For an ideal gas in an adiabatic reversible turbine or compressor:

\[\frac{T_2}{T_1} = \left(\frac{P_2}{P_1}\right)^{\frac{R}{C_P}} \]

where \(T_1\) and \(P_1\) are the inlet temperature and pressure and \(T_2\) and \(P_2\) are the outlet temperature and pressure. Absolute temperature must be used in this equation. \(R\) is the ideal gas constant and \(C_P\) is the constant-pressure heat capacity, which must be independent of temperature to use this equation.

Turbine efficiency: 

\[ \eta = \frac{W_{irreversible}}{W_{reversible}} \]

For an adiabatic turbine or compressor:

\[S_1 = S_2 \]

(i.e., inlet entropy = outlet entropy) This equation is used to determine outlet conditions for a reversible turbine if the feed is not an ideal gas.

Compressible efficiency:

\[ \eta = \frac{W_{reversible}}{W_{irreversible}} \]