Carnot Cycle

Carnot Cycle was proposed by the Famous French scientist Sadi Carnot planned an engine having no defect or loss. Actually it is not possible no one could make and will not invent that type of engine has no loss because we know from second law of thermodynamics there a loss must converting energy of form to another.

Carnot cycle has four steps evolving isothermal and adiabatic process. First two steps is isothermal expansion and adiabatic expansion second two are isothermal compression and adiabatic compression.

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Carnot’s cycle runs with reversible process considering no loss which is impossible we know that very well. Carnot cycle is based on Carnot non defective engine.

Components of Carnot engine are:

i) Cylinder

ii) Heat source

iii) Heat sink

iv) Plat form

v) Working substance

i) Cylinder: A cylinder having non frictional piston is considered by Carnot. The cylinder consists of working substance such as gas for work done.

ii) Heat source: The heat source temperature remains constant. It is a hot body kept at absolute temperature having high capacity.

iii) Heat sink: It is a cold body of having very very low temperature compared to heat source. It’s temperature also remains constant according to Carnot ideal engine theory.

iv) Plat form: A pure insulator or resistance of heat is used as plat form. Heat source, heat sink and cylinder are placed on the surface of the plat form. Heat source and heat sink are very high capacity so that the heat exchange with the cylinder with them does not change their temperature. Temperatures of the source and sinks remains unchanged. Cylinder, source and sink on the plat from can be removed without any friction.

v) Working substance: The working substance remains inside the system of the engine i.e. gas which takes heat as input and does work. It varies engine to engine. Petrol is the working substance of petrol engine, diesel is the working substance of diesel engine.

To understand clearly it is important to have clear conception about isothermal, adiabatic, reversible and irreversible process.

# Isothermal process: Isothermal process that process where temperature remains constant or same changing volume and pressure.

Mathematically, V ∝ 1/P

PV = K

How the temperature of the system remains same changing volume and pressure. Generally we know when volume increases temperature goes down and decrease of volume temperature rises.

For isothermal process two conditions must be satisfied a) volume increment or decrement should be slowly b) the body of the system or cylinder must be good conductor to maintain constant temperature.

When volume decrease the temperature raises if the system body is good conductor of heat and volume decrement process is gradual then compression heat rise of the system will be gone by the cylinder conducting body into the environment.

When the volume raises the system of the cylinder loses temperature which is not expected in isothermal process. In this situation heat is applied from outside to maintain the constant temperature.

In this way temperature remains constant in isothermal process maintaining two condition viz. volume change should be gradual process as the extra heat produce can be gone outside and the body of the cylinder must be good heat conductor to pass heat.

#Adiabatic Process: Adiabatic process is the process where no heat can go inside and no heat come out from inside. Temperature, volume and pressure will increase or decrease but system heat exchange will be zero.

Mathematically, ΔQ = 0

The body of the system cylinder is insulated greatly as the heat from inside or outside can go in or out such way heat exchange is zero.

For adiabatic process entropy remains constant.

# Reversible and irreversible process: Reversible process is that process which can be reversed at same temperature there will be no loss in this process.

Irreversible process is that process which cannot reverse at the same temperature. If the process is reversed it takes two different temperatures for forward and reverse process.

There is no reversible process in the real world all the process of the world is in irreversible process.

Carnot Cycle:

Carnot ideal engine which has no loss works with four steps knows as Carnot’s Cycle. First two steps are volume expansion with the two process isothermal and adiabatic process.

From our diagram we get volume expansion from A to B at temperature T₁ remains constant because for isothermal process where volume V₁ increases to V₂ with the pressure P₁ decrease to P₂. We know pressure decreases increase of volume so A to B is expansion of volume but decrease of pressure.

AB is called heat intake step. Work done for AB is W₁.

The second step of the Carnot cycle is B to C happens with adiabatic process which means the system does not take or out any heat but temperature, volume and pressure changes. BC is expansion of volume so that the system gas becomes cold at V₃ volume and P₃ pressure.

As the system heat remains constant no heat in or out hence ΔQ = 0. Work done of BC is W₂ in adiabatic process. In this step the temperature of gas inside gradually decreases because of volume expansion.

The third and fourth step of Carnot cycle happens in compression of gas. CD compression happens in isothermal. In this process when the gas gets colder from B to C temperature falls and starting from C to D the low temperature remains constant because it does in isothermal process we know the temperature always constant for this process.

Work done for CD is –W₃.

The final step of Carnot cycle D to A happens in adiabatic process means no heat can go inside or outside the system but temperature, volume and pressure changes. This is the second step for volume compression means temperature raise. As the volume compress in adiabatic process ΔQ = 0. Work done is –W₄.

In four steps the total work done by the Carnot engine is

W = W₁ + W₂ – W₃ – W₄

In this way Carnot cycle works in four steps with the help of engine working substance i.e. gas inside the system with two isothermal processes and two adiabatic processes. The graph represents the total work done the ideal Carnot engine.

Carnot engine is an ideal engine has no loss which is not practically possible.

Efficiency of Carnot Engine:

The efficiency of Carnot engine is more than practical engine. The efficiency of the Carnot engine is the ratio of output and input which means heat transformed into work and heat absorbed from the source.

Suppose the engine working substance takes Q₁ heat from the source and reject Q₂ heat into the sink. If we consider in temperature intake temperature T₁ and rejection temperature T₂ into the sink.

This is the equation of engine in term of percentage.

According to Carnot Q₂ = 0 so that

Which is actually not possible in real life. There is no engine without loss. Carnot imagined his engine works in reversible process with no loss but there is a loss must.