GATE 2024 CH – Question 61
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 ______
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Correct answer: 0.24 to 0.26
Explanation
The corresponding Carnot efficiency of the whole process is set by the hottest and the coldest temperatures: $1 - \frac{300}{400} = 0.25$. (The two Carnot stages in series, $1 - 0.9 \times 0.8333$, give the same 0.25.) The actual efficiency is 50% of this, 0.125, so the power is $2 \times 0.125 = 0.25$ kW.