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A heat engine extracts heat (Q_H) from a thermal reservoir at a temperature of 1000 K and rejects heat (Q_L) to a thermal reservoir at a temperature of 100 K, while producing work (W). Which one of the combinations of (Q_H, Q_L and W) given is allowed?

1. Q_H = 2000 J, Q_L = 500 J, W = 1000 J
2. Q_H = 2000 J, Q_L = 750 J, W = 1250 J
3. Q_H = 6000 J, Q_L = 500 J, W = 5500 J
4. Q_H = 6000 J, Q_L = 600 J, W = 5500 J

Correct answer: Q_H = 2000 J, Q_L = 750 J, W = 1250 J

Solution

This combination satisfies the first law of thermodynamics, where the work done by the engine (W) is equal to the heat extracted from the hot reservoir (Q_H) minus the heat rejected to the cold reservoir (Q_L), confirming that W = Q_H - Q_L.

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