Second Law of Thermodynamics: key terms and equations.
S = entropy (another state function).
∆S = ∫ qrev / T
Even if a system undergoes an irreversible process its entropy change MUST be
calculated via a reversible path that takes us from the initial to final state, this is
why the equation includes the term “qrev” - the reversible heat exchange.
How to calculate ∆S of a system for different processes:
1. Reversible Isothermal:
(a) expansions/compressions: ∆S = nRln(V2/V1) = nRln(P1/P2)
(b) phase changes (melting, vaporization): ∆S = ∆Hmelt,vap/Tmelt,vap
∆Hmelt,vap = enthalpy at equilibrium (i.e. normal) melting or boiling point.
2. Temperature is changing: q is a function of T
(a) const. P process: ∫ (nCP /T)dT
(b) const V process: ∫ (nCV /T)dT
(c) Reversible adiabatic: ∆S = 0
3. Complex or irreversible processes: construct multi-step reversible path from
initial to final state using one or more of the above steps.
Entropy and Disorder.
For system at constant internal energy and volume, the equilibrium state has the
highest disorder; disorder and entropy are synonymous.
S = klnΩ where Ω = total number of possible distributions
lnΩ = ln(N!/NA!NB!) = NlnN – NAlnNA - NBlnNB for large N values.
G = Gibbs free energy = H – TS
A= Helmholtz free energy = U – TS
∆G = ∆H - ∆(TS)
At const. T and P: ∆G = ∆H – T∆S
At equilibrium systems minimize their free energy: this is achieved by their
attempting to lower their H and maximize their S.
Thermal expansion / compressibility.
Thermal expansion = α =1/V(dV/dT)P units K-1
Compressibility = β = -1/V(dV/dP)T units atm-1
For any material Cp – Cv = TVα2/β
Obtained by combining 1st and 2nd laws: dG = VdP – SdT