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

The gas undergoes free expansion. During this process the work done `dw=0`(zero). As the system is thermally insulated `dQ=0` (zero). Hence there is no change is internal energy or temperature.
a) Initial stage of gas P,V final state after expansion `P_(1), 2V` from Bolyer law `PV=P_(1) 2V`
` :. P_(1)=P/2 " " :. "Pressure is halved" `
b) `dU=0`
c) `dT=0`
d) During the intermediate stages, the parameters change quickly and the gas does not attain equilibrium. So the gas does not obey gas equation hence they do not appear on P,V,T surface.