A turbine has stagnation inlet temperature 1200 K and outlet temperature 900 K. The outlet-to-inlet stagnation pressure ratio is 0.14 and γ=1.2. Find turbine isentropic efficiency in percent (nearest integer).
The isentropic exit temperature is $T_{02s}=1200(0.14)^{(1.2-1)/1.2}$. Turbine efficiency is actual temperature drop divided by isentropic drop: $\eta_t=(1200-900)/(1200-T_{02s})\simeq0.895$. Therefore approximately 89%.
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