What is a carnot engine?

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 ##W = Q_1 - Q_2##

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 = W/Q_1 = 1 - (Q_2)/(Q_1)##

It may be shown thermodynamically that ##(Q_2)/(Q_1) = (T_2)/(T_1)##