Carnot cycle

Ø   The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded by others in the 1830s and 1840s.

Ø   This is most efficient cycle for converting a thermal energy into work or creating a temperature different by doing a given amount of work.

Ø   Every thermodynamics process exits in different state when a system is taken through these series of different state and then returned its final state a thermodynamics cycle is said to have occurred.

Ø   In the process of going through this cycle the system may perform work on its surrounding, thereby acting as a heat engine.

Ø   Although such a perfect engine is only a theoretical limit and cannot be built in practices.

1. Reversible isothermal expansion of the gas at the "hot" temperature, T₁ (isothermal heat addition or absorption)

Ø    During this step ( In the Figure A to B )  the gas is allowed to expand and it does work on the surroundings.

Ø   The temperature of the gas does not change during the process, thus it is an isothermal expansion.

Ø   The gas expansion is propelled by absorption of heat energy Q₁ and of entropy ΔS = Q₁  from the higher
                                                   T₁
temperature reservoir.

    
2.Isentropic (reversible adiabatic) expansion of the gas (isentropic work output).

Ø    For this step ( In the Figure B to C ) the mechanisms of the engine are assumed to be thermally insulated, thus they neither gain nor lose heat.

Ø   The gas continues to expand, doing work on the surroundings, and losing an equivalent amount of internal energy.

Ø   The gas expansion causes it to cool to the "cold" temperature, T₂. The entropy remains unchanged.

3.Reversible isothermal compression of the gas at the "cold" temperature, T₂. (isothermal heat rejection)

Ø     ( In Figure C to D) Now the surroundings do work on the gas, causing an amount of heat energy Q₂ and of entropy ΔS = Q₂  to flow

                           T₂

out of the gas  to the low temperature reservoir..

Ø   ΔS = Q₁ = Q₂  ( Clausius ineqality )
         T₁     T₂

4.Isentropic compression of the gas (isentropic work input).

Ø    (In Figure D to A) Once again assumed thermally insulated mechanisms of the engine.

Ø   During this step, the surrounding do work on the gas, increasing its internal energy and compressing it causing the temperature to rise T₁.

Ø   The entropy remain unchanged At this point the gas is in the same state as at the start if step 1.

Work done is given by W = Q₁ – Q₂

Efficiency η = W = Q₁ – Q₂ = T₁ – T₂

                       Q₁        Q₁             T₁