state the basic assumptions of the kinetic theory of gases

Published by Patrick Mutisya · 14 days ago

Kinetic Theory of Gases – A-Level Physics 9702

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.

AssumptionExplanation
Large number of particlesThe gas consists of a huge number of identical atoms or molecules moving in random directions.
Negligible particle volumeThe 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 collisionsAll collisions—particle‑particle and particle‑wall—are perfectly elastic, so kinetic energy is conserved in each collision.
Collision time ≪ mean free timeThe duration of a collision is extremely short compared with the average time between successive collisions.
Kinetic energy ↔ temperatureThe 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.

Suggested diagram: Schematic showing particles moving randomly, colliding with each other and with the walls of a container, illustrating momentum transfer that produces pressure.