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Clausius’s Inequality

If 1 – 2 process is reversible adiabatic, then d QR = 0 or from (8.8) we have Ds = d QR / T = 0

or                                 S = C = constant i.e., 52= 51

Thus a reversible adiabatic process is an isentropic process. Fig. 8.7

 

8.5.2 Reversible Isothermal Process

QR = 2ʃ1 T Ds = T 2ʃ1 Ds

= T ( S2 –S1)

 

8.5.3 Carnot Cycle in T -S Plot

 

Refer Fig. 7.1 in section 7.1 of chapter 7, we have the following process.

Process 1 – 2 = reversible isothermal

Process 2- 3 = reversible adiabatic T

Process 3 – 4 = reversible isothermal

Process 4-1 = reversible adiabatic

ɳ carnot = Q1 – Q2 / Q1= T1 ( S2 – S1 – T2 ( S3 – S4) / T1( S2 – S1)

= T1 ( S2 – S1) – T2 ( S2 –S1)  T1 ( S2 –S1)

= ( T1 –T2) ( S2 – S1) / T1 ( S2 – S1) = T1 – T2 / T1 = 1 – T2 / T1