Project ForgeA heat engine extracts heat (QH) from a thermal reservoir at a temperature of 1000 K and rejects heat (QL) to a thermal reservoir at a temperature of 100 K, while producing work (W). Which one of the combinations of [QH, QL and W] given is allowed?
- AQH = 2000 J, QL = 500 J, W = 1000 J
- QH = 2000 J, QL = 750 J, W = 1250 J
- CQH = 6000 J, QL = 500 J, W = 5500 J
- DQH = 6000 J, QL = 600 J, W = 5500 J
Explanation
The Carnot (maximum possible) efficiency for reservoirs at 1000K/100K is 1−100/1000=0.9. Option (A) violates energy balance (QL+W=1500≠QH=2000). Option (C) satisfies energy balance (500+5500=6000) but has efficiency 5500/6000=0.917>0.9, exceeding the Carnot limit — impossible. Option (D) violates energy balance (600+5500=6100≠6000). Only (B) satisfies energy balance (750+1250=2000) with efficiency 1250/2000=0.625<0.9 — feasible.
Source: GATE ME 2023 Official Paper (2023)
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