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An ideal gas heat engine operates in a Carnot cycle between 227°C and 127°C. It absorbs 6 × 10⁴ cals of heat at higher temperature. Amount of heat converted to work is

1. 4.8 × 10⁴ cals
2. 6 × 10⁴ cals
3. 2.4 × 10⁴ cals
4. 1.2 × 10⁴ cals

Correct answer: 4.8 × 10⁴ cals

Solution

The efficiency of a Carnot engine is given by η = 1 - (T₂/T₁), where T₁ and T₂ are the absolute temperatures of the hot and cold reservoirs, respectively. Converting to Kelvin, T₁ = 227 + 273 = 500 K and T₂ = 127 + 273 = 400 K. Thus, η = 1 - (400/500) = 0.2. The work done is η × Q₁ = 0.2 × 6 × 10⁴ = 1.2 × 10⁴ cals.

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