The "hot shot" heat engine operating between 40°C and 380°C has an efficiency that is 60% of that of an ideal Carnot engine operating between the same temperatures. If the "hot shot" engine
Absorbs heat at a rate of 60 kW, at what rate does it exhaust heat?
A) 41 kW
B) 36 kW
C) 60 kW
D) 57 kW

Question

Quizplus · Accepted Answer

The efficiency of an ideal Carnot engine is given by $ \eta = 1 - \frac{T_c}{T_h} $, where $ T_c $ and $ T_h $ are the cold and hot reservoir temperatures in Kelvin, respectively. Converting the given temperatures to Kelvin gives $ T_c = 40 + 273 = 313 $ K and $ T_h = 380 + 273 = 653 $ K. Thus, the efficiency of the ideal Carnot engine is $ \eta = 1 - \frac{313}{653} $.The "hot shot" engine's efficiency is 60% of this, so its efficiency is $ 0.6 \times \left(1 - \frac{313}{653}\right) $.The rate at which work is done (or power output) by the engine is the product of its efficiency and the rate at which it absorbs heat, which is $ 0.6 \times \left(1 - \frac{313}{653}\right) \times 60 $ kW.The rate at which it exhausts heat is the difference between the rate at which it absorbs heat and the rate at which it does work. Thus, the rate at which it exhausts heat is $ 60 $ kW - $ 0.6 \times \left(1 - \frac{313}{653}\right) \times 60 $ kW. Calculating this gives approximately 41 kW.

The "Hot Shot" Heat Engine Operating Between 40°C and 380°C