Kinetic TheoryNEET Physics · Class 11 · NCERT Chapter 12

You can expect 1 to 2 questions from Kinetic Theory in NEET 2027. The chapter has medium PYQ frequency. RMS speed, kinetic temperature, equipartition of energy and specific heats from degrees of freedom are the most repeated topics.

P equals one third of rho times v_rms squared, where rho is the mass density of the gas and v_rms is the root mean square speed. Equivalently, P V equals one third of N m v_rms squared, with N the number of molecules and m the mass of each molecule. This derivation assumes elastic collisions with the container walls and isotropic molecular motion.

Temperature is a direct measure of the average translational kinetic energy of the molecules. Specifically, the average translational KE per molecule equals three halves k_B T, where k_B is the Boltzmann constant 1.38 times 10 to the minus 23 J per K. So at a higher temperature, the molecules move faster on average.

For a Maxwell-Boltzmann distribution, v_p (most probable) is the smallest, then v_avg, then v_rms is the largest. The ratios are v_p : v_avg : v_rms equals approximately 1 : 1.128 : 1.224. v_rms equals the square root of (3 R T over M), v_avg equals the square root of (8 R T over pi M), v_p equals the square root of (2 R T over M).

Each quadratic degree of freedom of a molecule carries an average energy of half k_B T. So a monoatomic gas (3 translational degrees) has three halves k_B T per molecule. A diatomic gas at room temperature (3 translational plus 2 rotational) has five halves k_B T per molecule. This is why Cv equals (f over 2) R per mole.

The mean free path lambda is the average distance a molecule travels between successive collisions. lambda equals 1 over (square root of 2 times pi d squared n), where d is the molecular diameter and n is the number density. At standard conditions for air, lambda is about 70 nanometres, far larger than the molecular size.

The ideal gas law P V equals n R T fails at high pressures (where molecular volumes matter) and at low temperatures (where intermolecular forces matter). Real gases are described by the van der Waals equation. For NEET problems, you can almost always treat the gas as ideal unless the question explicitly says otherwise.