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Kinetic Theory of Gases · one page

Formula sheet

Notation: k · R · N_A · M · m' · m · ρ · n₀ = N/V · f · λ · v_rms, v_mean, v_mp. k = 1.38 × 10⁻²³ J/K, R = 8.314 J/mol·K, 1 atm = 76 cm Hg = 1.013 × 10⁵ Pa.

Learning path · Formula sheet · Practice set

Print and revise: Revision sheet (PDF) · Formula sheet (PDF, one page)

Part 2 · Gas Laws

P_{1} V_{1} = P_{2} V_{2}

Boyle's law

\frac{V _{1}}{V _{2}} = \frac{T _{1}}{T _{2}}

Charles and Gay-Lussac's law

\frac{V}{T} = constant

Charles and Gay-Lussac's law

P V = n R T

Ideal gas equation

P V = N k T

Ideal gas equation

n = \frac{N}{N _{A}} = \frac{m}{M}

Ideal gas equation

P = \frac{ρR T}{M}

Ideal gas equation

N_{A} = 6.023 \times 1 0^{23} mo l^{- 1}

Avogadro's number and hypothesis

k = \frac{R}{N _{A}} = 1.38 \times 1 0^{- 23} J/K

Avogadro's number and hypothesis

P_{total} = P_{1} + P_{2} + \dots + P_{n}

Dalton's law of partial pressures

M_{mix} = \frac{\sum n _{i} M _{i}}{\sum n _{i}}

Dalton's law of partial pressures

Part 3 · Real Gases, Change of Phase and van der Waals Equation

(P + \frac{a n ^{2}}{V ^{2}}) (V - nb) = n R T

van der Waals gas equation

Part 4 · Pressure of Air and Barometric Relation

P = h ρ g

Torricellian barometer

P = P_{0} e^{- M g h / R T}

Barometric relation

Part 5 · Distribution of Molecular Speeds

f (v) = 4 π N v^{2} (\frac{M}{2 π R T})^{3/2} e^{- M v^{2} /2 R T}

Maxwell–Boltzmann distribution

v_{rms} = \frac{3 R T}{M}

Average velocity, rms, mean and most probable speed

v_{mean} = \frac{8 R T}{π M}

Average velocity, rms, mean and most probable speed

v_{mp} = \frac{2 R T}{M}

Average velocity, rms, mean and most probable speed

Part 6 · Pressure, Kinetic Energy and Temperature

P = \frac{1}{3} ρ v_{rms}^{2}

Pressure exerted by a gas

P = \frac{1}{3} \frac{N}{V} m^{'} v_{rms}^{2}

Pressure exerted by a gas

P = \frac{2}{3} E (E = KE per unit volume)

Pressure exerted by a gas

E_{K} = \frac{1}{2} m^{'} v_{rms}^{2} = \frac{3}{2} k T

Kinetic energy of gas molecules

E_{total} = \frac{3}{2} N k T = \frac{3}{2} n R T

Kinetic energy of gas molecules

T = \frac{2}{3} \frac{E _{T}}{k}

Microscopic interpretation of temperature

Part 7 · Degrees of Freedom and Equipartition of Energy

⟨ v_{x}^{2} ⟩ = ⟨ v_{y}^{2} ⟩ = ⟨ v_{z}^{2} ⟩ = \frac{v _{rms}^{2}}{3}

Translational degrees of freedom

\frac{1}{2} m^{'} ⟨ v_{x}^{2} ⟩ = \frac{1}{2} k T

Translational degrees of freedom

E = \frac{f}{2} k T per molecule

Law of equipartition of energy

Part 8 · Internal Energy of a Gas

U = \frac{f}{2} n R T