GATE 2019 ME (ME1) – Question 60
An air turbine has isentropic efficiency 0.70 at pressure ratio 3. The ratio increases to 5 with inlet conditions and actual specific work unchanged. Treat air as perfect with γ = 1.4. Find new isentropic efficiency, to two decimal places.
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Correct answer: .50 to .52
Explanation
Isentropic work is $c_pT_1(1-r^{-2/7})$. Equal actual work requires $\eta_5(1-5^{-2/7})=0.70(1-3^{-2/7})$. Thus $\eta_5=0.5108$, or **0.51**.