Entropy

Thermodynamic Efficiency:

\( \eta _{th} = \frac{W_{net}}{Q_{in}} \)

Isentropic Efficiency (Turbines):

\( \eta _s = \frac{W_{actual}}{W_{ideal}} = \frac{\Delta h_{actual}}{\Delta h_{ideal}} \)

Isentropic Efficiency (Compressors):

\( \eta _s = \frac{W_{ideal}}{W_{actual}} = \frac{\Delta h_{ideal}}{\Delta h_{actual}} \)


Entropy Change for Ideal Gasses in Constant Variable Processes

Isometric:

\( \Delta s = C_v ln ( \frac{T_2}{T_1} ) = C_v ln ( \frac{P_2}{P_1} ) \)

Isobaric:

\( \Delta s = C_p ln ( \frac{T_2}{T_1} ) = C_p ln ( \frac{v_2}{v_1} ) \)

Isothermal:

\( \Delta s = R ln ( \frac{v_2}{v_1} ) = -R ln ( \frac{P_2}{P_1} ) \)


Entropy Change for Ideal Gasses in Other Processes

\( s_2 - s_1 = C_v ln (\frac{T_2}{T_1}) + R ln (\frac{v_2}{v_1}) \)

\( s_2 - s_1 = C_p ln (\frac{T_2}{T_1}) - R ln (\frac{P_2}{P_1}) \)

\( s_2 - s_1 = C_p ln (\frac{v_2}{v_1}) + C_v ln (\frac{P_2}{P_1}) \)