1. The problem statement, all variables and given/known data Consider two rigid cylinders, P and Q, with respective volumes VP and VQ with VP << VQ. They are connected by a capillary. Initially cylinder Q is empty and cylinder P contains an ideal monatomic gas at 300K and pressure 1 bar. A moveable piston in P is used to maintain the pressure in P at 1 bar completely expelling all the gas into Q through the capillary. The system is thermally isolated and the walls/capillary have negligible heat capacity. What is the final temperature of the gas once it has reached thermal equilibrium in Q? 2. Relevant equations Thermodynamic definition of work: Work done by piston W = -PdV Internal energy of monatomic gas: U = (3/2)nRT 3. The attempt at a solution Since the pressure in the cylinder P is unchanged, there is no pressure difference across the piston and so the external pressure supplied by the piston is equal to 1 bar. The piston does work on the n moles of gas moving them into the cylinder Q. Since the system is thermally isolated and the walls have negligible heat capacity, this work goes into increasing the internal energy of the gas. So write -Pi(VQ-VP) = (3/2)nR(TQ-TP), where the system is the n moles of gas originally in P ending up in Q. The term VQ-VP ≈ VQ by the question so sub this in, where VQ = nRTQ/Pi. Rearranging, I get that TQ = (3/5)TP, but I don't think this makes sense. I argued that the final pressure inside Q is the same as in P since if it wasn't the gas would flow back into P if it was greater and it wouldn't reach thermal equilibrium. So Pf = Pi of the n moles, and from ideal gas law, if V is increased, then T must go up to keep P constant. Many thanks.