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Two cyclinder A and B of equal capacity ...

Two cyclinder A and B of equal capacity are connected to eachother via a stopcock. The cyclinder A contains an ideal gas at standard temperature and pressure, while the cyclindr 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 temperature of a gas?
(d) Do the intermidiate states of the system (before settling to the final equilibrium state)lie on its `P-V-T` surface?

Text Solution

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(a) When a 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 temperture of the gas as gas does not work in expansion.
(d) No, because the process called free expansion is rapid and cannot be controlled. The intermediates states are non-equilibrium staes and do not satisfy the gas equation. In due course, the gas does return to an equilibrium state.
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