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Thermodynamics — Advanced

Statistical mechanics, entropy, and thermodynamic potentials

E
entropy_enjoyer 22 terms Jan 18, 2026
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Terms 22

1
Thermodynamic System
Isolated (no exchange), closed (energy only), or open (energy and matter)
2
State Function
Property depending only on current state, not path; e.g. U, H, S, G
3
Internal Energy (U)
Total kinetic and potential energy of molecules; dU = δQ − δW
4
Enthalpy (H)
H = U + PV; heat flow at constant pressure; ΔH < 0 is exothermic
5
Entropy (S)
Measure of disorder; dS = δQ_rev/T; S = k_B ln(Ω) (Boltzmann)
6
Gibbs Free Energy (G)
G = H − TS; spontaneous at constant T,P if ΔG < 0; minimum at equilibrium
7
Helmholtz Free Energy (A)
A = U − TS; minimum at equilibrium at constant T,V
8
Maxwell Relations
Thermodynamic identities from mixed second partial derivatives of state functions
9
Heat Capacity (Cv vs Cp)
Cv = (∂U/∂T)_V; Cp = (∂H/∂T)_P; Cp − Cv = nR for ideal gas
10
Equipartition Theorem
Each quadratic degree of freedom contributes ½k_BT to average energy
11
Carnot Efficiency
η = 1 − T_cold/T_hot; maximum efficiency for heat engine between two reservoirs
12
Clausius Inequality
∮ δQ/T ≤ 0; equality for reversible cycle; foundational statement of second law
13
Boltzmann Distribution
P(E) ∝ e^(−E/k_BT); probability of state with energy E at temperature T
14
Partition Function (Z)
Z = Σ e^(−βE_i); sum over all states; all thermodynamic quantities derivable from Z
15
Chemical Potential (μ)
μ = (∂G/∂n)_{T,P}; free energy per mole; determines direction of mass flow
16
Phase Equilibrium
Phases coexist when chemical potentials are equal: μ_liquid = μ_vapor
17
Clausius-Clapeyron Equation
dP/dT = ΔH_vap / TΔV; describes slope of phase boundary on P-T diagram
18
Van der Waals Equation
(P + a/V²)(V − b) = nRT; corrects ideal gas for intermolecular forces and volume
19
Activity and Fugacity
Real-gas and real-solution corrections to equilibrium expressions; replace P and concentration
20
Le Chatelier's Principle
System at equilibrium shifts to oppose imposed stress (temperature, pressure, concentration)
21
Hess's Law
ΔH for reaction = sum of ΔH for steps; enthalpy is a state function
22
Third Law and Absolute Entropy
Entropy of perfect crystal at 0 K = 0; allows calculation of absolute entropy values