Two cylinders A and B of equalcapacity are connected to each other via a stopcock. A containsa gas at standard temperature and pressure. B is compeltely 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 temperatureof the gas (d) Do the intermediate states of the system (before setting to the final equilibrium state) lie on its P-V-T surface?

Two cylinders A and B of equalcapacity are connected to each other via

1.	Two cylinders A and B of equalcapacity are connected to each other via a stopcock. A containsa gas at standard temperature and pressure. B is compeltely 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 temperatureof the gas (d) Do the intermediate states of the system (before setting to the final equilibrium state) lie on its P-V-T surface?
Answer» Solution :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 state of gas P, V final 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.