Chemegate

GATE 2024 Chemical Engineering, Q61 · Thermodynamics

The correct answer is 0.24 to 0.26.

Question

Heat is available at a rate of 2 kW from a thermal reservoir at 400 K. A two-stage process harnesses this heat to produce power. Stages 1 and 2 reject heat at 360 K and 300 K, respectively. Stage 2 is driven by the heat rejected by Stage 1. If the overall process efficiency is 50% of the corresponding Carnot efficiency, the power delivered by the process, in kW, rounded off to 2 decimal places, is ______

Official answer: 0.24 to 0.26

Why

GATE 2024 official key: 0.24 to 0.26. Overall Carnot efficiency (400 K to 300 K) = 1−300/400 = 0.25. Actual efficiency =0.5×0.25=0.125.= 0.5 \times 0.25 = 0.125. Power =0.125×2=0.25= 0.125 \times 2 = 0.25 kW.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.