PHYSICS · Multi-part · CBSE · Physics · Kinetic Theory · Kinetic Theory
Problem
A single helium atom of mass m moves in a straight, frictionless, one-dimensional tube and collides elastically with a rigid end wall that is perpendicular to the tube’s axis. Immediately before the collision the atom’s speed is v0. Assume the duration of the collision is negligible compared with the time between successive collisions.
Parts a–c relate microscopic collision details to the macroscopic idea of pressure.
(a) Describe qualitatively how the change in the atom’s momentum during one collision can result in a measurable force on the wall when averaged over many collisions.
(b) The atom strikes the same wall repeatedly with period T. Express the average force Favg exerted on the wall in terms of m, v0, and T, and explain each step in your reasoning.
(c) The tube is then filled with many identical atoms moving in random directions. Explain why, despite the fact that collisions with the wall occur only at the boundary, the pressure inside the gas is considered uniform throughout the entire volume.