The most effective cycle of a heat engine is the Carnot heat cycle. It consists of two isothermal and two adiabatic processes. The second law of thermodynamics establishes that not all the heat supplied to a heat engine can be used to perform work. The efficiency of such an engine that implements the Carnot cycle gives the limiting value of that part of it that can be used for these purposes.

## A few words about the reversibility of physical processes

The physical (and in the narrow sense, thermodynamic) process in a certain system of bodies (including solids, liquids, gases) is reversible, if after it has been implemented, it is possible to restore the state in which the system was before it began. If it cannot return to its original state at the end of the process, then it is irreversible.

Reversible processes do not occur in nature. This is an idealized model of reality, a kind of tool for its research in physics. An example of such a process is the Carnot cycle. An ideal heat engine is a model of a real system that implements a process, named after the French physicist Sadi Carnot, who first described it.

## What causes process irreversibility?

Factors that lead to it include:

• heat flows from the heat source to the consumer at a finite temperature difference between them;
• unlimited gas expansion;
• mixing two gases;
• friction;
• the passage of electric current through resistance;
• inelastic deformation;
• chemical reactions.

The process is irreversible if any of these factors are present. The Carnot ideal cycle is a reversible process.

## Internally and externally reversible processes

When the process is carried out, the factors of its irreversibility can be located within the framework of the system of bodies itself, as well as in its vicinity. It is called internally reversible if the system can be restored to the same state of equilibrium in which it was in its beginning. At the same time inside it there can be no factors of irreversibility as long as the process under consideration lasts.

If the factors of irreversibility are absent outside the system's borders in the process, then it is called externally reversible.

A process is called fully reversible if it is both internally and externally reversible.

## What is the Carnot cycle?

In this process, realized by an ideal heat engine, the working fluid — heated gas — performs mechanical work due to the heat obtained from the high-temperature heat reservoir (heater) and also gives off heat to the low-temperature heat reservoir (refrigerator).

The Carnot cycle is one of the most famous reversible cycles. It consists of four reversible processes. And although such cycles are unattainable in practice, but they set the upper limits of the performance of real cycles. In theory, it is shown that this direct cycle performs, with the highest possible efficiency, the conversion of thermal energy (heat) into mechanical work.

## How does the ideal gas cycle Carnot?

Consider an ideal heat engine containing a cylinder with gas and a piston. The four reversible processes of the cycle of operation of such a machine are:

1. Reversible isothermal expansion. At the beginning of the process, the gas in the cylinder has a temperature TH.  Through the walls of the cylinder, it is in contact with a heater that has an infinitely small temperature difference with the gas. Consequently, there is no corresponding irreversibility factor in the form of a finite temperature difference, and there is a reversible process of heat transfer from the heater to the working fluid — gas. Its internal energy grows, it expands slowly, while doing the work of moving the piston and remaining at a constant temperature TH. The total amount of heat transferred to the gas by the heater during this process is QH,  however, only a part of it is further transformed into work.

2. Reversible adiabatic expansion. The heater is removed, and the gas that performs the Carnot cycle slowly expands further adiabatically (with constant entropy) without heat exchange through the walls of the cylinder or the piston. His work on the movement of the piston leads to a decrease in internal energy, which is reflected in a decrease in temperature from TH  up tL. If we assume that the piston moves without friction, then the process is reversible.

3. Reversible isothermal compression. The cylinder is brought into contact with a refrigerator having a temperature TL. The piston begins to push back the external force that does the work of compressing the gas. At the same time, its temperature remains equal to TL,  and the process involving heat transfer from gas to refrigerator and compression remains reversible. The total amount of heat removed from the gas in the fridge is QL .

4. Reversible adiabatic compression. The refrigerator is removed, and the gas is slowly compressed further adiabatically (with constant entropy). Its temperature rises from TL  to tH. The gas returns to its original state, which completes the cycle.

## Carnot principles

If the processes that make up the Carnot cycle of a heat engine are reversible, then it is called a reversible heat engine. Otherwise we have its irreversible option. In practice, all heat engines are such, since reversible processes do not exist in nature.

Carnot formulated the principles that are a consequence of the second law of thermodynamics. They are expressed as follows:

1. The efficiency of an irreversible heat engine is always less than that of a reversible one working from the same two heat reservoirs.

2. The efficiency of all reversible heat engines operating from the same two heat reservoirs are the same.

That is, the efficiency of a reversible heat engine does not depend on the working fluid used, its properties, the duration of the work cycle and the type of heat engine. It is only a function of the temperature of the tanks:

where QL  - the heat transferred to the low-temperature tank, which has a temperature TL;  QH  - the heat transferred from the high-temperature tank, which has a temperature TH;  g, F - any functions.

## Carnot Heat Engine

They call such a heat engine, which works on a reversible Carnot cycle. The thermal efficiency of any heat engine, reversible or not, is defined as

where QL  and QH  are quantities of heat transferred in a cycle to a low-temperature tank at temperature TL  and from a high-temperature tank at temperature TH respectively. For reversible heat engines, thermal efficiency can be expressed in terms of the absolute temperatures of these two tanks:

The efficiency of a heat engine Carnot is the highest efficiency that a heat engine can reach by operating between a high-temperature tank at a temperature TH  and low-temperature tank at temperature TL. All irreversible heat engines operating between the same two tanks have lower efficiency.

## Reverse process

The cycle in question is completely reversible. Its cold option can be achieved by reversing all the processes involved in it. In this case, the Carnot cycle operation is used to create a temperature difference, i.e. thermal energy. During the reverse cycle, the amount of heat QL  the gas is received from the low-temperature reservoir, and the amount of heat QH  It is given to them in a high-temperature heat reservoir. Energy wnet, in  required to perform a loop. It is equal to the area of ​​the figure bounded by two isotherms and two adiabats. PV diagrams of the forward and reverse Carnot cycles are shown in the figure below.

## Refrigerator and heat pump

A refrigerator or heat pump that implements a Carnot reverse cycle is called a Carnot refrigerator or a Carnot heat pump.

Efficiency reversible or irreversible refrigerator (ηR  ) or heat pump (ηHP)  is defined as:

where QH  - the amount of heat removed in the high-temperature tank;
QL  - the amount of heat obtained from the low-temperature tank.

For reversible refrigerators or heat pumps, such as Carnot refrigerators or Carnot heat pumps, efficiency can be expressed in terms of absolute temperatures:

where tH  = absolute temperature in a high-temperature tank;
TL  = absolute temperature in the low temperature tank.

ηR  (or ηHP  ) are the highest efficiency of the refrigerator (or heat pump) that they can achieve by operating between a high-temperature tank at temperature TH  and low-temperature tank at temperature TL. All irreversible refrigerators or heat pumps operating between the same two tanks have lower efficiency.

## Household refrigerator

The basic idea of ​​a home refrigerator is simple: it uses the evaporation of the refrigerant to absorb heat from the cooled space in the refrigerator. There are four main parts in any refrigerator:

• Compressor.
• Tubular radiator outside the refrigerator.
• Expansion valve.
• Heat transfer tubes inside the refrigerator.

Reverse Carnot cycle when the refrigerator is running in the following order:

• Adiabatic compression. The compressor compresses the refrigerant vapor, increasing their temperature and pressure.
• Isothermal compression. High-temperature and compressor-compressed refrigerant vapor dissipates heat into the environment (high-temperature tank) as it flows through the radiator outside the refrigerator. Refrigerant vapor is condensed (compressed) into the liquid phase.
• Adiabatic expansion. Liquid refrigerant flows through the expansion valve to reduce its pressure.
• Isothermal expansion. The cold liquid refrigerant evaporates as it passes through the heat exchange tubes inside the refrigerator. In the process of evaporation, its internal energy grows, and this growth is ensured by the removal of heat from the internal space of the refrigerator (low-temperature tank), as a result of which it cools. Then the gas enters the compressor to compress again. The reverse Carnot cycle is repeated.