Question

"Equal gas containers are connected by a capillary. One is kept in a higher temperature then the other. If the capillary not to thin system will reach mechanical equilibrium. Th cold container will then have more molecules then the hot one. the entropy per molecule is higher in hot gas.
If entropy maximum subject to temperature constraint molecules would move from cold to hot!!!
Chemical potential will be different on the tow sides in steady state.
Zero lows does not apply!!!"
How can i solve this exercise?

Answer 1

Wow, this is a tough one for me. I vaguely remember thermo. For systems near equilibrium you can try Ohm's law.
Also, you can use Le Chatlier's Principle to try and argue this. Since this system is clearly at different temps, entropy is not at max when pressure is equal. Thats required by mechanical equilibrium

Answer 2

Le Chatelier' Principle says "If a system is disturbed from equilibrium it will return monotonically towards eqiulibrium as disturbance is removed."
i have a steady state that can't be governed by variational principle.

Answer 3

Well, what exactly are you trying to "solve" ?

Answer 4

well i have to show mathematically that the system reaches the mechanical equilibrium, and the entropy isn't max. I tried something but i didn't get the right conclusion.

Answer 5

Oh man, mathematically, I think you're going to be using Differential equations for this. But there are a few formulas I have in mind that you can use, but there's quite a few. You can use S as a partial differential and evaluate that at S(1)=0 to show entropy isn't max. Well, we can work on this together, yes?
Maybe @Frostbite has some input on this, he is better at chemical statistics than anyone else on here.
Maybe he has some input.

Answer 6

Okey, thank you for your suggestions! :)