Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases
Two vessels A and B of equal volume V₀ are joined by a narrow tube equipped with a valve. The vessels contain pistons that can be moved to alter the volumes. Initially, the valve is open, and both vessels hold an ideal gas ( C_p / C_V = ) at atmospheric pressure p₀ and atmospheric temperature T₀ . The walls of vessel A are diathermic, while those of B are adiabatic. The valve is then closed, and the pistons are slowl
Options
- AIn vessel A : T₀ 2^ - 1 , p₀ 2^ ; In vessel B : T₀ , p₀ 2
- BIn vessel A : T₀ , p₀ ; In vessel B : T₀ 2^ - 1 , p₀ 2^
- CIn vessel A : T₀ , p₀ 2 ; In vessel B : T₀ 2^ - 1 , p₀ 2^
- DIn vessel A : T₀ , p₀ 2 ; In vessel B : T₀ 2^ - 1 , p₀ 2^
Correct answer
C. In vessel A : T₀ , p₀ 2 ; In vessel B : T₀ 2^ - 1 , p₀ 2^
Step-by-step solution
Initially, both vessels contain an ideal gas at pressure p₀ , volume V₀ , and temperature T₀ . When the valve is closed, the gases in vessels A and B are isolated from each other. For vessel A , the walls are diathermic, which means it can exchange heat with the surroundings. Since the piston is pulled out slowly, the process is isothermal. The temperature remains constant at the atmospheric temperature T₀ . Using Boyle's law for the isothermal process in vessel A : p_A V_A = p₀ V₀ Given that the final volume V_A =