Consider a rigid adiabatic impermeable cylinder ie a closed

Consider a rigid, adiabatic, impermeable cylinder (i.e., a closed isolated system) that consists of two chambers (i.e., simple systems) that are separated by a wall that is permeable, immovable, and diathermal. Suppose that initially, the fluids in the two chambers are at the same temperature, T, but have different chemical potentials with µ2 > µ1. Using arguments considering entropy changes for heat transfer, demonstrate that

a. the fluid will flow from chamber 2 into chamber 1, and

b. this flow will continue until the two fluids are at the same chemical potential

Solution

a) From the Laws of thermodynamics, If the wall is permeable, Following conditions are necessary for chamber 1    equlibrium with chamber 2. The chamber 1 and chamber 2 temperaure are equal.

Pressure and chemicial potential of the Chambers are equal. Hence fluid flow from Chamber 2 to Chamber 1.

b) The fluid flow continiously from the chamber 1 to chamber 2 until the chemical potential are equal