Question

What is a carnot engine?

Answer 1

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

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