An alternative derivation of second law results to better relate derivation to practical exergy analysis

A more general and physically intuitive alternative to the classical macroscopic derivation of second law results is proposed. Instead of using imaginary reversible processes occurring within heat engines that operate between infinite temperature reservoirs, the new derivation is applicable to any arbitrary control volume across which heat and/or work interactions occur. The arbitrary control volume is discretized into infinitesimally small elements. So-called ‘Interface Equations’ are developed at the interfaces of these elements, utilizing the second law statement that heat transfer occurs from higher to lower temperatures. Terms from the interface equations are then rearranged at each element to show that dS\u3edQ/T; all other second-law formulation follow from this result. The derivation allows reversible processes to be mathematically defined, which in turn, allows irreversibilities and entropy generation to be understood in terms of spatial non-uniformity of temperature distribution