GATE 2020 ME (ME2) – Question 64

Thermal Engineering Applications · Power Engineering: vapour and gas power cycles, regeneration and reheat · 2 marks · Numerical answer

Steam at 10 MPa, 500°C expands isentropically until saturated vapour, reheats at constant pressure to 500°C, then expands isentropically to 20 kPa. Find total work of both turbines (kJ/kg), nearest integer. Superheated data (p MPa, T °C, h kJ/kg, s kJ/(kg·K)): (10,500,3373.6,6.5965), (1,500,3478.4,7.7621). Saturated data (p, T °C, h_f, h_g kJ/kg, s_f, s_g kJ/(kg·K)): (1 MPa,179.91,762.9,2778.1,2.1386,6.5965), (20 kPa,60.06,251.38,2609.7,0.8319,7.9085).

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Correct answer: 1500 to 1525

Explanation

Initial entropy6.5965 equals saturated-vapour entropy at1 MPa, so first outlet h2=2778.1. First-stage work=3373.6−2778.1=595.5. Reheat givesh3=3478.4,s3=7.7621. At20 kPa,$x=(7.7621-0.8319)/(7.9085-0.8319)$ andh4=251.38+x(2609.7−251.38). Total work is(3373.6−2778.1)+(3478.4−h4)≈**1513 kJ/kg**.