Carnot Idealized Reversible Thermodynamic Cycle

An idealized reversible thermodynamic cycle.

In 1824 Carnot showed that the amount of heat which could be converted into mechanical work by an ideal perfect heat engine using a perfect gas as the working fluid, depended solely upon the working range of temperature.

As no gas is perfect, and in practice a perfect engine cannot be constructed, the Carnot cycle gives a ready means of comparing the actual performance of any engine, with the best theoretical performance possible under the same working range of temperature.

This shows the pressure-volume or indicator diagram of an engine working on this cycle.

Starting at point a the gas expands isothermally at constant temperature T1, heat being supplied to keep the temperature constant, from volume va to volume vb. The supply of heat is then shut off and the gas expands adiabatically to volume vc the temperature falling to T2. On the return stroke of the piston the gas is compressed isothermally from volume vc to volume vd at constant temperature T2, heat being taken from it to keep the temperature constant, the cycle being completed by compressing adiabatically from volume vd and temperature T2 to volume va and temperature T1.

A closed cycle is thus obtained, the pressure, volume and temperatures of the gas being the same at the end as at the beginning of the cycle.

To find the proper place to stop the isothermal compression, the point d must be chosen so that an adiabatic drawn through it will pass through the starting point a.

The efficiency of the cycle is given as:

The efficiency of the cycle is given as:

This is then simply expressed given the two working temperatures as:

The area of the temperature-entropy diagram represents the work done.

The work done by the gas during the stage ab is represented by area fabe = φT1

The work done on the gas during the stage cd is represented by area fdce = φT2

Therefore, net work done = fabe – fdce = area dabc

A simple overview of the idealized reversible thermodynamic cycle.

steam indicator diagram

Steam Indicator Diagram – the pressure in the cylinder is plotted versus the cylinder volume. This was developed by James Watt and John Southern to improve the efficiency of the steam engine. The work done is the area within the red curve.

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