Kinetic Theory of Gases Revision Notes for NEET Physics PDF Download
🌡️ KINETIC THEORY OF GASES · KTG
Ideal gas • Pressure derivation • Kinetic energy • Degrees of freedom • Specific heats • Maxwell distribution • NEET problems
📐 IDEAL GAS EQUATION
PV = nRT (n = number of moles, R = 8.314 J/mol·K)
Also: PV = NkT (N = number of molecules, k = Boltzmann constant = 1.38×10⁻²³ J/K)
R = NAk (Avogadro's number NA = 6.022×10²³ mol⁻¹)
📜 POSTULATES OF KINETIC THEORY
- Gas consists of large number of molecules in random motion.
- Molecules are point masses (volume negligible).
- No intermolecular forces except during elastic collisions.
- Collisions with walls cause pressure.
- Average kinetic energy ∝ absolute temperature.
⚡ PRESSURE & RMS SPEED
Pressure: P = (1/3) ρ vrms² = (1/3) (Nm/V) vrms²
RMS speed: vrms = √(3RT/M) = √(3kT/m)
Mean speed: vavg = √(8RT/πM) = √(8kT/πm)
Most probable speed: vmp = √(2RT/M) = √(2kT/m)
📊 Maxwell speed distribution curve
🔋 KINETIC ENERGY & TEMPERATURE
Average translational KE per molecule: Eavg = (3/2) kT
For 1 mole: U = (3/2) RT (monatomic ideal gas)
Internal energy depends only on temperature for ideal gas.
🎯 DEGREES OF FREEDOM (f) & EQUIPARTITION
Each degree of freedom contributes (1/2)kT of energy per molecule.
Monatomic (He, Ar)
f = 3 (translational)
U = (3/2)nRT
Cv = (3/2)R, Cp = (5/2)R, γ = 5/3 = 1.67
Diatomic (O₂, N₂)
At room temp: f = 5 (3 trans + 2 rot)
U = (5/2)nRT
Cv = (5/2)R, Cp = (7/2)R, γ = 7/5 = 1.4
Polyatomic (non‑linear)
f = 6 (3 trans + 3 rot)
U = 3nRT
Cv = 3R, Cp = 4R, γ = 4/3 ≈ 1.33
📊 RELATION BETWEEN Cp & Cv
Cp – Cv = R (molar specific heats)
γ = Cp/Cv = 1 + 2/f
For monatomic: γ = 5/3; diatomic: γ = 7/5; polyatomic: γ = 4/3.
📏 MEAN FREE PATH (λ)
Average distance between collisions: λ = 1/(√2 π d² n) (d = molecular diameter, n = number density)
Also λ = kT/(√2 π d² P)
💡 NEET TIPS & SHORTCUTS
- vrms = √(3RT/M) → use in pressure problems.
- For a mixture, average molar mass = total mass / total moles.
- Internal energy of ideal gas depends only on temperature.
- In adiabatic process, TVγ–1 = constant, PVγ = constant.
⚠️ COMMON MISTAKES
- Using vrms formula with mass in grams instead of kg.
- Confusing degrees of freedom for different gases at different temperatures.
- Assuming Cp – Cv = R for solids/liquids (only for ideal gas).
- Forgetting that k = R/NA in energy equations.
📌 QUICK REVISION CARD
Ideal gas law: PV = nRT = NkT
vrms: √(3RT/M)
Average KE: (3/2)kT per molecule
Cp – Cv = R
γ = 1 + 2/f
Mean free path: λ = 1/(√2 π d² n)