Isentropic Expansion Process:

Now the air is expanded isentropically as indicated by the curve 3-4 on p-v & T-s diagrams. The pressure of air reduces from p₃ to p₄, particular volume enhances from v₃ to v₄ & temperature reduced from T₃ to T₄. We know that throughout isentropic expansion, no heat is absorbed or discarded by the air.

Isothermal Expansion Process:

Now the air is expanded isothermally (that is at constant temperature, T₄ = T₁) as indicated through the curve 4-1 on p-v & T-s diagrams. Throughout this procedure, the pressure of air reduced from p₄ to p₁ and particular volume enhance from v₄ to v₁. We know that the heat absorbed by the air throughout isothermal compression per kg of air,

q_4-1 = area 4-1-2'-3'

           = T₄ (s₁ - s₄)

           = T₄ (s₂ - s₃)

            = T₁ (s₂ - s₃)

We know that work completed throughout the cycle per kg of air

= Heat rejected - Heat absorbed

= q^2-3 - q^4-1

= T₂ (s₂ - s₃) - T₁ (s₂ - s₃)

So, coefficient of performance of the refrigeration system functioning on reversed Carnot cycle,