Maxwell-Boltzmann Distribution and Kinetic Theory of Pressure

Vocabulary flashcards covering Maxwell-Boltzmann distribution, speeds (mean, most probable, RMS), number density, and kinetic-derivation concepts for pressure.

Maxwell-Boltzmann distribution of speeds

The probability distribution of molecular speeds in an ideal gas at temperature T; f(v) = 4π(m/(2πkT))^(3/2) v^2 e^{-mv^2/(2kT)}; describes how speeds are distributed (zero at v=0 and skewed toward higher speeds).

Most probable speed (v_mp)

The speed at which the Maxwell-Boltzmann distribution peaks; v_mp = sqrt(2kT/m).

Mean speed ⟨v⟩

The average speed of particles in the distribution; ⟨v⟩ = sqrt(8kT/(πm)).

Root-mean-square speed v_rms

The square root of the mean of v^2; v_rms = sqrt(⟨v^2⟩) = sqrt(3kT/m).

Mean squared speed ⟨v^2⟩

The average of v^2 over the distribution; ⟨v^2⟩ = 3kT/m.

Number density n

Number of particles per unit volume; n = N/V.

Pressure from kinetic theory

Pressure arises from momentum transfer of gas particles colliding with container walls; P = NkB T / V (or P = n kB T).

Momentum transfer per wall collision

For an elastic collision with a wall perpendicular to x, the change in momentum along x is Δpx = 2 m vx.

Boltzmann constant k_B

Constant relating temperature and energy; kB ≈ 1.38×10^-23 J/K; kB = R/N_A.

Universal gas constant R

R = NA kB; R ≈ 8.314 J/(mol·K); relates P, V, T for n moles via PV = nRT.

Ideal gas law

PV = nRT (or PV = Nk_B T); fundamental relation for ideal gases connecting pressure, volume, and temperature.

Temperature effect on MB distribution

Increasing temperature broadens the distribution and shifts to higher speeds; heavier particles have slower speeds at the same T; at higher T speeds increase overall.