A Carnot engine has an efficiency of 50% when its source is at a temperature 327°C. The temperature

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Question

A Carnot engine has an efficiency of 50% when its source is at a temperature 327°C. The temperature of the sink is

Accepted Answer

Correct Answer: A — 27°CStep-by-step Solution:Carnot efficiency: η = 1 − T₂/T₁T₁ = 327°C = 327 + 273 = 600 K, η = 50% = 0.50.5 = 1 − T₂/600T₂/600 = 0.5 → T₂ = 300 K = 300 − 273 = 27°CWhy other options are wrong:B (15°C = 288 K): η = 1 − 288/600 = 0.52, not 0.5.C (100°C = 373 K): η = 1 − 373/600 = 0.378, not 0.5.D (200°C = 473 K): η = 1 − 473/600 = 0.212, not 0.5.Key Concepts:Carnot efficiency: η = 1 − T₂/T₁ = (T₁ − T₂)/T₁, where T₁ = source temperature, T₂ = sink temperature (both in Kelvin).Carnot engine is the most efficient heat engine operating between two temperatures.Always convert Celsius to Kelvin (K = °C + 273) before substituting.

A Carnot engine has an efficiency of 50% when its source is at a temperature 327°C. The temperature of the sink is

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A Carnot engine has an efficiency of 50% when its source is at a temperature 327°C. The temperature of the sink is

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