Reversible mass exchange between two multicomponent systems of different temperatures

The concept of reversible work in nonequilibrium systems, which has been used for the derivation of thermal diffusion coefficients, is critically examined. For this purpose heat and mass exchange between two multicomponent systems of different temperatures and pressures is treated in detail. It is shown both by general considerations and by a specific example that calculating the reversible work--the work performed in case of reversible mass exchange--is essentially the same as calculating the dissipation function describing the corresponding irreversible process. Although the dissipation function is the starting point for the description of irreversible processes in nonequilibrium thermodynamics, it is not obvious how it could be used to obtain an expression for the thermal diffusion coefficient.