Hello guy's welcome to new post. In this post we are discuss Carnot engine that what is Carnot engine? How to work Carnot engine and its principle? 

And we will discuss some parts of Carnot engine. So lets start and discuss Carnot engine.

Carnot's Engine

A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. Sadi Carnot in 1824 proposed this ideal engine using only isothermal and adiabatic process. 

He showed that a heat engine operating in an ideal reversible cycle between two heat reservoirs at different temperatures would be the most efficient engine. In most practical cases, the cold reservoir is nearly at room temperature. 

So the efficiency can only be increased by increased by raising the temperature of hot reservoir. All real heat engines are less efficient than Carnot engine due to friction and other heat losses.

Principle

Carnot's engine works on the same principle as that of cyclic heat engine. It takes heat from hot body, concert a part of it into work and reject the remaining part to cold body.

Working

A Carnot cycle using an ideal gas as a working substance is shown in PV-diagram. It consists of following four steps.

1. Isothermal expansion 

2. Adiabatic Expansion 

3. Isothermal compression 

4. Adiabatic compression

 

1. Isothermal expansion

The gas is allowed to expand isothermally at temperature T, absorbing heat Q, from the hot reservoir. The process is represented by curve AB.

2. Adiabatic Expansion

The gas is then allowed to expand adiabatically until its temperature drop to T2. The process is represented by BC curve.

3. Isothermal compression

The gas at this stage is compressed isothermally at temperature T2 rejecting heat Qz to the cold reservoir. The process is represented by curve CD.

 

4. Adiabatic compression

Finally the gas is compressed adiabatically to restore its initial state at temperature T. The process is represented by curve DA. Thermal and mechanical equilibrium is maintained all the time so that each process is perfectly reversible.

Thermal and mechanical equilibrium

Thermal and mechanical equilibrium is maintained all the time so that each process is perfectly reversible. As the working substance returns to the initial state, there is no change in its internal energy i.e. AU = 0. 

The net work done. during one cycle equals to the area enclosed by the path ABCDA of the PV diagram. It can also be estimated from net heat Q absorbed in one cycle.

The energy transfer in an isothermal expansion or compression turns out to be proportional to Kelvin temperature. So Q and Q are proportional to Kelvin temperatures T and T2 respectively and hence,

 

Expression for Efficiency

As the working substance returns to the initial state, there is no change in its internal energy i.e., AU = 0. 

The net work done during one cycle equals to the area enclosed by the path ABCDA of the PV diagram. It can also be estimated from net heat AQ absorbed in one cycle.

Dependence of Efficiency

Efficiency of a Carnot Engine depends on the temperature of hot & cold reservoir. It is independent of the nature of the working substance. The larger the temperature difference of the two reservoirs, the greater is the efficiency. In most practical cases the cold reservoir is near room temperature. So the efficiency can be increased by raising the temperature of hot reservoir

Can efficiency of heat engine be 100%?

It can never be one or 100% unless cold reservoir is at absolute temperature zero. Such reservoirs are not available & hence maximum efficiency is always less than one.

Carnot's Theorem

No heat engine can be more efficient than a Carnot engine operating between the same two temperatures.

Extended statement

All Carnot's engines operating between the same two temperatures have the same efficiency, irrespective of the nature of working substance.

Note

All real heat engines are less efficient than Carnot engine due to friction & heat losses.