Effect of Turbine Efficiency
Steam at 500°C and 10 bar is expanded in an adiabatic turbine 1 bar.
(a) Compute the final temperature of the steam and work obtained if the process is 100% efficient.
(b) Compute the final temperature of the steam and work obtained if the process has an isentropic efficiency of 85%.
a) From the steam tables, the thermodynamic properties of the initial state are
\begin{aligned}\hat{H}(T&\left.=500^{\circ} C , 1.0 MPa \right)=3478.5 kJ / kg \text { and } \\\hat{S}(T&\left.=500^{\circ} C , 1.0 MPa \right)=7.7622 kJ / kg K\end{aligned}The final fluid conditions are
P=0.1 MPa \text { and } \hat{S}=7.7622 kJ / kg KInterpolating from the data in the steam tables, we have T = 183.7°C and
H = 2843.0 kJ/kg therefore,
of work produced by the isentropic turbine
b) For the non-isentropic turbine the work obtained is
and the final enthalpy = 3478.5 – 540.2 = 2938.3 kJ/kg. At 0.1 MPa, this enthalpy corresponds to a temperature of 238°C.
Comment
Note that less work is obtained from the non-isentropic turbine. Since energy is conserved, a greater portion of the energy in the initial steam now appears in the exiting steam in the form of a higher temperature.