A well-insulated cylinder is rigid and adiabatic. The cylinder has an internal piston that is initially adiabatic, impermeable, and fixed in place. The two sides of the cylinder are charged with a binary mixture of ideal gases as shown below: At the start of the experiment, the dividing piston is replaced by one that is fixed in place, diathermal, and permeable only to component 

A. Assume CV = 20.9 J/mol K for both gases. Under these conditions, equality of chemical potentials μ1 = μ2 is equivalent to equality of partial pressures x1PI = x2PII, where xi is the mole fraction of component i. a. Derive the criteria for equilibrium. 

b. Derive the criteria for equilibrium if the piston were moveable