# What is a carnot engine?

Jan 10, 2017

A Carnot's engine is an idealised engine whose working is perfectly reversible. This engine uses an ideal gas as the working substance and performs a 4-stroke process to complete one cycle.

It draws heat (say ${Q}_{1}$) from source and rejects heat (say ${Q}_{2}$) to sink thereby performing an amount of work $W = {Q}_{1} - {Q}_{2}$

#### Explanation:

The Carnot's engine is a reversible engine working between two temperature limits.

The complete cycle incorporates -

1) Isothermal expansion of ideal gas at the temperature of the source ${T}_{1}$ drawing an amount of heat ${Q}_{1}$

2) Adiabatic expansion of ideal gas. In this process, the temperature of the ideal gas falls from source temperature ${T}_{1}$ to sink temperature ${T}_{2}$.

3) Isothermal compression of ideal gas at sink temperature ${T}_{2}$. In doing so, it rejects heat ${Q}_{2}$ to the sink.

4) Adiabatic compression of ideal gas where the temperature naturally raises from ${T}_{2}$ to ${T}_{1}$ and thus the working substance returns to its original state completing the cycle.

The efficiency is given as

$\eta =$ Work done $/$ Heat input

Thus, $W = {Q}_{1} - {Q}_{2}$ and heat input is obviously ${Q}_{1}$

This gives, $\eta = \frac{W}{Q} _ 1 = 1 - \frac{{Q}_{2}}{{Q}_{1}}$

It may be shown thermodynamically that $\frac{{Q}_{2}}{{Q}_{1}} = \frac{{T}_{2}}{{T}_{1}}$