Thermodynamics
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Question : 6
Total: 10
Two cylinders A and B of equal capacity are connected to each other via a stopcock. The cylinder A contains a gas at standard temperature and pressure, while the cylinder 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 setting to the final equilibrium state) lie on its P-V-T surface?
(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 setting to the final equilibrium state) lie on its P-V-T surface?
Solution:
(a) When the stopcock is suddenly opened, the volume available to the gas at 1 atmosphere pressure will become two times. Therefore, pressure will decrease to one-half, i.e., 0.5 atmosphere.
(b) There will be no change in the internal energy of the gas as no work is done on/by the gas.
(c) Also, there will be no change in temperature of the gas as gas does no work in expansion.
(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. In due course, the gas does return to an equilibrium state.
(b) There will be no change in the internal energy of the gas as no work is done on/by the gas.
(c) Also, there will be no change in temperature of the gas as gas does no work in expansion.
(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. In due course, the gas does return to an equilibrium state.
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