Statistical Physics Problem 1a - MIT OCW

[ehrenfest]

[SOLVED] statistical physisc

Homework Statement

http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/AC9B128C-9358-4177-BFE6-A142E0FD897B/0/ps4.pdf
I am working on Problem 1a. I am really confused about this question. Do I set the two equations equal to each other and solve for something? Do I just randomly write down 3 equations for t in terms of the respective variables of the 3 systems and then plug the given equations into to them to see if they are equal?

Homework Equations

The Attempt at a Solution

 

[Mapes]

Try assuming the gases are ideal and use the correct equation of state. Did you read the lecture notes?

 

[ehrenfest]

Yes, I read the lecture notes. Speaking of that, go here http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/D4B27A47-C2E6-4D06-B646-177DC744CC2A/0/lec10.pdf
In the third slide, why is the predictor t = c_g PV/N and not t = c_g PV/NT ? It seems like they want the same constant whenever the system is in equilibrium, so doesn't that mean they want the same constant regardless of what T is at equilibrium.
In the current problem, they say the coordinates of the system are P and V, so I assume that means N is constant. So, can I define t = PV-nbP, t'' = P''V'' and then the first equation makes t = t'' at equilibrium, but I have no idea what to do about the second equation? Should I just guess and check or is there a systematic way to do this? Is there only one answer?

 

[Mapes]

If temperature is the predictor of thermal equilibrium, then is it better to define the predictor to be t = c_g PV/N or t = c_g PV/NT for an ideal gas? It seems to me that the first one is a better match for the ideal gas law PV = nRT. The other way doesn't make much sense from a dimensional point of view.

But I see now that you don't need to assume ideal gases in problem 1a. Use the zeroth law: if A and C are at equilibrium and B and C are at equilibium, then A and B are at equilibium. Try calculating P'' from the first equation and from the second equation and setting the values equal to each other. Use your definitions t = PV-nbP and t'' = P''V'', and t' should emerge.