 #1
 239
 20
Homework Statement:

A horizontal cylindrical container is divided into two equal chambers by an airtight movable partition. The walls of the cylinder and the partition are adiabatic. Each chamber is filled with 1 mol of a monoatomic ideal gas. The gas in the left chamber is hotter, the one in the right chamber is colder.
The partition moves until the pressure in the two chambers is the same. Find the final temperatures in the two chambers.
Relevant Equations:
 Equation of state for an ideal gas. Relations between p, V and T for an adiabatic process. Internal energy for a monoatomic ideal gas. First law of thermodynamics.
The actual data for the problem and my (and my friend's) attempt at a solution are in the attached file.
In a nutshell, this is what happened.
I obtained a solution based on the fact that the system is isolated. Thus the initially hot gas moves the partition doing work onto the initially cold gas, but the total amount of internal energy stays the same. I thought I used the conservation of the total volume, but somehow this does not appear to be the case.
A friend of mine obtained a different solution explicitly requiring that the total volume of the cylindrical container should be the same for the initial and final states of the systems.
My solution has the problem that the final volume is not the same as the initial one.
My friend's solution has the problem that the total internal energy of the final state is not the same as in the initial state.
So, probably both of us are making a (different) mistake.
Possibly, both of us are introducing different assumptions on how the process comes about (although we both initially assumed that the system is isolated and that the volume does not vary).
Can someone advise, please?
In a nutshell, this is what happened.
I obtained a solution based on the fact that the system is isolated. Thus the initially hot gas moves the partition doing work onto the initially cold gas, but the total amount of internal energy stays the same. I thought I used the conservation of the total volume, but somehow this does not appear to be the case.
A friend of mine obtained a different solution explicitly requiring that the total volume of the cylindrical container should be the same for the initial and final states of the systems.
My solution has the problem that the final volume is not the same as the initial one.
My friend's solution has the problem that the total internal energy of the final state is not the same as in the initial state.
So, probably both of us are making a (different) mistake.
Possibly, both of us are introducing different assumptions on how the process comes about (although we both initially assumed that the system is isolated and that the volume does not vary).
Can someone advise, please?
Attachments

107.1 KB Views: 52