Question

Argon gas expands in an adiabatic turbine steadily from 600C600^{\circ} \mathrm{C} and 800 kPa to 80 kPa at a rate of 2.5 kg/s. For isentropic efficiency of 88 percent, the power produced by the turbine is (a) 240 kW (b) 361 kW (c) 414 kW (d) 602 kW (e) 777 kW

Solution

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The final temperature for an isentropic process is:

T2s=T1(P2P1)R/cp=873(80800)0.2081/0.5203K=347.57K\begin{align*} T_{2s}&=T_{1}\Bigg(\dfrac{P_{2}}{P_{1}}\Bigg)^{R/c_{p}}\\ &=873\cdot\Bigg(\dfrac{80}{800}\Bigg)^{0.2081/0.5203}\:\text{K}\\ &=347.57\:\text{K} \end{align*}

The actual final temperature is obtained from the efficiency:

T2a=T1η(T1T2s)=873K0.88(873347.57)K=410.62K\begin{align*} T_{2a}&=T_{1}-\eta(T_{1}-T_{2s})\\ &=873\:\text{K}-0.88\cdot(873-347.57)\:\text{K}\\ &=410.62\:\text{K} \end{align*}

The power output is obtained from the energy balance:

W˙=m˙cp(T1T2a)=2.50.5203(873410.62)kW=601.44kW\begin{align*} \dot W&=\dot mc_{p}(T_{1}-T_{2a})\\ &=2.5\cdot0.5203\cdot(873-410.62)\:\text{kW}\\ &=\boxed{601.44\:\text{kW}} \end{align*}

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