Container with two gas compartments separated by piston

[sabinscabin]

Homework Statement

This is Reif, Fundamentals of Statistical Mechanics, problem 5.4

A cylindrical container 80 cm long is separated into two compartments by a thin piston, originally clamped in position 30 cm from the left end. The left compartment is filled with 1 mole of helium gas at a pressure of 5 atm; the right compartment is filled with argon gas at 1 atmosphere pressure.

These gases may be considered ideal. The cylinder is submerged in 1 liter of water, and the entire system is initially at the uniform temperature 25 deg C. The heat capacities of the cylinder and piston may be neglected. When the piston is unclamped, a new equilibrium situation is ultimately reached with the piston in a new position.

a) What is the increase in temperature of the water?
b) How far from the left end of the cylinder will the piston come to rest?
c) What is the increase of total entropy of the system?

Homework Equations

PV = nRT
dE = TdS - PdV

The Attempt at a Solution

This is a confusing problem because of all the possible ways heat can flow. The fact that part a) asks for the temperature increase of the water means that heat can flow across the cylinder boundary. It also says to ignore the specific heat of the cylinder and piston, which suggests that heat can also flow across the piston.

What I'm pretty sure of is that the piston will move to the right until the pressures of the two sides are equal (at which point the piston will stop due to the balance of force).

Now if no heat flowed in this problem, this would leave the left side at colder than 25 C (since it was the side that pushed the piston and did work) and the right side at hotter than 25 C (since the piston did work on it).

Now if we look at the temperatures, we have:
water: 25 C
left side: <25 C
right side: >25 C

this means that heat will flow in several different ways:
water --> left
right --> left
right --> water

With all these different heat flows, I have no idea where to begin in this problem.

 

[queenofbabes]

I don't think there is a need to worry exactly how the heat flows, the important thing is that the final temperature and pressure will be the same in both parts of the cylinder.