Chapter 23 · Class 11-12 & JEE/NEET
Thermal Properties of Matter
49 topics in 6 parts
Celsius-Fahrenheit conversion Celsius-Kelvin conversion Linear thermal expansion Length after thermal expansion Area thermal expansion Volume thermal expansion
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 49 topics in Thermal Properties of Matter
Heat & Thermometry
- Temperature & Zeroth Law of Thermodynamics
- Scales of Temperature & Conversions
- Thermometers & Temperature Measurement
Thermal Expansion
- Linear & Superficial Expansion
- Volume & Cubical Expansion
- Expansion in Liquids
- Anomalous Expansion of Water
- Bimetallic Strip
- Thermal Stress in Rigidly Fixed Rod
- Variation of Density & Upthrust with Temperature
- Effect of Temperature on Pendulum Time Period
- Error in Scale Reading
- Expansion of Cavity
- Thermal Effects on Rotation
Calorimetry
- Principle of Calorimetry
- Specific Heat Capacity & Heat Capacity
- Phase Change & Latent Heat
- Heating Curve
- Water Equivalent
- Mechanical Equivalent of Heat
- Units of Heat
Conduction
- Laws of Thermal Conductivity & Coefficient
- Rate of Heat Flow in Differential Form
- Conduction in Metallic Rod
- Steady-State Conduction
- Temperature Gradient
- Thermal Resistance to Conduction
- Slabs in Series & Parallel Combination
- Equivalent Thermal Conductivity & Composite Slabs
- Electrical Analogy for Thermal Conduction
- Radial Heat Conduction
- Growth of Ice on Lake
- Searle's Experiment
- Transient Conduction & Pre-Steady State
Convection
- Modes of Heat Transfer
- Natural & Forced Convection
Radiation
- Properties of Radiation & Interaction with Matter
- Emissive Power, Absorptive Power & Emissivity
- Perfectly Black Body
- Prevost's Theory of Heat Exchanges
- Kirchhoff's Law
- Energy Spectrum of Black Body
- Stefan-Boltzmann Law
- Rate of Loss of Heat
- Temperature of the Sun & Solar Constant
- Wien's Displacement Law
- Newton's Law of Cooling
- Initial Rate of Fall in Temperature
- Determination of Specific Heat of Liquid by Cooling