A gas is initially contained inside an insulated container A, at initial conditions P1, V1, m, and T1. These quantities represent pressure, volume, mass, and temperature, respectively. A valve is then opened which allows the gas to expand freely into an insulated container B, which is initially empty. After the gas has settled, the final conditions of the gas are P2, V2, m, and T2. In thermodynamics, a process is said to be reversible if it produces no entropy. This means that the process can happen in the reverse direction. Explain why the process described is not reversible.
Answers
Since the containers are insulated, no heat transfer occurs between the gas and the external environment, and since the gas expands freely into container B there is no resistance "pushing" against it, which means no work is done on the gas as it expands. As a result, the internal energy of the gas remains the same, before and after the expansion. To return the gas to its original state, it would have to be compressed back into container A. This unavoidably takes place against a resistive pressure force (exerted by the gas), which means that work is required to do so. This would add energy to the gas, thereby increasing its internal energy, resulting in a temperature and pressure of the gas greater than its initial temperature and pressure (inside container A). It would then have to be cooled to bring it back to the conditions P1 and T1. This would add heat to the environment which would increase entropy. Hence, the gas cannot be returned to its initial state under the reverse conditions, and the process described in the problem is therefore not reversible.