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Why for the same turbine exit condition, if the pressure and temperature of the air vapor entering the turbine are increased, the power produced by the turbine is greater?

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For approximately adiabatic reversible operation of the turbine, the variation of enthalpy per mole of gas passing through the turbine is given by $$dh=C_pdT=vdP=\frac{RT}{P}dP$$. This integrates to $$\frac{T_{out}}{T_{in}}=\left(\frac{P_{in}}{P_{out}}\right)^{\frac{(\gamma-1)}{\gamma}}$$From this it follows that the power delivered per mole of air passing through the turbine is given by $$\dot{p}=C_p(T_{in}-T_{out})=C_pT_{in}\left[1-\left(\frac{P_{out}}{P_{in}}\right)^{\frac{(\gamma-1)}{\gamma}}\right]$$So the higher $T_{in}$ and $P_{in}$, the higher the power delivered per mole of air.

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Assuming an adiabatic steam turbine, the power output equals the enthalpy per unit time of the incoming steam, $\dot h_i$, minus the enthalpy per unit time of the exiting steam, $\dot h_e$. Increasing the temperature and pressure of the incoming steam increases $\dot h_i$. Therefore for the same $\dot h_e$ output power increases.

Hope this helps.

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