Chapter 24, Problem 54A

To increase the efficiency of a heat engine, would it be better to increase the temperature of the reservoir while holding the temperature of the sink constant, or to decrease the temperature of the sink while holding the temperature of the reservoir constant? Show your work.

To determine

To identify: Whether it is better to increase the temperature of reservoir or to decrease the temperature of sink in order to increase the efficiency of heat engine.

Answer to Problem 54A

A heat engine with a decreasing sink temperature has greater efficiency.

Explanation of Solution

Introduction:

The efficiency of a heat engine is calculated as the ratio of the temperature difference between source and sink, and the source temperature i.e.

  $\eta =\frac{{\text{T}}_{\text{source}}{\text{-T}}_{\text{sink}}}{{\text{T}}_{\text{source}}}$

If source temperature is increased and sink temperature is kept constant then after evaluating the efficiency of the heat engine will give no doubt will give greater efficiency. But, if source temperature is kept constant and sink temperature is decreasing then after checking and comparing with the previous heat engine, results of the efficiency of the heat engines will be way more surprising.

It is assumed that if one temperature is kept constant and the other varies with the proportionate values then results must be the same. But, here results are much more contrasting. The heat engine with the decreasing sink temperature when source temperature is kept constant will have greater efficiency as compared with the former one. Because with the decreasing sink temperature, the amount of useful work done by the system is increasing. Since less amount of heat is wasting now.

Conclusion:

Thus, with the decreasing sink temperature when keeping source temperature constant, greater efficiency and more useful work will be obtained as compared with the former one.