💨 Kinetic Theory

1. Ideal Gas Equation

Combining Boyle's, Charles', and Avogadro's laws gives the ideal gas equation.

PV = nRT Where P is pressure, V is volume, n is number of moles, R is gas constant, and T is absolute temperature.

2. Postulates of Kinetic Theory

A gas consists of large number of identical, tiny, spherical molecules.
Molecules are in constant random motion.
Collisions between molecules and container walls are perfectly elastic.
No intermolecular forces of attraction (except during collisions).
The volume of molecules is negligible compared to the container volume.

3. Pressure Exerted by Gas

P = (1/3) ρ (v_rms)². Pressure is directly proportional to the density and the square of the root-mean-square speed of molecules.

Kinetic Interpretation of Temperature: The average kinetic energy of a gas molecule is directly proportional to the absolute temperature. E = (3/2) kT.

4. Law of Equipartition of Energy

💨 Degrees of Freedom (f)

The number of independent ways a molecule can possess energy.

Monatomic gas: f=3. Diatomic gas: f=5. Polyatomic: f=6.

Law of Equipartition: In thermal equilibrium, the total energy of the system is shared equally among all active degrees of freedom, and the average energy per degree of freedom is ½ kT.

5. Mean Free Path

The average distance traveled by a molecule between two successive collisions. λ = 1 / (√2 π n d²).