## What is Heat Engine?

A heat engine is a device that converts heat to work. It takes heat from a reservoir then does some work like moving a piston, lifting weight etc, and finally discharging some of the heat energy into the sink. Schematically it can be represented as:

## The efficiency of heat engine:

Let us derive an expression for the efficiency of a heat engine. The engine efficiency is defined as:

\(η\)

Where,

\(W \)

\(Q_1\)

After each cycle, the engine returns to its initial state so,

\(∆U\)

So from the figure it is clear that,

\(W\)

Hence the engine efficiency is:

\(η\)

\(η \)

So for \(Q_2\)

## Heat pump:

So now that we have seen the above system we will now see what a refrigerator is. Before getting into the working of refrigerator we will define Heat pump. It is a device used to pump heat into the system. So it is similar to a refrigerator but works exactly opposite to it. A refrigerator takes out heat from a lower temperature \(T_2\)

In this case we define coefficient of performance. It is defined as:

\(α\)

Where, \(Q_2 \)

W = Work done on the refrigerator

Similar to heat engine after a cycle the refrigerator returns to its original state hence ∆U = 0. So from the figure,

\(W\)

Therefore,

\(α \)

A refrigerator will not be able to function without external work so its coefficient of performance can never be infinite.

Below video will help you visualize and understand the concept of transition of heat.

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