COMPLETE FORMULAS DEVELOPED TO CALCULATE THE ENTROPY CHANGES OF IDEAL GASES

The entropy change of a system in a process is a key criterion to distinguish if the process is actual or ideal. The process without the entropy change is a perfect process called an isentropic process. Typical cycles involving the isentropic processes are the Otto, Ranking, and Brayton cycles. Two kinds of thermodynamic systems in the cycles are commonly encountered in engineering practices: closed and open. The equations calculating the entropy changes of ideal gases in processes are derived from the first Tds relation, the Gibbs equation, and the second Tds relation. Generally, the first Tds relation is applied to the closed systems, and the second Tds relation is applied to the open systems. There are two approaches used to analyze the entropy changes of ideal gases. They are the approximate analysis and the exact analysis, respectively. Equations relating to the Gibbs equation for the closed system in the precise analysis needed to be included in thermodynamics. This paper presents the development of the missing equations. The author describes the derivation of the complete equations to calculate the entropy changes of ideal gases and the correlated properties in the isentropic processes from the Tds relations for approximate and exact analysis. Examples illustrate the calculation using the equations for the entropy changes of air and the correlated properties in the isentropic processes.