state the basic assumptions of the kinetic theory of gases

Kinetic Theory of Gases

Objective

State the basic assumptions of the kinetic theory of gases.

Basic Assumptions

The kinetic theory of gases is built on a set of idealised assumptions that allow us to relate the microscopic motion of particles to macroscopic properties such as pressure and temperature.

Assumption	Explanation
Large number of particles	The gas consists of a huge number of identical atoms or molecules moving in random directions.
Negligible particle volume	The actual volume occupied by the particles themselves is tiny compared with the volume of the container; the gas can be treated as point particles.
No intermolecular forces (except during collisions)	Particles exert no attractive or repulsive forces on one another while they are apart; interactions occur only during brief, instantaneous collisions.
Elastic collisions	All collisions—particle‑particle and particle‑wall—are perfectly elastic, so kinetic energy is conserved in each collision.
Collision time ≪ mean free time	The duration of a collision is extremely short compared with the average time between successive collisions.
Kinetic energy ↔ temperature	The average translational kinetic energy of the particles is proportional to the absolute temperature: $$\langle E_{\text{kin}} \rangle = \frac{3}{2}\,k_{\mathrm B}T$$ where $k_{\mathrm B}$ is Boltzmann’s constant.

Implications of the Assumptions

• Pressure arises from the momentum transfer when particles strike the container walls.
• The ideal gas equation $PV = nRT$ can be derived from these assumptions.
• Root‑mean‑square speed of particles is given by $$v_{\text{rms}} = \sqrt{\frac{3k_{\mathrm B}T}{m}}$$ where $m$ is the mass of a single particle.