A Carnot engine take 5000 kcal of heat from a reservoir at 727°C and gives heat to a sink at 127°C. The work done by the engine is:
Text Solution
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Temperature Conversion to Kelvin
Source Temperature:
T₁ = 727°C + 273 = 1000 K
Sink Temperature:
T₂ = 127°C + 273 = 400 K
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Carnot Efficiency (η)
η = 1 - (T₂ / T₁) = 1 - (400 / 1000) = 1 - 0.4 = 0.6 (60%)
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Heat Input Conversion (Q₁)
Given: Q₁ = 5000 kcal
Conversion factor: 1 kcal = 4184 J (or 4.184 × 10³ J)
Q₁ = 5000 × 4184 = 20,920,000 J = 20.92 × 10⁶ J
(Note: If using the approximation 1 cal ≈ 4.2 J, Q₁ = 5000 × 4200 = 21 × 10⁶ J)
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Work Done (W)
W = η × Q₁
Using 4184 J/kcal:
W = 0.6 × (20.92 × 10⁶ J) = 12.552 × 10⁶ J ≈ 12.6 × 10⁶ J
Using 4.2 J/cal (4200 J/kcal):
W = 0.6 × (21 × 10⁶ J) = 12.6 × 10⁶ J
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