Chapter 4, Problem 4.1CYU

Check Your Understanding What is the efficiency of a perfect heat engine? What is the coefficient of performance of a perfect refrigerator?

To determine

The efficiency of a perfect heat engine and the coefficient of performance of a perfect refrigerator.

Explanation of Solution

Introduction:

A device which is used to extract heat from the source and convert it into mechanical work is known as a heat engine. A perfect heat engine is the one that converts all its heat input into the work. A perfect refrigerator transports heat from a cold reservoir to a hot reservoir without work input.

The efficiency of the heat engine is the ratio of the work done and the heat input. Since a perfect heat engine converts all the input heat into mechanical work, then the efficiency of the perfect heat engine is $100\%$ and its coefficient is $1$. The work input required in a perfect refrigerator is zero; that means the coefficient of performance, which is the ratio of the heat removed by the cold reservoir to the work done, will be infinite.

Conclusion:

Therefore, the efficiency of a perfect heat engine is $100\%$ and the coefficient of performance of a perfect refrigerator is infinite.