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%.

Question

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%.

Accepted Answer

a) From the steam tables, the thermodynamic properties of the initial state are

[latex]\begin{aligned}\hat{H}(T&\left.=500^{\circ} C , 1.0 MPa ight)=3478.5 kJ / kg ext { and } \\hat{S}(T&\left.=500^{\circ} C , 1.0 MPa ight)=7.7622 kJ / kg K\end{aligned}[/latex]

The final fluid conditions are

[latex]P=0.1 MPa ext { and } \hat{S}=7.7622 kJ / kg K[/latex]

Interpolating from the data in the steam tables, we have T = 183.7°C and
H = 2843.0 kJ/kg therefore,

[latex]W_{S}=2843.0-3478.5 kJ / kg =-635.5 kJ / kg[/latex]

of work produced by the isentropic turbine
b) For the non-isentropic turbine the work obtained is

[latex]W_{A}=0.85 W_{S}=-540.2 kJ / kg[/latex]

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.

Question 5.3.1: Effect of Turbine Efficiency Steam at 500°C and 10 bar is ex...

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