12.6 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 the 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 P-V-T surface?
a) The volume of the gas is doubled when the stopcock between cylinders A and B is opened and the pressure will be halved of the original value. Since the initial pressure of the gas is 1 atm, the pressure in each cylinder will be 0.5 atm.
b) The internal energy of the gas can change only when there is a change in the temperature of the gas. Since the temperature of the gas remains the same, the change in internal energy is equal to zero.
c) Since no work is being done by the gas during the expansion of the gas, the temperature of the gas will not change at all.
d) The gas is freely expending, the intermediate states do not follow the ideal gas equation and since they are in non-equilibrium states, they do not lie on the P-V-T surface of the system.
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