Thermodynamics & Statistical Physics

Isochoric Process

A thermodynamic process occurring at constant volume, during which no mechanical boundary work is performed.

ΔV = 0 ⇒ W = 0, Q = ΔU = n Cv ΔT J

Isothermal Process

A thermodynamic change in state occurring at a constant temperature throughout the system.

ΔT = 0 ⇒ ΔU = 0, Q = W = n R T ln(V2/V1) J

Thermodynamics & Statistical Physics

Joule-Thomson Effect

The temperature change experienced by a real gas when throttled through an insulated porous plug or valve at constant enthalpy.

μ_JT = (∂T / ∂P)_H K/Pa

Thermodynamics & Statistical Physics

Latent Heat of Fusion

The amount of thermal energy required to change a unit mass of a substance from solid to liquid at constant melting temperature.

Q = m L_f J/kg

Thermodynamics & Statistical Physics

Latent Heat of Vaporization

The thermal energy required to convert a unit mass of liquid into gas at constant boiling temperature.

Q = m L_v J/kg

Thermodynamics & Statistical Physics

Linear Thermal Expansion

The fractional change in length of a solid material per degree change in temperature.

ΔL = α L0 ΔT K⁻¹ (°C⁻¹)

Thermodynamics & Statistical Physics

Macrostate

The macroscopic state of a thermodynamic system defined by observable thermodynamic variables like pressure, volume, temperature, and total…

Defined by (P, V, T, N, U) N/A

Thermodynamics & Statistical Physics

Maxwell Relations

A set of thermodynamic equations derived from equality of second partial derivatives of thermodynamic potentials (U, H, F, G).

(∂T/∂V)_S = -(∂P/∂S)_V, (∂T/∂P)_S = (∂V/∂S)_P, etc. Various

Thermodynamics & Statistical Physics

Maxwell-Boltzmann Distribution

The probability distribution describing particle speeds in an ideal gas in thermal equilibrium.

f(v) = 4π (m / (2π kB T))^(3/2) v² exp(-m v² / (2 kB T)) s/m

Thermodynamics & Statistical Physics

Mean Free Path

The average distance traveled by a moving gas particle between successive collisions with other particles.

λ = 1 / (√2 π d² n_V) m

Thermodynamics & Statistical Physics

Microstate

A specific detailed microscopic configuration of a thermodynamic system, specifying exact positions and momenta of all constituent…

S = kB ln Ω N/A

Thermodynamics & Statistical Physics

Molar Heat Capacity

The heat energy required to raise the temperature of one mole of a substance by one Kelvin.

C_m = Q / (n ΔT), C_p - C_v = R J/(mol·K)

Thermodynamics & Statistical Physics

Most Probable Speed

The particle speed corresponding to the maximum peak of the Maxwell-Boltzmann speed distribution curve.

v_mp = √(2 kB T / m) = √(2 R T / M) m/s

Thermodynamics & Statistical Physics

Partition Function

The central mathematical function in statistical mechanics that encodes statistical properties of a system in thermodynamic equilibrium.

Z = ∑ exp(-E_i / (kB T)) = ∑ g_i exp(-E_i / (kB T)) Dimensionless

Thermodynamics & Statistical Physics

Principle of Mixtures

The heat conservation principle stating that in an isolated system, heat lost by hotter components equals heat gained by cooler components…

∑ Q = 0 ⇒ ∑ m_i c_i (T_f - T_i) = 0 J

Thermodynamics & Statistical Physics

Refrigerator / Heat Pump

A thermodynamic device operating in reverse that consumes mechanical work to extract heat from a cold region and reject it into a warmer…

COP_ref = Q_cold / W, COP_hp = Q_hot / W Dimensionless (Coefficient of Performance)

Thermodynamics & Statistical Physics

Reversible Process

An idealized thermodynamic process that can be reversed by infinitesimal changes in system variables without leaving any net trace on…

dS_universe = 0 N/A

Thermodynamics & Statistical Physics

Second Law of Thermodynamics

The law asserting that spontaneous physical processes increase total entropy in isolated systems, placing fundamental limits on heat engine…

ΔS_total ≥ 0 J/K

Thermodynamics & Statistical Physics

Stefan-Boltzmann Law

The physical law asserting that total radiant power emitted per unit surface area of a blackbody is proportional to the fourth power of its…

E = σ T⁴, σ = 5.670374 × 10⁻⁸ W/(m²·K⁴) W/m²

Thermodynamics & Statistical Physics

Sublimation

The direct phase transition of a substance from solid to gas state without passing through an intermediate liquid phase.

ΔH_sub = ΔH_fus + ΔH_vap J/kg or J/mol

Thermodynamics & Statistical Physics

Temperature

A macroscopic scalar measure of the average translational kinetic energy of constituent particles in a physical system.

1 / T = (∂S / ∂U)_V, E_avg = (3/2) kB T K (°C, °F)

Thermodynamics & Statistical Physics

Thermal Conduction

The transfer of thermal energy through a stationary medium via microscopic particle collisions and free electron movement without bulk…

q = -k A (dT/dx) (Fourier's Law) W/m² (k in W/(m·K))

Thermodynamics & Statistical Physics

Thermal Convection

The transfer of heat energy between a solid surface and an adjacent moving fluid, driven by bulk fluid motion.

q = h A (T_surface - T_fluid) (Newton's Law of Cooling) W (h in W/(m²·K))

Thermodynamics & Statistical Physics

Thermal Efficiency

The dimensionless ratio of net mechanical work produced by a heat engine to total thermal energy input supplied.

η = W_net / Q_input = 1 - (Q_out / Q_in) Dimensionless (%)