A Carnot engine with a hot-reservoir temperature of 380 degree C has the same th

Question

A Carnot engine with a hot-reservoir temperature of 380 degree C has the same thermal efficiency. What is the cold-reservoir temperature in degree C. The heat engine does 200{ m J} of work per cycle while exhausting 700{ m J} of heat to the cold reservoir. The engine's thermal efficiency is 22.2%.

Explanation / Answer

(i) Part A Conservation of energy requires, that heat added to the engine equals work done plus heat exhausted by the engine. Qh = W + Qc => W = Qh - Qc = 51kJ - 36kJ = 15kJ Part B Efficiency is the ratio of (useful) work done divided by heat spend from hot reservoir ? = W/Qh = 15kJ/51kJ = 0.294 = 29.4% (ii) Part A ? = W/Qh = (Qh - Qc)/Qh = 1 - Qc/Qh = 1 - 300/500J = 0.4 = 40% Part B For ideal heat engine no entropy is produced. Hence entropy transferred to engine by Qh and entropy rejected by Qc are equal. Qh/Th = Qc/Tc => ? = 1 - Qc/Qh = 1 - Tc/Th => Tc = (1 - ?)·Th = (1 - 0.4)·683K = 410K = 137°C

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