PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Thermodynamic potentials and the formal structure of thermodynamics · Thermodynamic potentials and the formal structure of thermodynamics
Thermal Physics, Ch Chemical potential, open systems and chemical equilibrium
Problem
Two rigid flasks, labelled 1 and 2, are joined by a narrow tube fitted with a valve. The pair is isolated from the surroundings, each flask has a fixed volume, and both flasks are at the same temperature T. When the valve is opened a small number dN1 of molecules passes into flask 1 from flask 2, so that N1+N2 is fixed; the transfer is slow and small enough that each flask's internal energy and temperature may be taken as unchanged, and the coupling between the flasks is weak, so the entropy of the pair is the sum of the two entropies.
((a)) Show that the entropy change of the pair is d(S1+S2)=(μ2−μ1)dN1/T.
((b)) Hence state which way molecules move when μ1>μ2, and the condition on μ1 and μ2 at equilibrium.