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 ?
(a).
Cylinders, A and B are of equal capacity, so when the stopcock is suddenly opened, the pressure in both the cylinders decreases to half the initial value. Since volume is inversely proportional to pressure, therefore when the stopcock is opened, the volume gets doubled for the gas and hence pressure gets halved.
(b).
As there is no work done by or on the system, also there is no heat interaction, therefore internal energy of the system remains the same.
(c).
The expansion of the gas is not due to any external work done on the system and hence, temperature of the system will not change.
(d).
Free expansion is a very fast process and it cannot be controlled. As the intermediate states are non-equilibrium states, hence they can’t be on the P − V − T surface of the system.
(a).
Cylinders,
(b).
As there is no work done by or on the system, also there is no heat interaction, therefore internal energy of the system remains the same.
(c).
The expansion of the gas is not due to any external work done on the system and hence, temperature of the system will not change.
(d).
Free expansion is a very fast process and it cannot be controlled. As the intermediate states are non-equilibrium states, hence they can’t be on the
