On the exergy balance equation and the exergy destruction

The exergy balance equation can be written expressing the useful work for a general process as depending on the useful work for the corresponding reversible process and the exergy destruction term. However, this can be made only if the terms (other than the exergy destruction term) on the exergy balance equation for the general process lead to the same result as the terms on the exergy balance equation for the corresponding reversible process. It is shown that this is not generally the case for unsteady processes, and that this can be the case for steady processes, for both closed and open systems. It is also shown that this is not generally the case for unsteady processes in terms of instantaneous powers, but that this can be the case for the whole unsteady processes. This is an important result, for: (i) Expressing the useful work for a general process as depending on the useful work for the corresponding reversible process and the exergy destruction; (ii) Exergy analysis; and (iii) The teaching/learning process of exergy and exergy analysis, and a better understanding and application of the exergy balance equation.