Carnot Cycle

The cycle was first suggested by Nicolas Leonard Sadi Carnot in 1824 which works on reversible cycle and to analyse the problem of the efficiency of a heat engine.

Any fluid may be used to operate the Carnot cycle. The working substance is subjected  to a cyclic operation consisting of two isothermal and two reversible adiabatic or (isentropic) operations. The P-V and T-S diagram of this cycle is shown below:

Following are the four process of Carnot cycle:

Process A-B (Isothermal Expansion): During isothermal expansion, the heat supplied is fully absorbed by the air and is utilised in doing external work.

Heat Supplied = Workdone by air during isothermal expansion

                       = P₁V₁ ln (V₂/V₁)

                       = 2.3 P₁V₁ log r

                       = 2.3 mRT₁ log r         ::: r = V₂/V₁ = Expansion ratio

Process B-C (Isentropic Expansion): During reversible adiabatic or isentropic expansion, no heat is absorbed or rejected by the air.

Decrease in Internal energy = Workdone by the air during adiabatic expansion

Process C-D (Isothermal Compression: During isothermal compression, the heat is rejected and its equal to the workdone on the air.

Heat Rejected = Workdone on the air during isothermal compression

                       = P₃V₃ ln (V₃/V₄)

                       = 2.3 P₃V₃ log r

                       = 2.3 mRT₂ log r         ::: r = V₃/V₃ = Compression ratio 

Process D-A (Isentropic Compression): During reversible adiabatic or isentropic compression, no heat is absorbed or rejected by the air.

Increase in Internal energy = Workdone on the air during adiabatic compression.

 

 Workdone:
                         = Heat Supplied - Heat Rejected
Efficiency: