Carnot Engine/ Carnot Cycle

Since, we know that thermodynamics is concerned with the conversion of heat into work and work into heat. That's why we need a machine that converts heat into work. That is a HEAT ENGINE. Engine is the heart of any vehicle.  

......."A heat engine is a machine that operates between two reservoirs in which one acts as a heat source while the other acts as a heat sink. Its function is to convert heat into work by absorbing heat from the heat source and transfer the remainder to the heat sink after producing work from heat".........

Another thing to remember is that heat cannot be completely converted into work.

Every single thermodynamic system exists in a particular state. When a system passes through a series of different states and finally returns to its initial state, a thermodynamic cycle is said to have occurred. In the process of going through this cycle, the system can do work on its surroundings, for example by moving a piston, thereby acting as a heat engine. 

The engine working in a cycle is called the "Carnot Engine" and the cycle is known as "Carnot Cycle". In this article, we're interested in learning more about Carnot Cycle, also known as the Carnot heat engine cycle in detail.

CARNOT ENGINE

Of course, the thermal efficiency of a heat engine will depend on the degree of reversibility of its operation. In fact, a heat engine operating in a completely reversible manner is very special, and is called a "Carnot Engine". 

......."A Carnot Engine is a special type of heat engine whose efficiency is the maximum possible efficiency relative to the efficiency of any other heat engine".........

Although such a "Perfect Engine" is only a theoretical construction and cannot be made in practice. It provides an upper limit on the efficiency. 

The characteristics of such an ideal engine were first described by N.L.S. Carnot in 1824. He also gives the concept of Carnot Cycle and their Principle. This "Carnot Cycle" consists of an alternative series of two reversible isothermal processes and two reversible adiabatic processes. He suggested that, if a heat engine is passed through these thermodynamic stages, then it may be possible to get 100% efficiency of the heat engine. 

!!!!This Engine Is Called The Carnot Engine Or Ideal Heat Engine!!!!!

Thus, Carnot Engine works on the basis of Carnot Cycle. 

Sadi Carnot suggested the working process for this Carnot engine. He explained about the different parts of engine and he also explain about all the processes involved in the working of the engine. During this theory on engine, he made few assumptions;

1) This engine is an ideal engine (or hypothetical engine). 

2) Sadi Carnot designed this engine which is 100% efficient.

In Fact: 

Carnot engine is just an ideal engine (or hypothetical engine). No engine has 100% efficiency according to second law of thermodynamics.

Parts Of Carnot Engine

Carnot heat engine consists of four parts and these are;

1) Insulated Non Conducting Stand

(Carnot heat engine consists of an insulated stand which does not conduct heat through it)

2) Hot Reservoir

(This is also known as heat source and it's temperature remains constant)

3) Cold Reservoir

(Remains at the constant lower temperature. This cold reservoir is also known as heat sink where heat is released)

4) Cylinder With A Working Fluid 

(Now here is the main part. A cylinder which is having non conducting walls through which no heat transfer takes place. The cylinder is fitted with a piston which reciprocates up and down)

Carnot Cycle And It's Operations

"Carnot cycle is a reversible cycle and hence it is an ideal cycle". Each process of Carnot cycle will be reversible process and therefore we can consider that each process of Carnot cycle is reversed and cycle is being operated in reverse direction also. 

We must note it here that if a reversible process is reversed then all types of energy, such as heat energy or work energy, associated with the process will have same magnitude but the direction of energy interaction will be reversed.

      

"The engine working on this cycle is called the Carnot Engine". Carnot engine will have the highest efficiency and hence, it is also termed as highest efficient heat engine. Efficiency of a reversible heat engine depends only on the working temperature limits and not on the properties of working substance. 

How A Carnot Cycle Being Operate,

Consider, there is a working fluid inside the cylinder which expands and contracts during the process. "In this we use an ideal gas as the working substance".

                      ➛ " T₁>T₂ "

P-V Diagram

All the processes occurring in the Carnot engine is represented graphically on a P-V diagram;

[Ideal Reversible Closed Thermodynamic Cycle]

The four steps that make up the Carnot cycle are performed in the following order;

(All the steps or processes in this cycle are reversible.)

STEP: 1 

"AB- Isothermal Expansion Of An Ideal Gas"

Here, Q₁ is the amount of heat absorbed by the working substance (or ideal gas) within the system from the heat source (or high temperature reservoir) placed at temperature T₁. Thus, the system's temperature rises and this high temperature causes the gas particles to expands; pushing the piston upwards and doing work on the surrounding.

STEP: 2

"BC- Adiabatic Expansion Of An Ideal Gas"

Here, The gas continuously expands and does work on the surroundings (like- piston is raised), although there is no heat interaction between system and the heat source (ஃ no heat is absorbed from the heat source) but the temperature changes from T₁ to T₂. The expansion of the gas without heat input causes it to cool down from T₁ to T₂.

STEP: 3

"CD- Isothermal Compression Of An Ideal Gas"

Here, Q₂ is the amount of heat released to the heat sink (or low temperature reservoir) as work is done on the system by the surrounding which pushes the piston downward at a constant temperature T₂.

STEP: 4

"DA- Adiabatic Compression Of An Ideal Gas"

Here, again the system is insulated from the heat sink and work is done continuously on the system by the surrounding which pushes the piston downwards further so that the piston returns to its initial position. Due to this, the temperature T₂ also comes back to its initial position T₁.

We must note it here that during the process CD and process DA, work will be done over the system by the surrounding. And during the process AB and process BC, work will be done by the system over the surrounding.

!!!!After The Last Step, The Gas Returns To Its Initial Stage And This Complete Cycle Is Known As Carnot Cycle. The Engine Working On This Cycle Is Called The Carnot Engine!!!!!

Carnot Principles Or Carnot Theorem

Carnot's theorem also known as Carnot's law or Carnot principle was developed by Nicolas Leonard Sadi Carnot in the year 1824. Carnot's theorem states that;

"For two given heat/thermal reservoirs, the efficiency of all irreversible heat engines is less than the efficiency of all reversible heat engines (such as the Carnot engine)". 

This means that the thermal efficiency of any engine cannot be greater than that of a Carnot engine.

Corollary To The Carnot's Theorem

For two given heat/thermal reservoir, all reversible heat engines (such as Carnot Engine) have the same thermal efficiency, regardless of the working substance. Thus, the efficiency of a Carnot engine is independent of the nature of the working material and depends only on the temperature of the hot and cold reservoirs.

Efficiency of Carnot Engine

As we know that heat engine efficiency is defined as the ratio of work output to the heat input or heat supplied. It is denoted by a symbol, 'η'.

FOR A CASE OF CARNOT ENGINE,

Since the cycle is theoretically reversible, no entropy is generated during the cycle; That is, entropy is conserved.

In this case,

                    ∆S₁ ＝ ∆S₂

                          Or 

                  Q₁/T₁ ＝ Q₂/T₂ 

           ➩ { Q₁/Q₂＝ T₁/T₂ }

Thus the Carnot's engine efficiency becomes;

Here,

      T₁ is the temperature of heat source 

            (Or hot temperature reservoir)

      T₂ is the temperature of heat sink

           (Or low temperature reservoir)

Above equation is known as "Carnot's Equation".

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