Chapter 24 · Class 11-12 & JEE/NEET
Thermodynamics
33 topics in 9 parts
First law of thermodynamics First law of thermodynamics Thermodynamic work Isobaric work Isochoric work Isothermal ideal-gas work
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 33 topics in Thermodynamics
Thermodynamic System
- Zeroth Law of Thermodynamics
- State Variables
- Ideal Gas Law
- Gas Law Graphs
- Pressure of an Ideal Gas
- Quasi-Static Process
- Thermodynamic Process
- Piston & Vessel Problems
- Work Done by an Ideal Gas
- P–V Diagram Analysis
Heat in Thermodynamics
- Heat (Q)
- Specific Heat of Gases
- Molar Heat Capacity
- Heat Capacity Ratio
- Degrees of Freedom
Gaseous Mixture
- Equilibrium State of Mixed Gases
- Specific Heat & Molar Mass of Mixture
First Law of Thermodynamics
- Internal Energy
- Heat, Work & Internal Energy Relation
Different Processes in First Law of Thermodynamics
- Adiabatic Process
- Cyclic & Non-Cyclic Process
- Free Expansion
- Isobaric Process
- Isochoric or Isometric Process
- Isothermal Process
- Polytropic Process
Reversible & Irreversible Processes
- Irreversible Process
- Reversible Process
Heat Engine
- Efficiency
- Otto Cycle
Second Law of Thermodynamics
- Carnot Engine
- Entropy
Refrigerator & Heat Pump
- Coefficient of Performance