Carnot Cycle - thermodynamics:

Carnot Cycle: Sadi carnot; this is based on second law of thermodynamics introduced the concepts of reversibility and cycle in the year 1824. He shows that the temperature of heat source and heat sink are basis for determining thermodynamics efficiency of reversible cycle. He showed that all such cycles should reject heat to the sink and efficiency is never 100 percent. 

To show a non existing reversible cycle, Carnot invented his famous but hypothetical cycle called as Carnot cycle. Carnot cycle comprise of of two isothermal and two reversible adiabatic or isentropic operation. The cycle is illustrated in P-V and T-S diagrams

Operation 1-2: T = C

Q₁  = W_1-2  = P₁V₁lnV₂/V₁  = mRT₁lnV₂/V₁

Operation 2-3: PV_y  = C

Q = W = 0

Operation 3-4:  T = C

Q₂  = W_3-4  = P₃V₃lnV₄/V₃  = P₃V₃lnV₄/V₃   = mRT₂lnV₃/V₄

Operation 4-1: PV_y  = C

Q = W = 0Net WD = mRT₁lnV₂/V₁ - mRT₂lnV₃/V₄ ; As the compression ratio = V₃/V₄ = V₂/V₁, T₂ = T₃

W = mRlnV3/V4(T₁  - T₃)