Dual gas (coupled) cyclic processes?

[Philip Koeck]

TL;DR Summary

If two gases in different cylinders undergo thermodynamic cycles that are coupled to each other in some particular way, can both be reversible? Can we learn anything else from such constructions.

I have a somewhat open question here and maybe the beginning of some interesting ideas.

I came across this paper [unacceptable reference removed by the Mentors], which claims to give an example of a system that defies the second law.

This got me thinking about where the proposed idea starts failing (and also, generally, about systems coupled in this way).

For example if we have 2 gases in 2 separate cylinders and one of them undergoes a Carnot cycle.
The 2 cylinders are connected mechanically in such a way that dW for the one is always equal to -dW of the other, so clearly when one expands the other has to be compressed and the expansion and compression rates have to be carefully adjusted.
Obviously the pressures in the 2 gases have to be different from each other most of the time.

So, one of my questions is: Can such a coupled process be reversible or quasistatic even in principle?

All comments and ideas welcome. Have coupled systems been studied? (My googling didn't result in anything other than the mentioned paper.)

Could this idea lead to some interesting student projects or teaching tools?

 

[Chestermiller]

TL;DR Summary: If two gases in different cylinders undergo thermodynamic cycles that are coupled to each other in some particular way, can both be reversible? Can we learn anything else from such constructions.

I have a somewhat open question here and maybe the beginning of some interesting ideas.

I came across this paper (https://www.researchgate.net/public...consuming_external_energy#fullTextFileContent), which claims to give an example of a system that defies the second law.

This got me thinking about where the proposed idea starts failing (and also, generally, about systems coupled in this way).

For example if we have 2 gases in 2 separate cylinders and one of them undergoes a Carnot cycle.
The 2 cylinders are connected mechanically in such a way that dW for the one is always equal to -dW of the other, so clearly when one expands the other has to be compressed and the expansion and compression rates have to be carefully adjusted.
Obviously the pressures in the 2 gases have to be different from each other most of the time.

So, one of my questions is: Can such a coupled process be reversible or quasistatic even in principle?

All comments and ideas welcome. Have coupled systems been studied? (My googling didn't result in anything other than the mentioned paper.)

Could this idea lead to some interesting student projects or teaching tools?

This paper is idiotic, and the mathematics makes no sense to me. Have you tried making a simple model calculation using an ideal gas and, say, a van der Waals gas to see how it plays out in detail? According to this paper , heat is transferred from cold to hot in a combination of cycles without doing any work. In the > 150 years since the 2nd law was identified, no one else has successfully refuted it until these clowns claim to do so.

 

[Philip Koeck]

This paper is idiotic, and the mathematics makes no sense to me. Have you tried making a simple model calculation using an ideal gas and, say, a van der Waals gas to see how it plays out in detail? According to this paper , heat is transferred from cold to hot in a combination of cycles without doing any work. In the > 150 years since the 2nd law was identified, no one else has successfully refuted it until these clowns claim to do so.

I haven't actually managed to make him clearly state the assumptions. He just avoids the question (see the comments on RG). So I don't really know how the systems are supposed to be coupled.
Anyway, I did think the idea of coupled systems was interesting, at least for teaching.
It's probably not very useful, though, otherwise, or could it be?

 

[berkeman]

Anyway, I did think the idea of coupled systems was interesting, at least for teaching.

Since the link you posted is not a valid reference, we need to close this thread. If you want to start a new thread to discuss the coupled systems idea, that could be okay as long as you leave out questionable links like that one. Thanks.

 

[berkeman]

Chet has requested that the thread be reopened to continue the valid part of the discussion. The unacceptable paper reference has been redacted from the OP.

 

[Chestermiller]

To get a handle on this, and to see how it plays out for the case of an ideal gas, consider the following problem for an ideal gas:

You have a cylinder with a massless, frictionless piston situated in the middle, initially containing an ideal gas of volume $2V_0$, temperature $T_0$, and pressure $P_0$; so each chamber has initial volume $V_0$. For the first (isothermal) step of the process, let the cylinder be in contact with an ideal isothermal reservoir at $T_0$. Heat is added very slowly to the left chamber, and added or removed very slowly from the right chamber so that the gas in the left chamber experiences an isothermal expansion to $V_0+\Delta V$ and the gas in the right chamber experiences an isothermal compression to $V_0-\Delta V$, Whatever work necessary can be extracted from this system by applying additional force to the piston. What amount of work is done, what is the final state in each chamber, and what is the change in internal energy in each chamber?

According to your understanding, aside using ideal gases in both chambers, does this description capture the first (isothermal) step in the process described in the OP?

 

[Philip Koeck]

According to your understanding, aside using ideal gases in both chambers, does this description capture the first (isothermal) step in the process described in the OP?

I'll answer your last question first and then we can discuss the setup you suggest.

I think they claim in the "paper" that the work supplied by one gas is always used completely by the other gas at every time point. To achieve this some mechanical device like a transmission is assumed.
They also seem to say that one gas follows a Carnot cycle.

For me it's not obvious that, under the conditions they seem to suggest, the second gas can follow a closed cycle at all, let alone a reversible one.

Unfortunately the author doesn't want to specify the assumptions more clearly so it's really not possible to discuss with him/her.

 

[Philip Koeck]

To get a handle on this, and to see how it plays out for the case of an ideal gas, consider the following problem for an ideal gas:

You have a cylinder with a massless, frictionless piston situated in the middle, initially containing an ideal gas of volume $2V_0$, temperature $T_0$, and pressure $P_0$; so each chamber has initial volume $V_0$. For the first (isothermal) step of the process, let the cylinder be in contact with an ideal isothermal reservoir at $T_0$. Heat is added very slowly to the left chamber, and added or removed very slowly from the right chamber so that the gas in the left chamber experiences an isothermal expansion to $V_0+\Delta V$ and the gas in the right chamber experiences an isothermal compression to $V_0-\Delta V$, Whatever work necessary can be extracted from this system by applying additional force to the piston. What amount of work is done, what is the final state in each chamber, and what is the change in internal energy in each chamber?

The inner energies of both gases are constant if they are ideal.

The work required to compress gas B (I'll call it that from now) is larger than the work supplied by the expansion of gas A, so extra work has to be supplied from outside.

The work supplied by gas A is:
W_A = n R T₀ ln((V₀+ΔV)/V₀)

The work (negative and larger in magnitude than W_A) needed to compress gas B is:
W_B = n R T₀ ln(V₀/(V₀-ΔV))

The extra work supplied from outside (also negative) is the sum of W_A and W_B.

To keep the inner energies constant the heat supplied by the surroundings to gas A is equal to W_A and the heat removed from gas B is equal to W_B.

This also means that the entropy change for both gases and the surroundings together is zero.

So whether the total process is reversible or not should only depend on how the extra work is produced, by a reversible or an irreversible engine.

The whole system is like a spring that stores work in a pressure difference.

 

[Philip Koeck]

Let's complete the cycle now in a very simple way.
I'll stick to 2 ideal gases in 2 parts of a cylinder separated by a movable dividing wall so that the sum of volumes is constant. When one gas expands the other has to be compressed by the same amount.

I'll use 2 isochors and another isotherm to complete the cycle (Stirling process).

One way to do this is that both gases follow the same cycle but in opposite directions so that one is an engine, the other a pump.
That would mean all the work produced by the engine is used by the pump.
This device would only run if it's pushed away from mechanical equilibrium to start with and then it would just continue for ever in the absence of friction, without any effect on the surroundings.

Another way of connecting the two gases would be to let them both run as engines.
This would require 3 different, for example equally spaced, isotherms. Both gases would follow the middle isoterm, but in opposite directions. The pV-graph would show 2 Stirling cycles stacked on top of each other (in the p-direction).
The interesting thing is that this construction behaves like a single engine with twice the temperature difference. The device could easily be extended to include several gases.
If a regenerator is used to recycle the isochoric heat-output the efficiency of such a device would be e = 1 - T_min/T_max even though the individual gases only need to be undergo much smaller temperature changes.

This sounds like something that should be used somewhere already.