# Carnot cycle

The Carnot cycle is the most efficient heat engine cycle invented to date, consisting of two isothermal and two adiabatic processes . It can be considered as the most efficient heat engine cycle allowed by physical laws when the second law of thermodynamics tells us that all the heat that is supplied in a heat engine cannot be used, the Carnot efficiency establishes the limit value of the fraction of heat that can be used . The Carnot cycle has the highest efficiencypossible of an engine based on the assumption of the absence of incidental waste processes , such as friction , and the assumption that there is no heat conduction between different parts of the engine at different temperatures.

Formula

a → b  = Q a → b

## What is the Carnot cycle?

The Carnot cycle is a process cyclic reversible and theoretical using a perfect gas and which is formed by two types of transformations isothermal and two type adiabatic which can become heat the work.

• What is the Carnot cycle?
• Who proposed it
• History
• Stages of the Carnot cycle
• Theorems
• Carnot cycle formulas
• Inverted Carnot cycle
• Importance of the Carnot cycle

## What is the Carnot cycle?

The Carnot cycle consists of a thermodynamic cycle that is used as a standard to be able to establish a series of comparisons with other cycles that are real. It is a cycle that shows us that, even in ideal conditions , a heat engine cannot convert all the heat energy it has into mechanical energy and for this reason, it must reject a part of this energy. A machine then accepts heat energy from a source that has a high temperature or from a hot body , and converts part of the energy into mechanical work or electrical discharging the remaining energizes between the source and the drain, thereby producing greater efficiency in the machine.

It consists, then, first of all, in an isentropic type compression , which then, when heat is added , also produces an isentropic expansion that ends in an isothermal heat rejection process . Compression , heat addition , expansion, and heat discharge processes are part of the cycle. The effect of the cycle that occurs is given by constantly adding heat at high temperatures and discharging less heat at a low but constant temperature and the algebraic sum of the amounts of heat that represent the work that has been performed by the cycle.

## Who proposed it

Nicolas Léonard Sadi Carnot , also known as Sadi Carnot was a French physicist and engineer who explored the study of Thermodynamics and who is recognized as the founder or Father of Thermodynamics and creator of the Carnot Cycle.

## History

The history of the Carnot cycle arises with one of the engineers French major, Carnot, who was commissioned to study the scientific principles underlying regarding the operation that had the machine of steam with the aim to obtain maximum power output achieving maximum efficiency . Carnot began his studies by observing that heat did not flow by itself from a cold body to a warm one , but caused heat to flow from a different part.

## Stages of the Carnot cycle

The stages of the Carnot cycle are as follows:

#### Stage A) Isothermal expansion

This stage is an isothermal process and as a perfect gas is used, the temperature is kept constant T 1 . The gas is in an  initial equilibrium state  that is represented by p 1 , V 1 , T 1 , inside the cylinder. In this stage there is an isothermal expansion between 1 and 2, until it achieves the values ​​p 2 , V 2 , T 1 , the system performs  positive work W 1 , so that the volume increases , producing positive work , communicating energy to the environment, on the other hand, since the variation of internal energy must be zero, it takes a heat from the equivalent environment Q 1 :

1 = Q 1

As it is an adiabatic process, there is no type of heat transfer, the gas must do the work, raising the  plunger , and to achieve this, the cylinder must be thermally insulated, reaching the values ​​p 3 , V 3 , T 2 .

#### Stage C) Isothermal compression

It is possible to reach the values ​​p 4 , V 4 , T 2 , being the work done by the piston. It is a compression work where energy is received from the environment in the form of work and a certain amount of equivalent energy is granted in the form of heat :

2 = Q 2

The values ​​p 1 , V 1 , T 1 are reached again  without any type of heat transfer with the outside. The  net work  W that is done during the cycle by the system will be that represented by the surface enclosed in the path 1-2-3-4-1. The net amount  of heat energy  received by the system will be the difference between Q 2  and Q 1 .

## Theorems

Carnot’s theorem is a statement presented alternately with respect to the second principle of thermodynamics which is formulated from the comparison made between machines reversible machines and irreversible as performance having a thermal machine M The operation between two foci cannot be greater than that of a reversible machine that operates between the same foci, fulfilling the equality that tells us that if the machine M is also reversible and the inequality if it is irreversible. This theorem can be proved thanks to the Kelvin-Planck statement , which tells us that there is no type of perfect machine that has 100% performance . Carnot’s theorem tells us that there is a maximum for yield and states how to find that maximum.

## Carnot cycle formulas

The formulas associated with each of the phases of the cycle carried out in the Carnot machine are mentioned below.

#### Isothermal expansion (A → B):

a → b  = Q a → b

At the end of this phase of the cycle, it is also possible to obtain the pressure value using the ideal gas equation. Thus, we have the following:

2 * V b = n * R * T 1

Where:

• 2 : Pressure at the end of the phase.
• b : Volume at point b.
• n: Number of moles of the gas.
• A: Universal constant of ideal gases. R = 0.082 (atm * liter) / (moles * K).
• T1 : Absolute initial temperature, degrees Kelvin.

#### Adiabatic expansion (B → C)

Assuming it is an ideal gas, the theory holds that gas molecules only have kinetic energy . According to the principles of thermodynamics, this can be deduced by the following formula:

b → c  = n * C v * (T 2 – T 1 )

In this formula:

• b → c : Variation of internal energy of the ideal gas between points b and c.
• n: Number of moles of the gas.
• Cv: Molar heat capacity of the gas.
• T1: Absolute initial temperature, degrees Kelvin.
• T2: Absolute final temperature, degrees Kelvin.

## Inverted Carnot cycle

The reversible or reversed Carnot cycle is that the four processes that occur during the reversible cycle can be reversed in terms of the directions of the heat and work processes.

## Importance of the Carnot cycle

The importance of the Carnot cycle is that it shows us the greater efficiency that an engine can have based on the assumption of the lack of occasional waste processes, such as friction , and the assumption of no heat conduction between the different parts. engine at different temperatures .