# Is Carnot cycle a better one?

## What is meant by the Carnot cycle?

According to Carnot theorem, which is a corollary of the second law of thermodynamics, no cycle can be more efficient than a reversible cycle operating between the same temperature limits and the Carnot cycle is one such reversible cycle with two reversible isothermal and two reversible adiabatic processes.

Carnot theorem can be proved brilliantly by a logical analysis of the system which uses combined reversible and irreversible cycle for its operation! To know how it is proved then click/tap here

## How does a Carnot cycle Work?

We know that heat and work are mutually convertible. In the case of a heat engine heat is to be supplied to produce work as shown in the figure.

Since Carnot is a reversible cycle it can be used in the heat engine to produce work or in the refrigeration machine to produce a cooling effect.

whereas in the case of refrigeration machine, work is to be added to the machine to produce a cooling effect.

To know how the Carnot cycle in the refrigeration machine will work and does it makes an efficient refrigerating machine? then click/tap here

## Various Processes of the Carnot cycle

To produce a work or cooling effect or heating effect using the Carnot cycle, the working substance in the engine or machine must undergo various processes of the Carnot cycle.

Let us consider a heat engine which uses a piston cylinder arrangement with a working substance inside the cylinder to produce work using the Carnot cycle as shown in the figure.

### T-S diagram of Carnot cycle

• Heat is transferred isothermally to the working substance from a high temperature reservoir.
• The high temperature reservoir is called the source, and its temperature T1 is infinitesimally higher than the working substance.
• Work is done by the system during this process, and the amount of work done is equal to the area underneath path a-b of the pressure-volume (p-V) diagram.

• The working substance undergoes a reversible adiabatic (or isentropic) expansion.
• The system is thermally insulated during this process.
• The temperature of the working substance decreases from the high temperature T1 to the low temperature T2.
• Work is done by the system during this process, and the amount of work done is represented by the area underneath path b-c of the p-V diagram.

isothermal heat rejection process (c-d)

• Heat is transferred isothermally from the working substance to a low-temperature reservoir.
• Work is done on the system during this process.
• The amount of work done on the system is equal to the area underneath the path of c-d on the p-V diagram.

• The working substance is returned to its initial state at point a.
• The temperature of the working substance is raised from T2 to the initial high temperature T1.
• Work is done on the system and is equal to the area underneath path d-a of the p-V diagram.

## Formula for Carnot efficiency

To achieve maximum efficiency in a Carnot engine, the temperature at which heat is supplied should be made as high as possible, while the temperature at which heat is rejected remains fixed. Since low temperature reservoir or sink is generally fixed by atmospheric or cooling water temperature.

## Limitations

Even though Carnot cycle has high efficiency it can not be used in practice due to its low net work output for a given stroke volume. Even if you overcome the problem in reversible isothermal process using vapour as a working substance still this Carnot cycle is not practical to use.To know why then click/tap here

## Application

After knowing the limitation of the Carnot cycle we can conclude that it is useless to use in actual practice.

Since the Carnot cycle has high efficiency, It is useful Just to compare the efficiency of any cycle under consideration with it even though this cycle is impracticable to use.

For this purpose, any reversible cycle could be considered but for historic reasons, the Carnot cycle is generally used. The Carnot cycle, incidentally, is the most convenient to use because of two isothermal and two adiabatic processes.

## References

Refrigeration and Air Conditioning by C P Arora

Internal combustion engines by M.L. Mathur and R.P. Sharma

https://en.wikipedia.org/wiki/Heat_engine

Carnot’s theorem (thermodynamics) – Wikipedia