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 P-V-T surface ?

Explanation

(a) When the stopcock is suddenly opened the volume available to the gas at 1 atmospheric pressure will be doubled. Because the volume of both gases is same and its initial and final temperature are also same.
`therefore` From Boyle.s law ,
`P_1V_1=P_2V_2`
`therefore P_2=(P_1V_1)/V_2` but `V_2=2V_1`
`therefore P_2=(P_1xxV)/(2V_1)`
`therefore P_2=P_1/2` but `P_1` = 1 atm
`therefore P_2=1/2` = 0.5 atm
The pressure in A and B cylinders will be half atmosphere.
(b) Zero. Because temperature is constant and internal energy is proportional to temperature and hence internal energy is also constant means there is no change in internal energy.
(c) Since no work is done by the gas during the expansion of the gas the temperature of the gas will not change at all.
(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, it does not lies on surface P-V-T.
If gas does return to an equilibrium state then it lies on surface P-V-T.