Discussion
If an ideal heat engine with an efficiency of 40 % rejects heat at 27°C , then it should have absorbed heat at
Answer: C
The engine should absorb heat at 227°C.
The efficiency of an ideal (Carnot) engine is \(\eta = 1 - \frac{T_{2}}{T_{1}}\), with temperatures in kelvin. The sink is at 27 °C = 300 K.
\[ \begin{aligned} 0.4 &= 1 - \frac{300}{T_{1}} \\ T_{1} &= \frac{300}{0.6} = 500 \text{ K} = 227\,^\circ\text{C} \end{aligned} \]
500°C is the kelvin value written as Celsius, and 427°C comes from \(T_{1} = 700\) K, which would give an efficiency of about 57 %.
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