Chapter 24, Problem 46A

What happens to the efficiency of a heat engine when the temperature of the reservoir into which heat energy is ejected is lowered?

To determine

To explain: The effect on the efficiency of a heat engine when the temperature is lowered.

Explanation of Solution

Introduction:

A Carnot engine that operates between two given temperatures will have the greatest possible efficiency. Also, all engines that employ only reversible processes will have this much same maximum efficiency when they are operating between the same given temperatures.

Heat engines absorb heat from a hot reservoir with dumping of excess heat that is not converted to useful work in a cold reservoir. In terms of reservoir temperatures, the efficiency of heat engine is

  $\eta =\frac{T_w-T_c}{T_c}$

Where,

  $T_w$  is the hot reservoir temperature

  $T_c$  is the cold reservoir temperature

So, when the temperature of reservoir into which heat energy is lowered that is $T_c$ is lower, it will give a higher efficiency.

Conclusion:

Hence, the efficiency of the heat engine increases.