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Thermodynamics & Statistical Physics

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Thermodynamics & Statistical Physics

Adiabatic Process

A thermodynamic process in which no heat is transferred into or out of the system.

Q = 0 ⇒ ΔU = -W, P V^γ = constant J
Thermodynamics & Statistical Physics

Avogadro's Law

The law stating that equal volumes of all ideal gases at the same temperature and pressure contain equal numbers of molecules.

V1 / n1 = V2 / n2 (at constant P, T) m³/mol
Thermodynamics & Statistical Physics

Boyle's Law

An ideal gas law stating that pressure is inversely proportional to volume at constant temperature.

P1 V1 = P2 V2 (at constant T) Pa·m³
Thermodynamics & Statistical Physics

Brownian Motion

The random, erratic wandering movement of microscopic particles suspended in a fluid caused by relentless collisions with fast-moving fluid…

⟨x²⟩ = 2 D t, D = kB T / (6 π η r)
Thermodynamics & Statistical Physics

Calorimetry

The experimental science and practice of measuring heat energy changes during chemical or physical transformations.

Q_lost = Q_gained ⇒ m1 c1 (T1 - T_f) = m2 c2 (T_f - T2) J
Thermodynamics & Statistical Physics

Carnot Cycle

An ideal reversible thermodynamic cycle operating between two thermal reservoirs, establishing maximum theoretical efficiency for heat…

η_Carnot = 1 - (T_cold / T_hot) Dimensionless (%)
Thermodynamics & Statistical Physics

Charles's Law

An ideal gas law stating that gas volume is directly proportional to absolute thermodynamic temperature at constant pressure.

V1 / T1 = V2 / T2 (at constant P) m³/K
Thermodynamics & Statistical Physics

Chemical Potential

The change in system free energy per added particle at constant temperature and pressure.

μ = (∂G / ∂N)_{T,P} = (∂U / ∂N)_{S,V} J/particle (or J/mol)
Thermodynamics & Statistical Physics

Critical Point

The endpoint of a phase equilibrium curve in a P-T phase diagram where coexisting liquid and vapor phases become indistinguishable.

(∂P/∂V)_T = 0, (∂²P/∂V²)_T = 0 Pa, K
Thermodynamics & Statistical Physics

Deposition

The direct phase transition of a gas into a solid without passing through an intermediate liquid phase.

ΔH_dep = -ΔH_sub J/kg or J/mol
Thermodynamics & Statistical Physics

Emissivity

The dimensionless ratio of thermal energy radiated by a surface to that radiated by an ideal blackbody at the exact same temperature.

ε = E_surface / E_blackbody (0 ≤ ε ≤ 1) Dimensionless
Thermodynamics & Statistical Physics

Enthalpy

A thermodynamic potential defined as internal energy plus the product of pressure and volume, representing total heat content under…

H = U + P V, ΔH = Q_p J
Thermodynamics & Statistical Physics

Entropy

A fundamental thermodynamic property measuring the degree of microscopic disorder, randomness, or thermal energy unavailable for mechanical…

dS = dQ_rev / T, S = kB ln Ω J/K
Thermodynamics & Statistical Physics

Equipartition Theorem

A classical statistical mechanics theorem stating that every independent quadratic degree of freedom contributes ½ kB T to a system's…

E_avg = (f / 2) kB T J
Thermodynamics & Statistical Physics

First Law of Thermodynamics

A statement of universal energy conservation applied to thermodynamic systems, asserting that internal energy change equals net heat added…

ΔU = Q - W J
Thermodynamics & Statistical Physics

Gay-Lussac's Law

An ideal gas law stating that gas pressure is directly proportional to absolute thermodynamic temperature at constant volume.

P1 / T1 = P2 / T2 (at constant V) Pa/K
Thermodynamics & Statistical Physics

Gibbs Free Energy

A thermodynamic potential measuring maximum reversible work obtainable from a system at constant temperature and pressure.

G = H - T S, ΔG = ΔH - T ΔS J
Thermodynamics & Statistical Physics

Graham's Law of Effusion

The law stating that rate of effusion or diffusion of a gas is inversely proportional to square root of its molar mass.

Rate1 / Rate2 = √(M2 / M1) mol/s or m³/s
Thermodynamics & Statistical Physics

Heat Engine

A physical device that converts thermal energy absorbed from a high-temperature heat source into mechanical work, discharging waste heat to…

W = Q_hot - Q_cold, η = W / Q_hot W (J/s)
Thermodynamics & Statistical Physics

Helmholtz Free Energy

A thermodynamic potential measuring maximum reversible work obtainable from a closed system at constant temperature and volume.

F = U - T S, dF = -S dT - P dV J
Thermodynamics & Statistical Physics

Ideal Gas Law

The equation of state relating pressure, volume, temperature, and quantity of an ideal gas composed of non-interacting point particles.

P V = n R T = N kB T Pa·m³ = J
Thermodynamics & Statistical Physics

Intensive vs Extensive Properties

Classification of thermodynamic properties based on whether they depend on system size or amount of matter.

Extensive: U, V, S, m, H; Intensive: T, P, ρ, μ Various
Thermodynamics & Statistical Physics

Internal Energy

The total microscopic energy contained within a thermodynamic system, comprising kinetic energies of particle…

U = (f/2) n R T (for ideal gas) J
Thermodynamics & Statistical Physics

Isobaric Process

A thermodynamic change in state occurring under constant pressure conditions.

ΔP = 0, W = P ΔV, Q = ΔH = n Cp ΔT J