An ideal heat engine exhausting heat at 77∘ C is to have a 30% efficiency. It must take heat at ____ ∘ C.

η=1−T2T1 ⇒30100=1−77+273T1 ⇒310=1−350T1 ⇒350T1=1−310=710 ⇒T1=350×107=500KT1=500−273=227∘C

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An ideal heat engine exhausting heat at $77^{\circ} C$ is to have a 30% efficiency. It must take heat at ____ $^{\circ} C$ .

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answer is 227.

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Detailed Solution

$η = 1 - \frac{T_{2}}{T_{1}} \Rightarrow \frac{30}{100} = 1 - \frac{77 + 273}{T_{1}} \Rightarrow \frac{3}{10} = 1 - \frac{350}{T_{1}} \Rightarrow \frac{350}{T_{1}} = 1 - \frac{3}{10} = \frac{7}{10}$

$\Rightarrow T_{1} = \frac{350 \times 10}{7} = 500 K$

$T_{1} = 500 - 273 = 227^{\circ} C$

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