# Heat Engine Efficiency

## 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:

## Heat Engine Efficiency

Let us derive an expression for the efficiency of a heat engine. We can define heat engine efficiency as:

$η$ =${W}{Q_1}$

Where,

$W$= Work done by the engine

$Q_1$ = Heat taken from the source

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

$∆U$ =$0$.

So from the figure, it is clear that,

$W$ = $Q_1- Q_2$

Hence the heat engine efficiency is:

$η$ =$\frac{Q_1- Q_2}{Q_1}$

$η$ = $1- \frac{Q_2}{Q_1}$

So for $Q_2$ = $0$, efficiency will be 100% but, in actual, this is not possible because there will be some loss of energy in the system. Hence for every engine, there is a limit for its efficiency. The efficiency is maximum for a reversible engine such as Carnot heat engine.

## Types of Heat Engine

Following are the two types of heat engine:

• Internal combustion engine
• External combustion engine

### External combustion engine

In these heat engines, the fuel burns outside and away from the main engine where force and motion are produced. A steam engine is an example of external combustion engine.

### Internal combustion engine

In these heat engines, the fuel burns inside the cylinder. A car engine is an example of internal combustion engine.

Internal combustion engine is more efficient than external combustion engine as there is no energy wasted during heat transfer between boiler and the cylinder.

Following is the table explaining related concepts of heat engine:

## What is 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 $T_2$ and releases it to a higher temperature $T_1$. For this process to take place, work has to be done on the system. Below is the schematic representation of the process:

In this case, we define the coefficient of performance as:

$α$ = $\frac{Q_2}{W}$

Where,

• Q2 is the heat taken from the system
• W is the 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,

$W$ = $Q_1 – Q_2$

Therefore,

$α$=$\frac{Q_2}{Q_1 – Q_2}$

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.

Going further, we will see what second law of thermodynamics is and how Carnot heat engine is the most efficient engine.

## Frequently Asked Questions on Heat Engine

### What is a heat engine?

A heat engine is a device that converts heat to work.

### What is a heat pump?

A heat pump is a device that transfers heat from colder region to hotter region using mechanical energy.