Chapter 13 · Class 11-12 & JEE/NEET
Kinetic Theory of Gases
48 topics in 15 parts
Ideal gas law Pressure from molecular motion Root-mean-square speed RMS speed using molecular mass Mean molecular speed Most probable speed
Key ideas
4. Systematic Comparison & Parameter Classifications
| Body Shape | Axis of Rotation | Moment of Inertia (I) | Shape Factor (k² / R²) |
|---|---|---|---|
| Thin Ring / Hollow Cylinder | Central Axis Perpendicular to Plane | M R² | 1.0 (Slowest Down Incline) |
| Solid Disc / Solid Cylinder | Central Axis Perpendicular to Plane | (1/2) M R² | 0.50 |
| Solid Sphere | Diameter Axis | (2/5) M R² | 0.40 (Fastest Down Incline) |
| Spherical Shell (Hollow) | Diameter Axis | (2/3) M R² | 0.67 |
| Uniform Rod (Length L) | Through Center Perpendicular to Length | (1/12) M L² | L² / (12 R²) |
Exam Worked Example
Problem: A solid sphere and a solid cylinder of equal mass M and radius R roll down the same inclined plane without slipping from rest. Find the ratio of their accelerations down the incline.
● Step 1: Formula for linear acceleration in pure rolling: a = (g sin θ) / (1 + k²/R²).
● Step 2: For solid sphere, k²/R² = 2/5 = 0.4. Therefore, a_sphere = (g sin θ) / (1 + 2/5) = 5/7 g sin θ ≈ 0.714 g sin θ.
● Step 3: For solid cylinder, k²/R² = 1/2 = 0.5. Therefore, a_cyl = (g sin θ) / (1 + 1/2) = 2/3 g sin θ ≈ 0.667 g sin θ.
● Step 4: Ratio a_sphere / a_cyl = (5/7) / (2/3) = (5 * 3) / (7 * 2) = 15 / 14 ≈ 1.07. The solid sphere reaches the bottom first!
Checkpoint
1. When a ballet dancer pulls her arms inward during a spin on smooth ice, what happens to her kinetic energy?
All 48 topics in Kinetic Theory of Gases
Assumption of Ideal Gases (or Kinetic Theory of Gases)
- Pressure of an Ideal Gas
- Various Types of Speeds of Gas Molecules
- Assumptions of Ideal Gas Model
- Molecular Motion & Collisions
KTG (Derivation of Pressure)
- Derivation of Pressure Expression
- Momentum Transfer to Vessel Walls
Derivation of Gas Laws from Kinetic Theory of Gases
- Avogadro's Law
- Boyle's Law
- Charles's Law
- Dalton's Law of Partial Pressure
- Gay-Lussac's Law of Diffusion
- Graham's Law of Diffusion
Gas Laws
- Boyle's & Charles's Laws Applications
- Gas Law Graphs & P-V-T Relations
- Gas Density & Molar Mass
- Piston & Vessel Equilibrium Problems
Equation of State or Ideal Gas Equation
- PV = nRT Calculations
- Number of Molecules & Moles Calculation
- Variation of Pressure & Density
Relation Between Pressure & Kinetic Energy
- Pressure in Terms of Translational Kinetic Energy
- Energy Density of Ideal Gas
Average Translational Kinetic Energy Per Molecule of Gas
- Kinetic Energy Per Molecule
- Kinetic Energy Per Mole & Per Gram
- Temperature Dependence of Kinetic Energy
Maxwell's Speed Distribution Law
- Most Probable, Average & RMS Speeds
- Maxwell-Boltzmann Speed Distribution Curve
- Temperature & Mass Dependence of Distribution
Mean Free Path
- Formula & Functional Dependencies
- Collision Frequency & Mean Free Time
- Molecular Diameter & Number Density Effects
Degree of Freedom
- Degrees of Freedom of Monatomic, Diatomic & Polyatomic Gases
- Vibrational Degrees of Freedom
Law of Equipartition of Energy
- Energy Per Degree of Freedom
- Total Translational & Rotational Kinetic Energy
Internal Energy & Ideal Gas Equation
- Internal Energy of Monatomic & Polyatomic Gases
- Change in Internal Energy
Different Processes in Ideal Gas
- Isobaric Process
- Isochoric Process
- Isothermal Process
- Polytropic & Arbitrary Processes
Molar Specific Heats & Gas Mixtures
- Molar Specific Heat Capacities (Cv & Cp)
- Ratio of Specific Heats (Gamma)
- Equivalent Molar Mass & Specific Heat of Gas Mixtures
- Mixing of Gases in Insulated Vessels
Real Gases & Van der Waals Equation
- Deviations from Ideal Behavior
- Van der Waals Equation & Constants
- Compressibility Factor (Z)
- Critical Constants