- #1
kiyoshi7
- 7
- 0
Homework Statement
I don`t know if the image will show so I`m also adding a link to the image of the problem. This problem is a modification my professor made to the one in the link below(*), he changed the rigid diathermic partition into a movable partition. I`m supposed to find the equilibrium temperature and volume. He also mentioned that he isn`t sure that it can be solved, he kind of changed it spontaneously. Also sorry for the math, I don`t know how to format it here in the forums.
https://drive.google.com/open?id=18F64i9f9BeFHGuygQj4hpIK5yQjYzZPl
* taken from: thermodynamics and introduction to thermalstatistics vol. 2, Herbert B. Callen.
Homework Equations
S= AU1/3V1/3N1/3 + (BN1N2)/N
N = N1+N2
find equilibrium assuming the following
Tr = 2Tl = 400k
37B2 = 100A3V0
The Attempt at a Solution
I know how to solve it when the cylinder is separated by a rigid diathermic permeable partition, but I can`t figure out how deal with the movable partition in this problem. So I`ll describe the solution for the rigid partition.
first find the intensive parameters:
∂S/∂U = 1/T = (1/3)(AU1/3V1/3/N2/3)
∂S/∂N1 = -u1/T
then rewrite ∂S/∂U as U in function of temperature:
U = T3/2(A3/2V1/2N1/2)/(33/2)
Total Energy:
Ut= [(A3/2V1/2)/(33/2)]( Nr1/2 Tr3/2 + Nl1/2 Tl3/2 )
I imagine that here I`d do the same as I did with N and T ie: (V1/2l N1/2l T3/2l + V1/2r N1/2r T3/2r), But I can't figure out how to solve it after this