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

Question

Quizplus · Accepted Answer

The maximum theoretical efficiency of a steam engine is given by Carnot's theorem as:

efficiency = (Th - Tw) / Th

where Th is the absolute temperature of the hot reservoir (boiler) and Tw is the absolute temperature of the cold reservoir (waste heat).

Rearranging the equation, we get:

Th = Tw / (1 - efficiency)

Substituting the given values, we get:

Th = (38 + 273) / (1 - 0.6) = 682.5 K

Converting back to Celsius scale, we get:

Th = 409.5°C

Therefore, the temperature of the boiler is approximately 504°F (D).

A Steam Engine Is Operating at Its Theoretical Maximum Efficiency °\degree°

A Steam Engine Is Operating at Its Theoretical Maximum Efficiency $\degree$