Irreversible Exchange of Heat and Mass across Narrow Boundaries Under Specified Conditions

We extend here a set of earlier articles that deal with irreversible processes across a thin boundary separating a system from its surroundings. We consider the transfer of heat and material when the system and reservoir are held at constant volume, and the temperatures (T) and chemical potentials (?) differ by arbitrary amounts in the two parts of the compound system. Three distinct time variations for changing temperature and composition in the system are adopted. Although for any specified change of state the entropies associated with the transfer of heat and matter are quite different in the three cases, the overall entropy change remains the same, as is consistent with entropy being a function of state. The relation of the present approach to standard methodology is discussed.