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CARNOT CYCLE

DOI: 10.1615/AtoZ.c.carnot_cycle

The aim of all clockwise operating cycle processes is to produce work by transferring heat from a high-temperature energy reservoir to a low-temperature energy reservoir.

According to the First Law of Thermodynamics:

(1)

The maximum amount of heat converted into work is determined by the Second Law of Thermodynamics. For a reversible process,

(2)

For a system operating in a cyclic process,

(3)

and hence:

(4)

Combining Eqs. (1) and (4) provides the maximum amount of work obtainable for any quantity of heat supplied QH.

(5)

A cycle process to fulfil the above criteria was suggested by the French military engineer Sadi Carnot. It is depicted in Figure 2.

Power cycle.

Figure 1. Power cycle.

p-V and T-S diagrams of Carnot cycle.

Figure 2. p-V and T-S diagrams of Carnot cycle.

1-2. Gas is compressed reversibly and adiabatically from the initial state. Work is done on the system and the temperature increases from TL to TH.
2-3. The gas at temperature TH expands reversiblyand isothermally from state 2 to state 3. Work is done by the gas and heat is transferred from a high temperature energy reservoir to the system. Since the process is reversible, the temperature of the energy reservoir can only be infinitesimally higher than TH.
3-4. The gas expands reversibly and adiabatically from state 3 to state 4, doing work. During this process the temperature drops from TH to TL.
4-1. The gas is compressed isothermally, rejecting heat at TL to the low temperature energy reservoir. The temperature TL is only infinitesimally higher than the temperature of the reservoir, because the process is reversible.

The Carnot cycle is not limited to gas cycles; it can be executed in many different types of systems, such as gas, liquid, electric cell, soap film, steel wire and rubber band, as long as there are two energy reservoirs, a part of the surrounding that can do and absorb work and some means to periodically insulate the system. While the Carnot cycle discussed above produces work, a reversed Carnot cycle (operating counterclockwise) acts as a heat pump, requiring work to transfer heat from a low-temperature energy reservoir to a high-temperature energy reservoir. The efficiency of the Carnot cycle ηc is obtained from Eq. (5) as:

(6)

Note that the conditions of reversible Heat Transfer and engine operation imply infinitely large heat transfer surfaces and/or infinitely slow operation/heat transfer. Since these conditions are never met in practical applications, the efficiency of practical power cycles is always lower than the Carnot efficiency.

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