__Question 12.6__:
Two cylinders

(a) What is the final pressure of the gas in

(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

*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?

__Solution__:**(a)**The volume available to the gas is doubled as soon as the stopcock between cylinders

*A*and

*B*is opened. Since volume is inversely proportional to pressure, the pressure will decrease to one-half of the original value. Since the initial pressure of the gas is 1 atm, the pressure in each cylinder will be 0.5 atm.

**(b)**Zero

The internal energy of the gas can change only when work is done by or on the gas. Since in this case no work is done by or on the gas, the internal energy of the gas will not change.

**(c)**Zero

Since no work is being done by the gas during the expansion of the gas, the temperature of the gas will not change at all.

**(d)**No

The given process is a case of free expansion. It is rapid and cannot be controlled. The intermediate states do not satisfy the gas equation and since they are in non-equilibrium states, they do not lie on the

*P*-

*V*-

*T*surface of the system.

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