Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Quick Summary
Kinetic theory provides a microscopic explanation for macroscopic gas behaviour (gas laws, temperature, pressure). It connects molecular motion to measurable quantities. Important for both board exams and NEET.
Ideal Gas Laws
| Law | Statement | Formula |
|---|---|---|
| Boyle's | P ∝ 1/V (constant T) | PV = constant |
| Charles' | V ∝ T (constant P) | V/T = constant |
| Gay-Lussac's | P ∝ T (constant V) | P/T = constant |
| Avogadro's | Equal volumes at same T, P contain equal molecules | — |
| Ideal gas | Combined | PV = nRT |
Universal gas constant: R = 8.314 J mol⁻¹ K⁻¹
Boltzmann constant: k = R/Nₐ = 1.38 × 10⁻²³ J/K
Kinetic Theory — Key Results
Pressure of an ideal gas: P = (1/3) ρ v²_rms = (1/3)(mN/V)v²_rms
Average kinetic energy per molecule: KE = (3/2)kT
Temperature is a measure of average kinetic energy of molecules.
Molecular Speeds
| Speed | Formula |
|---|---|
| RMS speed | v_rms = √(3RT/M) |
| Mean speed | v_mean = √(8RT/πM) |
| Most probable speed | v_mp = √(2RT/M) |
Order: v_mp < v_mean < v_rms
Degrees of Freedom and Specific Heats
| Gas type | Degrees of freedom (f) | Cᵥ | Cₚ | γ |
|---|---|---|---|---|
| Monatomic | 3 | (3/2)R | (5/2)R | 5/3 |
| Diatomic | 5 | (5/2)R | (7/2)R | 7/5 |
| Polyatomic | 6 | 3R | 4R | 4/3 |
Law of equipartition of energy: Each degree of freedom contributes ½kT to average kinetic energy.
Mean Free Path
λ = 1 / (√2 π d² n)
where d = diameter of molecule, n = number density
Important Questions
One Mark
- State Boyle's law.
- Define mean free path.
- What is Boltzmann's constant?
- How many degrees of freedom does a diatomic gas have?
- What is the relation between average KE and temperature?
Short Answer (3 marks)
- Derive the ideal gas equation from the three gas laws.
- State the law of equipartition of energy. Calculate Cᵥ for a monatomic and diatomic gas.
- Explain the three types of molecular speeds and state their formulae.
Long Answer (5 marks)
- Derive the expression for pressure exerted by an ideal gas using kinetic theory. Hence derive the ideal gas equation PV = nRT.
- State the postulates of kinetic theory. Show that temperature is a measure of average kinetic energy of molecules.
Common Mistakes
- Using mass in kg instead of molar mass M in kg/mol in the RMS speed formula.
- Forgetting to convert temperature to Kelvin.
- Confusing degrees of freedom (3 for monatomic, 5 for diatomic) with number of molecules.
Board Exam Tips
- Derivation of gas pressure from kinetic theory is a standard 5-mark question.
- Numerical on RMS speed and kinetic energy appear frequently.
- NEET: Know all three speed formulas and their ratio v_mp : v_mean : v_rms = 1 : 1.128 : 1.225.