Kinetic Theory
1. Introduction to Kinetic Theory
- Kinetic theory explains the behavior of gases based on the idea that they are made of small particles in constant motion.
- Provides microscopic understanding of macroscopic properties like pressure, temperature, and volume.
2. Assumptions of Kinetic Theory of Gases
- Gas consists of a large number of identical molecules.
- Size of molecules is negligible compared to distance between them.
- Molecules move randomly in all directions.
- Collisions between molecules are perfectly elastic.
- No forces act between molecules except during collisions.
3. Pressure of an Ideal Gas
- Pressure arises due to collisions of molecules with container walls.
- Formula: P = (1/3) ρ ⟨v²⟩
- ρ = mass density of gas, ⟨v²⟩ = mean square speed
4. Kinetic Interpretation of Temperature
- Average kinetic energy of a gas molecule is directly proportional to temperature.
- E = (3/2) kT
- k = Boltzmann constant, T = temperature in Kelvin
5. Law of Equipartition of Energy
- Energy is equally distributed among all degrees of freedom.
- Each degree of freedom contributes (1/2)kT to energy per molecule.
6. Degrees of Freedom
- Number of independent ways in which a molecule can possess energy.
- Monoatomic gas: 3 degrees (translational)
- Diatomic gas: 5 degrees (3 translational + 2 rotational)
- Polyatomic gas: 6 degrees or more
7. Specific Heat Capacity of Gases
- At constant volume: Cv = (f/2)R
- At constant pressure: Cp = Cv + R
- Ratio of specific heats: γ = Cp / Cv
8. Mean Free Path
- Average distance a molecule travels between collisions.
- Formula: λ = 1 / (√2 π d² n)
- d = molecular diameter, n = number density