Entropy change for various process

Entropy change for constant pressure process

We know that

dS = ʃ δQ/T

for P = C, Q = mCpdT

dS = mCp ʃ dT/T

dS = mCp ln (T₂/T₁)

(V₁/V₂) = (T₁/T₂)

⇒(T₂/T₁) = (V₂/V₁)

dS = mCp ln(V₂/V₁)

Entropy change for isochoric process

We know that

dS = ʃ δQ/T

V = Constant

δQ = mCvdT

dS = mCv ln ʃ dT/T

(P₁/T₁) = (P₂/T₂)

(T₂/T₁) = (P₂/P₁)

dS = mCv ln (P₂/P₁)

Entropy change for isothermal process

We know that

dS = ʃ δQ/T

T = Constant, δQ = P₁V₁ ln (V₂/V₁)

dS = ʃ [P₁V₁ ln (V₂/V₁)]/T

PV = mRT ⇒P₁V₁ = mRT

dS = ʃ [mRT ln (V₂/V₁)]/T

= mR ln (V₂/V₁)

P₁V₁ = P₂V₂ = (V₂/V₁) = (P₁/P₂)

dS = mR ln (P₁/P₂)

Entropy change for reversible adiabatic process

dS = ʃ δQ/T

δQ = 0

dS = 0

⇒S = constant

As during reversible adiabatic process entropy does not change. Therefore it is called isentropic process.