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If the initial intake temperature (T₁) is 500 K and the new efficiency (η₂) is 50%, calculate the new sink temperature (T₂).

1. 300 K
2. 400 K
3. 500 K
4. 600 K

Correct answer: 300 K

Solution

The efficiency of a heat engine is given by η = 1 - (T₂/T₁). Rearranging for T₂, we get T₂ = T₁(1 - η). Substituting T₁ = 500 K and η₂ = 0.5, T₂ = 500(1 - 0.5) = 500 × 0.5 = 300 K.

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