Entropy is a thermodynamics property of a system which can be defined as the amount of heat contained in a substance and its interaction between two state in a process. Entropy increase with addition of heat and decrease when heat is removed.
dQ = T.dS; T = Absolute Temperature and dS = Change in entropy.
dS = dQ/ T
*T- Diagrams**
The area under T-* diagram represent the heat added or rejected. Entropy is a point function From first las
dQ = dU + dW
T.dS = dU + P.dV
Carnot efficiency η = (T1– T2)/T1 = dW/dQ
dW = η.dQ; If T1 – T2 = 1; η =1/T
dW = dQ/T = dS;
if Temperature difference is one.
dS represents maximum amount of work obtainable per degree in temperature.
Unit of Entropy = KJ/K
Principle of Entropy
From claucius inequality
∮ dQ T/ 0
Since dS = dQ/T for reversible process and dS > dQ/T for irreversible process
∮dQ T/ ≤ ∮ dS; or dQ/T d ≤ dS or dS e ≥ dQ/T
Change in Entropy During Process
1. V = C PROCESS
dQ = mCVdT
or, dQ/T = mCVdT/T
dS = mCVdT/T; or S2 – S1 = mCV ln P2/P1
2. P = C; PROCESS
dQ = mCPdT
or, dQ/T = mCPdT/T
dS = mCPdT/T; or S2 – S1 = mCP lnT2/T1 = mCP ln V2/V1
3. T = C; PROCESS
dQ = mRT ln V2/V1
or, dQ/T = (mRT/T) ln V2/V1
or S2 – S1 = mR ln V2/V1 = m(CP – CV) ln V2/V1 = mR ln P1/P2
4. PVy = C; PROCESS
dQ = 0; dS = 0
5. PVn = C; PROCESS
dQ = [(γ – n)/ (γ – 1)] dW
= [(γ – n)/ (γ – 1)] PdV
dQ/T = [(γ – n)/ (γ – 1)] PdV/T
dS = [(γ – n)/ (γ – 1)] mRdV/V
or S2 – S1 = [(γ – n)/ (γ – 1)] mR ln V2/V1
