoflagos said:

Certainly there was no ad hominem intended (and many sincere apologies if it appeared otherwise).

Accepted let's move on.

Clearly all those years of experience, plus more which must have been spent in study of the subject, have given you command of Applied Thermodynamics (along with other subjects).
As shown below

10 hours ago, sethoflagos said:

Secondly, the presentations claim that the gas has somehow contracted from some initial equilibrium state to occupy half of its original volume purely through its own internal mechanics. ie that the contraction happens without any external nett energy exchange with the environment. Again, for the heat pump case I've demonstated that all volumetric changes have exactly matching Q and W terms, so again, it seems uninformative.

Lastly, as stated earlier, it dawned on me on Saturday that there seemed to be a strong conservation of occupied volume arising from the conservation of angular momentum. I don't see how the heat pump example was leading us toward such a conclusion. In hindsight, perhaps a centrifuge would have been a more effective guiding light - the volume restoring forces here are quite explicit and macroscopically large.

You are not the only one who has had additional thoughts as a result of our discussion.
It has also made me realise something I should have realised before.
Thank you for that. +1

In another recent thread here at SF, a teacher of thermodynamics asked how to introduce the subject of entropy, without using the traditional second law approach.

The discussion in your thread made me realise that of course you cannot use much of the mechanism of the second law if you are going to do this.
This must be why the early diefintion did not mention entropy : entropy had yet to be defined.

Hindsight allows an applied thermodynamicst to use formulae and techniques out of the logical sequence of the definition.

This is in fact what I was doing and led me to my original agreement that you cannot use the classical approach to prove or disprove the kinetic interpretation.

You need additional material for this.

Perhaps my digression to show why the early pioneers always referred to cyclic processes was excessive, but I hope you have come to realise that since the kinetic approach is non cyclic in basis, you cannot use that part of classical thermodynamics which is defined only for cyclic processes.

So another way must be found.

But the kinetic question in the OP is not applied thermodynamics it is more fundamental than that.
So discussion must follow and hold to a formal logical sequence of definitions and results.

I don't know if you have heard of the Massieu and Planck functions ?

These two provide the (mathematically derivable) link between the classical and the statistical approach, so that this is often referred to as 'the Massieu Bridge'.

All of this is expounded detailed in Guggenheim's Advanced thermodynamics.

(I would not recommend the Wikipedia pages on this they are rather unhelpful and not completely comprehensive or correct)

However, just are there are several approaches to classical thermodynamics, there are several versions of the statistical approach.

Unfortunately the statistical versions do not always completely agree with the classical versions, fluctuations being one such area of divergence.

Epstein, in his famous textbook, included a whole chapter on the experimental evidence for and theoretical basis of such divergence.

Epstein A textbook of Thermodynamics

A free pdf is available here.

I am not sure of free pdfs for Guggenheim.

Edited by studiot

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Posted (edited)

Please try not to be offended by anything I post below. The issues you raise are deep ones and I fully recognise that a spectrum of opinion across intelligent parties is not only to be expected, but is very much a positive thing. If we refuse to look at an object from another viewpoint, our understanding of the object can never improve beyond speculation. We need the other's viewpoint. I'll try to be less robust in my presentation, but please remember that I'm schooled in producing an end product that nails a small target within limited budgets and tight deadlines. Not much opportunity to sit around philosophising.

10 hours ago, studiot said:

... of Applied Thermodynamics .

Does the stress here introduce a value judgment of a methodology based in its ontological classification (ie. what name you give to it)? I'll attempt to paraphrase Feynmann "If it disagrees with experiment, it's wrong". Conversely, all methodologies that agree like-for-like with measurements of the real world must be equivalently valid. In my experience ontology carries with it many hidden traps which makes me very wary. It's a branch of metaphysics and maybe best left to the theologians to play with.

10 hours ago, studiot said:

... you cannot use the classical approach to prove or disprove the kinetic interpretation.

You need additional material for this.

I'm faced here with trying to guess what real world differences result from such an ontological separation of what I currently view as different aspects of the same thing. To me, the distinction is one between experimental investigation of particle-particle interaction at the microscopic level (eg kinetic theory) compared to the empirically developed relationships between state variables in the bulk. Neither is necessarily complete in either their formulation or interpretation, but they are measurements taken on the same 'thing', only at different scales. They should therefore reduce to expressions of the same. If some particular interpretation suggests differences, then we must fall back on the weight of experimental evidence.  Can this count as the additional material you refer to?

10 hours ago, studiot said:

... since the kinetic approach is non cyclic in basis, you cannot use that part of classical thermodynamics which is defined only for cyclic processes.

Consider this:

An isolated system comprises a number of contiguous but measurably different regions which when plotted on a thermodynamic diagram yield a scatter plot centred around a central point P. This represents a system that is not (yet) in thermal equilibrium. Each region has a mass m and plots to a local equilibrium centre a distance r from P, and can be viewed as carrying a 'moment of disequilibrium' (my terminology) of magnitude mr(t) since obviously we have interest in the time evolution of the system(s). Clearly, the total moment of disequilibrium about P is dominated by those regions furthest away from P. We'll come back to this.

From a kinetic point of view, regions interact by the passage of a particle carrying a particular packet of mass and energy from one region into another resulting in the plotted points for each region moving in equal and opposite steps. I personally picture such an event as equivalent to equal and opposite transfers of Q, W and mass between regions, but that's simply a preferred style - they appear exactly synonymous to me.

Now let's focus on those more distant regions. We've not yet established that these regions must converge toward P (that comes later) but let's say that there is some hidden mechanism that preserves r. So now we have each of these regions moving stepwise clockwise or anticlockwise around an annular band centred on P. ie under the influence of a sequential transfer of particles between regions (regions performing work on each other in my language) we have an isolated system traversing a reasonably clearly defined closed thermodynamic cycle, regions at opposing sides of the cycle exchanging Q, W, and m as necessary to maintain the status quo.

Now remove the constraint on r, and let each region gradually make stepwise moves statistically approximating to a stroll in the direction of P as I hope we all agree is what it must do.

The system as a whole remains just as dynamic as ever, particles are exchanged with the same kind of frequency, the number of regions remains unchanged, each region remains in motion with the same size steps, and the system continues to trace out a closed cycle , only with reduced diameter and reduced overall moment of disequilibrium. Ultimately, all regions meet at P, so by definition, they are all at the same thermodynamic temperature and thermal equilibrium has been established.

But there is still a closed cycle whirring away behind that point. There is still a huge number of microstates (Boltzmann's W value) consistent with the energy content defined by point P on the chart. And each region remains in a state of constant fluctuation as they move stepwise through the W possible permutations defined by pointlike, stationary P which they visit in a well- orderly sequence particle exchange by particle exchange, tracing out that closed cycle.

Are we okay so far?

10 hours ago, studiot said:

Epstein A textbook of Thermodynamics

A free pdf is available here.

Many thanks for that. I think my Smith and van Ness ended up in the library of one of my trainee engineers.

Edited by sethoflagos
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13 hours ago, studiot said:

I don't know if you have heard of the Massieu and Planck functions ?

These two provide the (mathematically derivable) link between the classical and the statistical approach, so that this is often referred to as 'the Massieu Bridge'.

All of this is expounded detailed in Guggenheim's Advanced thermodynamics.

(I would not recommend the Wikipedia pages on this they are rather unhelpful and not completely comprehensive or correct)

No worries.

Majcek & Meijer Statistical Thermodynamics covers the relationship between state variables and the canonical partition function quite comprehensively. However, I'm sure you're aware that quantification of the latter seems to head off into QFM land even in the simplest cases.

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On 7/8/2020 at 9:59 PM, sethoflagos said:

Please try not to be offended by anything I post below. The issues you raise are deep ones and I fully recognise that a spectrum of opinion across intelligent parties is not only to be expected, but is very much a positive thing. If we refuse to look at an object from another viewpoint, our understanding of the object can never improve beyond speculation. We need the other's viewpoint. I'll try to be less robust in my presentation, but please remember that I'm schooled in producing an end product that nails a small target within limited budgets and tight deadlines. Not much opportunity to sit around philosophising.

Sounds good.

On 7/8/2020 at 9:59 PM, sethoflagos said:
On 7/8/2020 at 11:52 AM, studiot said:

... of Applied Thermodynamics .

Does the stress here introduce a value judgment of a methodology based in its ontological classification (ie. what name you give to it)? I'll attempt to paraphrase Feynmann "If it disagrees with experiment, it's wrong". Conversely, all methodologies that agree like-for-like with measurements of the real world must be equivalently valid. In my experience ontology carries with it many hidden traps which makes me very wary. It's a branch of metaphysics and maybe best left to the theologians to play with.

Not really, no, although ontology is too airy fairy for me.

I am fond of pointing out the twin complementary processess of analysis and synthesis.

Synthesis is largely practised by Applied Scientists and Engineers, (following the analysis of a problem)

In my opinion it is more difficult to create something that does not yet exist (a dam a motorway, a chemical plant a harbour etc) to meet a specification than to analyse something that is.

On 7/8/2020 at 9:59 PM, sethoflagos said:

Consider this:

An isolated system comprises a number of contiguous but measurably different regions which when plotted on a thermodynamic diagram yield a scatter plot centred around a central point P. This represents a system that is not (yet) in thermal equilibrium. Each region has a mass m and plots to a local equilibrium centre a distance r from P, and can be viewed as carrying a 'moment of disequilibrium' (my terminology) of magnitude mr(t) since obviously we have interest in the time evolution of the system(s). Clearly, the total moment of disequilibrium about P is dominated by those regions furthest away from P. We'll come back to this.

From a kinetic point of view, regions interact by the passage of a particle carrying a particular packet of mass and energy from one region into another resulting in the plotted points for each region moving in equal and opposite steps. I personally picture such an event as equivalent to equal and opposite transfers of Q, W and mass between regions, but that's simply a preferred style - they appear exactly synonymous to me.

Now let's focus on those more distant regions. We've not yet established that these regions must converge toward P (that comes later) but let's say that there is some hidden mechanism that preserves r. So now we have each of these regions moving stepwise clockwise or anticlockwise around an annular band centred on P. ie under the influence of a sequential transfer of particles between regions (regions performing work on each other in my language) we have an isolated system traversing a reasonably clearly defined closed thermodynamic cycle, regions at opposing sides of the cycle exchanging Q, W, and m as necessary to maintain the status quo.

Now remove the constraint on r, and let each region gradually make stepwise moves statistically approximating to a stroll in the direction of P as I hope we all agree is what it must do.

The system as a whole remains just as dynamic as ever, particles are exchanged with the same kind of frequency, the number of regions remains unchanged, each region remains in motion with the same size steps, and the system continues to trace out a closed cycle , only with reduced diameter and reduced overall moment of disequilibrium. Ultimately, all regions meet at P, so by definition, they are all at the same thermodynamic temperature and thermal equilibrium has been established.

But there is still a closed cycle whirring away behind that point. There is still a huge number of microstates (Boltzmann's W value) consistent with the energy content defined by point P on the chart. And each region remains in a state of constant fluctuation as they move stepwise through the W possible permutations defined by pointlike, stationary P which they visit in a well- orderly sequence particle exchange by particle exchange, tracing out that closed cycle.

Are we okay so far?

I am worried about this since I picture say a red hot poker being thrust into a bucket of water as a line heat source or point heat source in any section.

Surely this meets the specification of your point P , but generates motion and dispersion away from P not towards it  ?

On 7/9/2020 at 1:17 AM, sethoflagos said:

Majcek & Meijer Statistical Thermodynamics covers the relationship between state variables and the canonical partition function quite comprehensively. However, I'm sure you're aware that quantification of the latter seems to head off into QFM land even in the simplest cases.

Maczek (as it is spelled on the fron of my copy) is a very good and clear basic book I would recommend to anybody.

He does not dilly dally with microstates like some but uses partition functions to the full.

What is you opinion of partition functions v microstates ?

You might also like to look into what Mandl   (Manchester Physics series Statistical Physics) about your youtube issue.

I think (please confrim or correct) that this is a description of it in his introduction to the second law.

He goes on to split the probability function into two functions by , not the states themselves, but of the size of the fluctuations as a result of the N or n.

He shows how the smaller N is the larger the expected fluctuations are from 'equilibrium'.

Fluctuations sizes for a single particle are 'off the scale'

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Posted (edited)
1 hour ago, studiot said:

I am worried about this since I picture say a red hot poker being thrust into a bucket of water as a line heat source or point heat source in any section.

Surely this meets the specification of your point P , but generates motion and dispersion away from P not towards it  ?

Nice picture! Let's run with it.

The red hot poker is initially one region in thermal equilibrium at T1, the bucket of water another at T2. When brought into contact, the poker starts losing heat at T1 the bucket absorbs heat at T2. The heat transferred across the boundary is identical but the bucket is gaining entropy much more quickly than poker is losing it due to the inequality of their absolute dQ/T values. Therefore, when everything settles down, to thermal equilibrium at a new temperature, the system entropy will have increased quite considerably. In real cases, numbers can be put to these nett changes with a high degree of accuracy. So far, so good.

But this is the bit I'm having difficulty getting my head around. I can take a snapshot at any instant of this new equilibrium state and draw an irregular partition carefully excluding any 'fast' particles close to the boundary, but capturing 'slow' ones. Effectively, I've now got a system in 'perfect' thermal equilibrium and a precisely known entropy, comprising two regions at arbitrarily different temperatures whose entropies sum to significantly less.

The picture must be wrong somewhere, and I can think of a couple of glib dismissals, but these are giving me no useful insight.

1 hour ago, studiot said:

What is you opinion of partition functions v microstates ?

Without partition functions the number of microstates in any ensemble is uncountable. It answers what I see as statistical mechanics' version of the UV catastrophe, though the analogy is probably a poor one.

Edited by sethoflagos
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Posted (edited)
6 hours ago, studiot said:

Synthesis is largely practised by Applied Scientists and Engineers, (following the analysis of a problem)

As in the Hegelian sense of 'thesis - antithesis - synthesis'? Then that's amusing for reasons I won't go into here. Undisputed.

You asked me earlier which formulation of the 2nd Law I used. Perhaps, in hindsight it was a fair question and deserved a more complete answer. This is my own personal overview of the heirarchy:

Classical Entropy (chemists' version?) : dS = dQ/T and all that follows from that, is the underlying principle behind internationally recognised methodologies of performing thermodynamic engineering design (obviously with appropriate allowances for real process behaviour).

Gibbs' Entropy : - kB * Summation of Pi ln(Pi)  I don't use, but is I understand synonymous with the above per  E.T. Jaynes; Gibbs vs Boltzmann Entropies; American Journal of Physics, 391 (1965)

Boltzmann H theorem : Flawed (same Jaynes) due primarily to the molecular chaos assumption - ie that collisions are uncorrelated. This is where my dialogue with swantont foundered, and it continues to sow confusion.

Boltzmann Entropy : k log W. Boltzmann's improvement on H-theory, and from which Gibb's Entropy follows (same Jaynes).

von Neumann Entropy : the - Summation nj ln(nj) form shows it's affinity with Gibbs' Entropy for which it is an extension (not a refutation) into the quantum realm. I understand that the collision correlation issue is addressed through terms covering the quantum entanglement between interacting regions under the umbrella 'entanglement entropy'. Zachos, C. K. (2007). "A classical bound on quantum entropy". Journal of Physics A: Mathematical and Theoretical.

I'm pretty clueless on quantum mechanics, but if von Neumann's entanglement entropy yields quantitatively the same collision correlation as classical conservation of linear and angular momenta (the 'applied' world) and I'd be very surprised if it didn't, then all the above, with the exception of H-theory seem to be mutually consistent. It's obvious which flavour I use as an everyday tool, but in principle, they all seem equivalent. The 2nd Law is the 2nd Law (as someone once said).

Therefore I see no problem with statistical mechanics as such. But I take issue with simplistic statistical methods that ignore standard conservation laws.

Edited by sethoflagos
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Posted (edited)
1 hour ago, sethoflagos said:

As in the Hegelian sense of 'thesis - antithesis - synthesis'? Then that's amusing for reasons I won't go into here. Undisputed.

Absolutely not.

That is even more obscure than ontology.

Some examples of what I mean by Analysis :

1a) I hand you a container of a a pure gas and ask you to measure the % carbon in the gas. result 83.7%

2a) I ask you to measure the contours of an existing embankment (survey it).

3a) I point to the pavement of a concrete road leading into a nuclear power station or petrochemical complex ask you to measure the stength  of the pavement concrete because I need to run plant along the road safely.

Examples of Synthesis

1s) I ask you to manufacture a canister of a pure gas containing 84.7% carbon

2s) I hand you a set of plans and ask you to construct an embankment according to those plans.

3s) I ask you to construct a new concrete road with strength at least 6,000 psi to accomodate the plant I need to run along it.

Does this make it any clearer?

In each pair of cases which do you think is the more difficult task?

Edited by studiot

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