1. The problem statement, all variables and given/known data A gas-tight frictionless piston of small thermal conductivity slides in a thermally insulated cylinder, dividing it into two compartments, A and B, each containing nA=n and nB=0.45n moles of ideal monatomic gas (n moles). Initially the temperature of the gas is To in compartment A and 4To in B. Assume that the system is in mechanical equilibrium at all times and that the mass of the piston and the effect of gravity are negligible. Consider the process by which the system reaches thermal equilibrium: (a) What is the final temperature, Tf? (b) What is the ratio of the volume of A to that of B initially, ri? (c) What is the ratio of the volume of A to that of B after thermal equilibrium is reached, rf? (d) Calculate the work done on the gas in compartment A, and then do the same for compartment B. I managed to answer (a), (b), and (c) correctly, getting values of 1.93To, 0.55, and 2.22 respectively. Having a bit of difficulty with (d) 2. Relevant equations dW = -PdV W = -∫ Pdv = -∫ (nRT/V)dV 3. The attempt at a solution The answer is to be in terms of nRT I computed the work integral and I have, W = -nRT ln (Vfa/Via) Getting stuck as to what the ratio of Vfa to Via is. I played around with the ideal gas law and have, (Vfa/Via) = (1.93Pia/Pfa) From here I am just running in circles. Any help is appreciated!