12.6 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 ?

<p><strong> (a)</strong> When the stopcock is opened, the volume became double between cylinders A and B. Since volume is inversely proportional to pressure, the pressure will become half. So the initial pressure of 1 atm in cylinder A will become ½ atm in cylinder A and B.</p><p>&nbsp;</p><p><strong> (b)</strong> The internal energy will change when there is work done by the gas. In absence of any work done, there will be no change in internal energy.</p><p>&nbsp;</p><p><strong> (c)</strong> In absence of any work done, there will be no change in the temperature.</p><p>&nbsp;</p><p><strong> (d)</strong> 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 non-equilibrium states, they do not lie on the P-V-T surface of the system.</p>

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