Two containers of equal volume are connected by a stopcock as shown below. One container is filled with a gas at a pressure of 1 atm and temperature of 293 K while the other container is evacuated so that it is under vacuum. The containers are thermally isolated from the surrounding so no heat enters or escaped from the system. The stopcock is then opened allowing the gas from one container to fill the other. What is the final temperature of the gas after it has come to equilibrium?

Question

Quizplus · Accepted Answer

Since the containers are thermally isolated, no heat is exchanged with the surroundings, and thus the internal energy of the gas in each container is conserved. The expansion of the gas from one container to the other is an irreversible process, which means that the total entropy of the system increases. However, the entropy change can only depend on the initial and final states of the system, and not on the path taken to get there. Therefore, the final temperature of the gas must be the same as the initial temperature, which is 293 K.

Two Containers of Equal Volume Are Connected by a Stopcock