# What is a Carnot Engine? | How does a Carnot Cycle work?

A heat engine that works according to the Carnot cycle is known as a Carnot engine. The Carnot cycle provides an estimation of the extreme possible efficiency that a heat engine converts heat into output work, on the contrary, working between two reservoirs (hot and cold).

In 1824, Nicolas Leonard Sadi Carnot invented the Carnot engine. This engine is known as a Carnot engine because of the name of its inventor (Sadi Carnot).

The Carnot engine is an ideal engine that uses processes with reversible mechanical and thermal exchanges. This statement represents that the engine can complete its movement and come back to its original condition without increasing entropy (without losing energy). For the engine to be able to return to its initial state without losing energy, it should be in thermal equilibrium condition during the entire cycle. Following are some terms for the existence of the Carnot engine:

• Mechanical interactions: During the mechanical interaction process (Q = 0), no heat transfer takes place because energy doesn’t drop due to friction. This process is called an adiabatic process.
• Thermal interaction: During the thermal interaction process, the heat transfer is very slow (called quasi-static). It means that the temperature variation between the input/output and the system heat is approximately the same, which means that the heat transfer takes place over an infinitely long time. During the thermal interaction, the system’s internal temperature must be constant. Therefore, this process is called the isothermal process.

The engine which uses the above-given interactions is called a Carnot engine.  This engine is a “fully reversible engine” with the highest thermal efficiency (ηmax).

## History of Carnot Engine

• In 1824, Nicolas Leonard Sadi Carnot designed the first model of the Carnot engine.
• In 1824, his research led to the proposal for the most efficient virtual duty cycle (Carnot cycle) between the same two reservoirs.
• In 1834, Benoit Paul Emile Clapeyron expanded the graphical model of the Carnot engine.
• In 1857, Rudolf Clausius mathematically examined the Carnot cycle. This work led to the basic thermodynamic concept of entropy.

Read also: Different types of Heat Engines

## Carnot Engine Working Principle

A Carnot engine works on the base of the Carnot cycle, which states that:

1. The irreversible heat engine’s efficiency operating between two reservoirs is always lower than that of a reversible Carnot heat engine’s efficiency operated between the 2 similar reservoirs.
2. All reversible heat engines working between the 2 similar reservoirs have the same efficiency.

The temperature of the combustion chambers must be higher to raise the thermal efficiency of the gas powerplant. For example, turbine blades can’t resist hot gases, which leads to premature fatigue.

## Carnot Cycle

A Carnot cycle works in the following four stages:

1. Isothermal Expansion
3. Isothermal Compression

Step 1) Isothermal Expansion (D to A): –

In the above diagram, the line A to B represents to Isothermal Expansion process. The word “isothermal” is a combination of “Iso” and “thermal.” The term “Iso” means same and “temperature” means heat, and the term “isothermal” represents no change in the temperature.

In this isothermal expansion process, the gas expands, and this expansion performs work on the surrounding by moving the piston upward. During this process, the pressure of the gas decreases from P1 to P2 (as shown in the above diagram). But during this whole process, the gas temperature doesn’t change; therefore, it is called a an isothermal expansion (constant temperature expansion).

During this isothermal expansion, the gas absorbs the heat energy QH from the high-temperature reservoir, which rises the gas entropy (energy).

Step 2) Adiabatic Expansion (B to C): –

After the completion of the isothermal process, the Isentropic process (B to C) starts. For the isentropic stage, assume that the cylinder and piston are thermally isolated. This stage is known as an ‘adiabatic’ process because heat can’t enter nor exit from the cylinder and piston. In simple words, no heat change takes place during this process.

During the adiabatic expansion process, the gas continuously expands. Its pressure further drops from P2 to P4 (as shown in the above diagram), volume increases, and temperature also reduces because some amount of the internal energy loses similar to the work done.

This gas expansion process further pushes the piston upward and performs work on the surrounding. Without input heat, the gas expansion cools the gas and converts its temperature to the “cold” temperature (Tc).

Step 3) Isothermal Compression: –

In this process, the surrounding performs work on the gas due to that heat transfers from the system to the cold reservoir. During the isothermal compression process, the temperature of the gas remains the same. Still, the pressure increases from P4 to P3 (as shown in the above diagram), and gas volume decreases.  This process forces the heat energy (Q2) to move from the system to the cold reservoir, and the system’s entropy drops.

The work in isothermal compression is lower than the work performed on the environment in the 1st stage. This is because this compression process starts at a low pressure which assists in transferring heat from the system to the cold reservoir, and some of the energy uses in this process.

Step 4) Adiabatic compression (D to A): –

In the above diagram, the line D to A represents to Adiabatic reversible compression process. During this process, the piston and cylinder are supposed again to be isolated, and the hot reservoir has been eliminated.

In this stage, the environment continuously performs work on the gas by moving the piston downward. As the piston further moves downward, it continuously compresses the gas and increases its temperature and pressure from P3 to P1 (as shown above). This process raises the internal energy of the gas, compresses the gas, and increases its temperature from Tc to Th. The entropy remains the same in the adiabatic process. After this process, the whole cycle repeats.

## Carnot Theorem

According to the Carnot theorem:

• All reversible heat engines working between the 2 similar reservoirs have the identical productivity.
• The reversible Carnot heat engine operating between the two reservoirs has higher productivity than the irreversible heat engines working on the same reservoirs.
• The maximum efficiency of a Carnot engine is given below:

In the above equation:

TH = Hot reservoir temperature

TC = Cold reservoir temperature

QH = Heat supplied to the system

W =   Work done by the system

The efficiency of a Carnot engine varies according to the temperature of the cold and hot reservoirs. It doesn’t depend on the working fluid nature.

## What is the Efficiency of the Carnot Engine?

The Carnot efficiency denotes the maximum thermal efficiency that a Carnot heat engine can achieve according to the 2nd law of thermodynamics. In 1824, Sadi Carnot was introduced this law. He came up with the idea of ​​maximizing the efficiency of a heat engine.

Sadi Carnot designed the Carnot engine that can theoretically deliver this productivity, the so-called Carnot motor. The efficiency of a Carnot engine varies according to the temperature of the cold (TL) and hot (Tc) reservoirs (as shown in the below diagram).

The following formula can calculate the maximum efficiency of the Carnot cycle:

TC = Temperature of the cold reservoir

TH = Temperature of the hot reservoir

As you can see in the above equation, the Carnot cycle efficiency can increase by decreasing the value of the TH or increasing the value of TL.

Carnot’s cycle represents that a heat engine can achieve 100% efficiency if the Tc =0 K. This 100% is only possible if the temperature of the cold sink is at absolute zero, but theoretically and practically, this is not possible.

A real heat engine can’t achieve such high efficiency as a Carnot engine. A Carnot engine can achieve up to 0.7 actual efficiencies; that’s its best efficiency.

## Modern diagram of Carnot Engine

The below-given diagram denotes the block diagram of a Carnot engine. In1850, Clausius presented a term known as the “working body” (system) that can be a vapor or fluid through that heat “Q” can transfer or introduce to generate output work (as shown in the below diagram).

Carnot had claimed that the body of the fluid could be any material that can expand, such as permanent gas, mercury vapor, alcohol vapor, water vapor, or air. In those early days, engines came in many designs, but generally, a boiler (in which the water was boiled by passing over the furnace) was used to supply heat (QH), and a condenser was used to supply QC.

The output work W denotes the piston motion. The piston was utilized to drive the pulley.   Still, it is used to rotate the crank arm.

## Components of Carnot engine

The Carnot engine has the following major components:

1. Source
2. Sink
3. Cylinder
4. Insulating Stand
5. Piston
##### 1) Source

A source is a hot body that operates at a constant temperature T1. It delivers heat to the system for working.

This source has unlimited heat volume. At a constant temperature (T1), you can withdraw heat from it according to your wish. The temperature of the heat source remains constant even after extracting large heat.

##### 2) Sink

It is a low-temperature body that has a constant low temperature (T2). The sink also has unlimited heat capacity. This means the heat supplied to a sink does not raise its temperature.

##### 3) Cylinder

The cylinder has a conductive bottom and a non-conductive wall. It is equipped with a completely frictionless and non-conductive piston. This piston moves up and down for gas compression. In the Carnot engine, an ideal gas uses as the working medium.

##### 4) Insulating stand

An insulating stand uses to operate an adiabatic operation. This part of the Carnot engine is made of non-conducting material.

##### 5) Piston

It is a reciprocating component that reciprocates inside the cylinder of the engine. The reciprocating motion of the piston causes the expansion and compression of the gas.

## Limitations Of Carnot Cycle

The Carnot cycle has the following limitations:

• It is an ideal cycle. In other words, the Carnot cycle doesn’t exist and cannot be constructed. Therefore, the Carnot cycle is only a theoretical concept.
• According to thermodynamics, in an isothermal process, the temperature doesn’t change, while the Carnot cycle says that there will be the addition of heat during isothermal expansion, which is impossible.
• The Carnot cycle only explains to heat engine while it doesn’t explain other types of equipment.
• Heat loss can occur in a real engine while the Carnot cycle has oppositive working.

## Why isn’t the Carnot cycle used in practical applications?

In a Carnot heat engine, the ideal gas uses as a working fluid trapped in a cylinder. The boundaries of this cylinder are fully isolated.

A Carnot cycle works in the following four processes:

1. Isothermal expansion
3. Isothermal compression

From the above four processes, two are reversible isothermal, and two are adiabatic processes.

The Carnot cycle can’t use in practical applications due to the following reasons:

1. The isothermal process is very slow, while the adiabatic is a very fast process. In reality, a fast and a slow process can’t operate at the same time.
2. Carnot’s cycle says that a heat engine can achieve 100% efficiency. This 100% is only possible if the temperature of the cold sink is at absolute zero, but theoretically and practically, this is not possible.

Due to the above-given reasons, the Carnot cycle can’t use with practical applications.

## FAQ Section

### Who Invented the Carnot Engine?

In 1824, Nicolas Leonard Sadi Carnot invented the Carnot engine.

### What is the working fluid in Carnot cycle?

An ideal gas uses as a working fluid in the Carnot cycle.

### Name the processes involved in the Carnot cycle?

A Carnot cycle works in the following four processes:

1. Isothermal expansion
3. Isothermal compression

### Does the Carnot engine exist?

A heat engine that utilizes only reversible processes (isothermal and adiabatic) is called a Carnot engine.

A Carnot engine doesn’t exist practically because, in a Carnot cycle, the Isothermal process is very slow while the adiabatic is a very fast process. In reality, a fast and a slow process can’t operate at the same time.

### Is the Carnot engine reversible?

Yes, because a Carnot engine uses a Carnot cycle which is fully reversible.

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