A steam engine is operating at its theoretical maximum efficiency of 60%. If the waste heat has a temperature of 100°F (38°C), what is the temperature of the boiler?
A) 350°C
B) 94°C
C) 225°C
D) 504°C
E) 775°C

Question

Quizplus · Accepted Answer

The efficiency of a heat engine is given by the Carnot efficiency:```η = 1 - T_c / T_h```where:* η is the efficiency* T_c is the temperature of the cold reservoir* T_h is the temperature of the hot reservoirIn this case, the efficiency is 60% and the temperature of the cold reservoir is 100°F (38°C). Solving for the temperature of the hot reservoir, we get:```T_h = T_c / (1 - η) = 38°C / (1 - 0.6) = 95°C```Converting to Celsius, we get:```T_h = 95°C + 273.15 = 368.15 K```Therefore, the temperature of the boiler is 368.15 K, which is closest to choice D) 504°C.

A Steam Engine Is Operating at Its Theoretical Maximum Efficiency