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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 (a)

Q12.6 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?

Answers (1)
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S Sayak

As the entire system is thermally insulated and as free expansion will be taking place the temperature of the gas remains the same. Therefore PV is constant.

Initial Pressure P1 = 1 atm

Initial Volume, V1 = V

Final Volume, V2 = 2V

Final Pressure P2 will be

\\P_{2}=\frac{P_{1}V_{1}}{V_{2}}\\ P_{2}=\frac{P_{1}}{2}\\ P_{2}=0.5\ atm

The final pressure of the gas in A and B is 0.5 atm.

b) Since the temperature of the gas does not change its internal energy would also remain the same.

c) As the entire system is thermally insulated and as free expansion will be taking place the temperature of the gas remains the same.

d) The intermediate states of the system do not lie on its P-V-T surface as the process is a free expansion, it is rapid and the intermediate states are non-equilibrium states.

 

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