A sample containing identical atoms (mass each) is confined to a cube of side length
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A sample containing N identical atoms (mass m each) is confined to a cube of side length L. The atoms move freely between perfectly elastic collisions with the walls.
(a) For a single atom moving only in the +x or −x direction with speed ∣vx∣, determine the change in its x-component of momentum in a single collision with the wall perpendicular to the x-axis.
(b) Calculate the time interval between two successive collisions of this atom with the same wall.
(c) Using your results from parts (a) and (b), determine the average force that this atom exerts on that wall.
(d) Generalize your result to all N atoms by replacing vx2 with the average value ⟨vx2⟩. Derive an expression for the pressure in terms of N, m, L, and ⟨vx2⟩.
(e) If the velocities are distributed isotropically, relate ⟨vx2⟩ to the root-mean-square speed vrms and write the final expression for the pressure in terms of number density n=L3N, m, and vrms.