First slide

Heat engine

Question

Efficiency of an engine working on Carnot cycle is 60%. If the temperature of sink is decreased by 25% and that of the source in increased by 25%, then new efficiency of the engine will be

Moderate

A

56%
B

82%
C

76%
D

65%

Solution

$n = 1 - \frac{T_{2}}{T_{1}} \Rightarrow 0.6 = 1 - \frac{T_{2}}{T_{1}} \Rightarrow \frac{T_{2}}{T_{1}} = 0.4$
$n^{1} = 1 - \frac{T_{2}^{1}}{T_{1}^{1}} = 1 - \frac{\frac{3}{4} T_{2}}{\frac{5}{4} T_{1}} = 1 - \frac{3}{5} . \frac{T_{2}}{T_{1}} = (1 - \frac{3}{5} \times 0.4) = 76 %$

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