Wall Collisions → Pressure
Δp = 2mv per elastic hit — pressure builds.
Key Notes
Gas molecules collide with container walls — these collisions create pressure.
Assume collisions are ELASTIC: kinetic energy and momentum conserved.
When molecule hits wall, momentum component perpendicular to wall REVERSES (Δp = 2m·v_perp).
Number of collisions per unit time per unit area = (1/4)·n·⟨v⟩, where n = number density.
Total force on wall = rate of momentum transfer = pressure × area.
Pressure P = (1/3)ρ·v_rms² — derived from kinetic theory.
Higher T ⇒ higher v_rms ⇒ higher pressure (at constant V, n).
Reflection assumed specular (angle of incidence = angle of reflection); real walls may have more complex interactions.
Formulas
Momentum change per collision
Perpendicular velocity component reverses.
Collision rate per unit area
Standard kinetic-theory result.
Pressure (kinetic theory)
Connects microscopic motion to macroscopic pressure.
Force on wall
Wall feels macroscopic force from countless molecular impacts.
Important Points
Pressure arises from MOMENTUM TRANSFER during collisions — not from molecular weight.
Each collision transfers 2m·v_perp of momentum to wall.
More molecules, faster molecules, or larger m ⇒ more pressure.
Pressure is uniform throughout a contained gas at equilibrium (Pascal's principle).
Walls feel a fluctuating force, but on macroscopic scales it averages to a steady pressure.
Elastic collision with wall ⇒ no energy lost ⇒ gas pressure stable indefinitely.
Wall Collisions → Pressure notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.