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 closed, and the pistons are slowly pul

Step-by-step solution

Initial state of the system: Both vessels A and B have volume V₀ , pressure p₀ , and temperature T₀ . Number of moles in each vessel: n_A = n_B = p₀ V₀ R T₀ . Total number of moles: n = n_A + n_B = 2 p₀ V₀ R T₀ . When the valve is closed and the pistons are slowly pulled out to double the volumes: For vessel A (diathermic walls): It remains in thermal equilibrium with the atmosphere. Thus, the process is isothermal. Final volume V_A' = 2V₀ Final temperature T_A' = T₀ For vessel B (adiabatic walls): The process is r