# Heat Engine and Refrigerator

Heat engine is a devive in which a working substance undergoes a cyclic process to convert heat to work. In one leg of the cyclic process, the working substance absorbs heat Q1 from source at high temperature T1. In another leg, it releases heat Q2 to a sink at lower temperature T2. The engine do work W in a complete cycle. The efficiency of heat engine is defined as the ratio of work done to the heat taken from the source \begin{align} \eta=\frac{W}{Q_1}=1-\frac{Q_2}{Q_1}. \end{align} A refrigerator (or heat pump) is reverse of heat engine. The working substance in a refrigerator extract heat Q2 from a cold reservoir at temperature T2, an external work W is done on it, and heat Q1 is released to the reservoir at high temperature T1. The coefficient of performance of a refrigerator is the ratio of heat extracted to the work done i.e., \begin{align} \alpha=\frac{Q_2}{W}=\frac{Q_2}{Q_1-Q_2}. \end{align}

The coefficient of performance is greater than 1 but it cannot be infinite. ## Second Law of Thermodynamics

The second law of thermodynamics is usually stated as Kelvin-Plank or Clausius statements:

Kelvin Plank Statement: No process is possible whose sole result is the absorption of heat from a reservoir and the complete conversion of the heat into work.

Clausius Statement: No process is possible whose sole result is the transfer of heat from a colder object to a hotter object.

## Questions on Heat Engine

Question 1: Which of the following statement is not true for a heat engine operating between temperature T1 and T2?

A. Its maximum efficiency is 1.
B. The first law of thermodynamics put a maximum limit of the efficiency.
C. The second law of thermodynamics put a maximum limit of efficiency.
D. Its maximum efficiency is less than the efficiency of the Carnot engine operating between the same temperatures.