Kinetic Theory of Gases — Formula Sheet

ΔL = α · L₀ · Δθ

ΔA = β · A₀ · Δθ

ΔV = γ · V₀ · Δθ

β = 2α and γ = 3α

ΔQ = m · C · Δθ

m₁C₁(θ₁ - θ) = m₂C₂(θ - θ₂)

PV = (1/3) M c̄²

P = (1/3) ρ c̄²

c_rms = √(c̄²) = √(3P/ρ) = √(3RT/M) = √(3kT/m)

KE per molecule = (1/2)mc̄² = (3/2)kT

KE per mole = (3/2)RT

k = R/Nₐ

c_rms ∝ √T

Formula

ΔQ = mCΔθ, where ΔQ = heat supplied (J), m = mass (kg), C = specific heat (J kg⁻¹ K⁻¹), Δθ = temperature rise (K or °C).

Linear expansion

Δl = α l₀ Δθ, where α = coefficient of linear expansion (unit: K⁻¹ or °C⁻¹)

Combining PV = (1/3)NmĈ² with ideal gas law PV = nRT gives the kinetic interpretation of temperature.

Mean kinetic energy per molecule = (1/2)mĈ² = (3/2)kT, where k = Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹

Formula

c = ΔQ/(m × ΔT)

Linear expansion

Δl = αl₀ΔT

From kinetic theory

PV = (1/3)Nmc̄².