Discussion
A carnot engine works between the temperatures 327oC and 227oC. If the work output of the engine is 1 kJ, then the amount of heat absorbed by the engine is
Answer: B
The heat absorbed is 6 kJ.
Convert to kelvin: \(T_{1} = 600\) K and \(T_{2} = 500\) K.
\[ \begin{aligned} \eta &= 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{500}{600} = \frac{1}{6} \\ Q_{1} &= \frac{W}{\eta} = 1 \times 6 = 6\ \text{kJ} \end{aligned} \]
Using Celsius temperatures by mistake gives \(\eta = 1 - \frac{227}{327} \approx 0.31\) and about 3.3 kJ, close to the 3 kJ distractor. Carnot efficiency always needs absolute temperatures.
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