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Stagnation Conditions in the Tds Equations

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Old   November 29, 2023, 12:53
Default Stagnation Conditions in the Tds Equations
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Is there a proof for why the stagnation conditions (T_0 and P_0) may be used in the Tds equations?

\Delta S = c_P \ln \left( \frac{T_2}{T_1} \right) - R \ln \left( \frac{P_2}{P_1} \right)

Denton 1993 states "the temperatures, pressures, and densities used in the Tds equations may be either all static values or all stagnation values because by definition the change from static to stagnation conditions is isentropic."

Further, some sources justify this with "the Tds equations apply between any two thermodynamic end states". Are stagnation temperature and stagnation pressure thermodynamic state variables?
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