Equilibria in Subsystems

Example 1.1 Equilibrium in subsystems Consider a closed isolated cylinder with two subsystems of 1 and 2 containing air with an equal volume of 1L and equal temperatures of 298.15 K. There is a fixed piston at the boundary of the subsystems, which have different pressures of Px = 2 atm and P2 1 atm. Estimate the temperature, volume, and pressure of the subsystems when the piston is released. Assume that the piston is impermeable to air, freely movable, and heat conducting. 

Assume that the air is an ideal gas with constant heat capacity. 

According to the first law and constant heat capacity Cv, we have 

This is a natural result as the internal energy of an ideal gas depends on the temperature only, and the system is isothermal at the initial and final conditions. 

With a total volume of 2 L, the final volumes and pressures become 

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