Discussion
A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an environment at 300 K is
Answer: A
The maximum power is 300 kW.
The most work any engine can extract from heat at 1200 K, rejecting to surroundings at 300 K, is that of a reversible (Carnot) engine:
\[ \begin{aligned} \eta_{max} &= 1 - \frac{T_{L}}{T_{H}} = 1 - \frac{300}{1200} = 0.75 \\ \dot{Q} &= \frac{24000}{60} = 400\ \text{kW} \\ \dot{W}_{max} &= 0.75 \times 400 = 300\ \text{kW} \end{aligned} \]
18000 is 0.75 times the heat rate left in kJ/min, without converting to kilowatts. Zero would apply only if the furnace and the environment were at the same temperature, and 150 kW is half the Carnot limit with no basis in the data.
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