A heat engine having the maximum possible efficiency has an efficiency of 25% when operating between two heat reservoirs.If the temperature of the cold reservoir is 300 K,what is the temperature of the hot reservoir?
A)350 K
B)375 K
C)400 K
D)450 K
E)500 K

Question

Quizplus · Accepted Answer

We know that the maximum efficiency of a heat engine operating between two heat reservoirs is given by:
η = 1 - Tc/Th     where η is efficiency, Tc is temperature of the cold reservoir and Th is the temperature of the hot reservoir.

Given η = 25% = 0.25 and Tc = 300 K.

Therefore, 0.25 = 1 - 300/Th

0.75Th = 300

Th = 400 K

Hence, the temperature of the hot reservoir is 400 K. Therefore, the best choice is C.

A Heat Engine Having the Maximum Possible Efficiency Has an Efficiency