An engineer uses a river (minimum temperature of 4°C) to cool his electrical plant, which heats water with a boiler operating at 220°C. His boiler uses 420 kW of energy to heat water to steam. What is the maximum power output under ideal circumstances?
A) 230 kW
B) 184 kW
C) 330 kW
D) 416 kW

Question

Quizplus · Accepted Answer

The maximum power output under ideal circumstances can be calculated using the Carnot efficiency formula, which is $ \eta = 1 - \frac{T_c}{T_h} $, where $ \eta $ is the efficiency, $ T_c $ is the cold reservoir temperature in Kelvin, and $ T_h $ is the hot reservoir temperature in Kelvin. Converting the given temperatures to Kelvin, we have $ T_c = 4°C + 273.15 = 277.15K $ and $ T_h = 220°C + 273.15 = 493.15K $. Thus, the efficiency is $ \eta = 1 - \frac{277.15}{493.15} \approx 0.438 $ or 43.8%. The maximum power output is then $ 0.438 \times 420 kW = 184 kW $.

An Engineer Uses a River (Minimum Temperature of 4°C) to Cool