Answer to Question #270152 in Physics for Jude

Question

Dissatisfied with the performance of his heat engine in the previous example, the engineer

wishes to increase its efficiency to 25%. To accomplish this, he decided to change the

temperature of the hot reservoir while keeping the temperature of the cold reservoir constant.

What must be the temperature of the hot reservoir of the engine?

Answer 1

The efficiency is

$$\eta=1-\frac{T_c}{T_h},\\\space\\ T_h=\frac{T_c}{1-\eta}.$$