Carnot Cycle and Reversed Carnot Cycle

Carnot Cycle

The Carnot cycle is a thermodynamic cycle that is known for the best possible efficiency. Carnot cycle changes the energy available in the form of heat to produce useful reversible-adiabatic (isotropic) and other processes.

Carnot engine efficiency is one minus the ratio of the temperature of the hot thermal reservoir to the temperature of the cold reservoir. The Carnot cycle is known for setting the highest efficiency benchmark that any cycle or engine can achieve.

Work is done by the working fluid during the first part of the cycle and work is done on the working fluid during the second part of the cycle. The difference between the two is the net work done.

The cycle efficiency can be maximized by utilizing the processes that requires the least amount of work and deliver the most by using the reversible processes. Practically, reversible cycles cannot be achieved due to irreversibility associated with each process which cannot be eliminated.

Refrigerators and heat engines that work on reversible cycles are considered as models for comparing the actual heat engines and refrigerators. In the development of the actual cycle, the reversible cycle serves as a starting point and modified in order to meet the requirement.

The Carnot cycle is composed of four reversible processes (2 nos. reversible- isothermal and 2 nos. reversible-adiabatic processes) are as follows:

The Carnot Cycle is demonstrated below through the relevant example of the piston:
STEP 1 – 2
(Reversible Isothermal Expansion, Th = Constant)

TH is the initial temperature of the gas and also the temperature of the reservoir, is in close contact with the cylinder head.

The temperature of the gas drops when the gas expands and the same is kept constant by transferring infinitesimal-heat (dT) from the reservoir to the gas.
The amount of heat transferred during the process to the gas is Qh

STEP 2 – 3
(Reversible adiabatic expansion temperature drop from TH to TL)

The system becomes adiabatic when the heat reservoir is replaced by insulation. During this process, the gas temperature drops to Tl from Th.

This process is called reversible as well as adiabatic (note that engineering thermodynamics has a specific definition for systems and processes).

STEP 3 – 4
(Reversible Isothermal Compression, Tl = constant)

At stage-3, the Heat sink replaced the cylinder head insulation at temperature Tl. When an external force pushes the piston inwards for doing the work on gas, then the temperature of the gas increases.

But the temperature of the gas maintained constant by rejecting the heat to the sink. The amount of heat rejected during the process is Ql.
STEP 4 – 1
(Reversible adiabatic compression temperature increases from Tl to Th)

The energy sink is replaced with insulation and the temperature of the gas increases from Tl to Th during the compression process.

Net Work Done

Work done by the gas during the expansion process is the area given under the curve 1-2-3.
Work-done on the gas during the compression process is the area given under the curve 3-4-1

Thus the net work done is given by the area under the path 1-2-3-4-1.

Importance of the Carnot Cycle

Heat engine efficiency depends on the maximum and minimum temperature of the cycle:
Carnot states that the efficiency of the heat engine is independent of the type of fluid and only depends upon the maximum and minimum temperatures during the cycle.

Thus the efficiency of the heat engine is higher when operates on super-heated steam temperature.
Carnot Cycle and Second law of thermodynamics:

Carnot cycle clearly demonstrated the fact that the heat is absorbed from the high-temperature source called reservoir and the heat is rejected to sink. This fact becomes the basis for the second law of thermodynamics. But external work is required in order to move the heat in the reverse direction.

Reversed Carnot Cycle

Carnot cycle is a reversible cycle, and it becomes the Carnot refrigeration cycle when the process reversed. The direction of heat and work interactions are totally reversed, thus
Thus,

• Heat absorbed from low-temperature-reservoir is Ql

• Heat rejected to a high-temperature-reservoir is Qh

• Work done is Wnet-in

Reversed Carnot cycle is the same as that of the conventional Carnot Cycle except for the direction of the processes.

History of Carnot Cycle

The Carnot cycle is named after “N. L. Sadi Carnot” who invented it in 1824. Sadi Carnot is referred to as the founder of thermodynamics for discovering the heat and work relationship. Carnot was one of the first to realize that heat is essentially works in a different form.

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