Kinetic Theory of Gases
What this domain tests
Kinetic Theory of Gases tests the ideal gas equation, kinetic interpretation of pressure and temperature, rms and mean speeds, degrees of freedom, specific heats and mean free path.
Core rules
- PV = nRT = NkT.
- Pressure P = (1/3)(mN/V)v_rms².
- v_rms = √(3RT/M) = √(3kT/m); v_avg = √(8RT/πM); v_mp = √(2RT/M).
- Average translational KE per molecule = (3/2)kT.
- Degrees of freedom: monatomic f = 3; diatomic f = 5 at ordinary temperatures; Cp − Cv = R; γ = Cp/Cv.
Worked example
Find v_rms for oxygen at 300 K. M = 32 g/mol = 0.032 kg/mol, R = 8.314 J mol⁻¹ K⁻¹. v_rms = √(3RT/M) = √(3 × 8.314 × 300/0.032) = √233,900 ≈ 484 m/s. Using 32 instead of 0.032 gives a value about 5.7 times too small, a common unit slip.
Traps
Forgetting to convert molar mass to kg/mol; using v_rms when the question asks for mean or most probable speed; assigning f = 6 to a diatomic gas at room temperature; treating Cp and Cv as equal; applying ideal-gas relations to a real gas near condensation without qualification.