The four postulates of Kinetic Molecular Theory (KMT):

1. Gas molecules are in constant, rapid, random motion in all directions.
2. Molecular collisions are perfectly elastic (no energy loss; total KE is conserved).
3. Intermolecular forces are negligible (molecules interact only during collisions).
4. Average kinetic energy is directly proportional to absolute temperature: KE ∝ T.

Mechanism of pressure:

Step 1: A molecule moving toward a container wall. Step 2: Molecule collides with wall and bounces back (elastic collision → direction reverses). Step 3: Change in momentum = 2mv (mass × velocity change). Step 4: Rate of momentum transfer to wall = pressure. Step 5: More molecules or faster molecules → more momentum transfer → higher pressure.

Mathematical result: $P = \frac{1}{3}\frac{N}{V}mc^2$

where N = number of molecules, m = mass per molecule, $c^{2}$ = mean square speed.

Connection to ideal gas law: Setting PV = (1/3)Nm$c^{2}$ equal to PV = nRT: $c^2 = \frac{3RT}{M} \Rightarrow v_{rms} = \sqrt{\frac{3RT}{M}}$

This derivation proves that temperature is a measure of average molecular kinetic energy.