Question
Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following:
(a) What is the final pressure of the gas in A and B?
(b) What is the change in internal energy of the gas?
(c) What is the change in the temperature of the gas?
(d) Do the intermediate states of the system (before settling to the final equilibrium state) lie on its PVT surface?
Solution
(a) When the stopcock is suddenly opened, the volume available to the gas at 1 atmospheric pressure will become double. Therefore, pressure will decrease to half, i.e., 0.5 atmosphere.
(b) Since no work is done on or by the gas, there will be no change in the internal energy of the gas.
(c) The temperature of the gas will remain constant because no work is being done by the gas during the expansion of the gas.
(d) No, because the process called free expansion is rapid and cannot be controlled. The intermediate states are non-equilibrium states and do not satisfy the gas equation. Hence, the gas does return to an equilibrium state. Intermediate state of the system does not lie on its PVT surface.
(b) Since no work is done on or by the gas, there will be no change in the internal energy of the gas.
(c) The temperature of the gas will remain constant because no work is being done by the gas during the expansion of the gas.
(d) No, because the process called free expansion is rapid and cannot be controlled. The intermediate states are non-equilibrium states and do not satisfy the gas equation. Hence, the gas does return to an equilibrium state. Intermediate state of the system does not lie on its PVT surface.
