Ideal Gases · revision map · A-Level 9702, Topic 15

TOPIC 15 · IDEAL GASES
CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 · ONE-PAGE REVISION MAP
thelucidstem.com
IDEAL GASES15
The Mole & Avogadro Constant

Amount of substance is an SI base quantity; its unit is the mole. Count molecules, do not weigh them.

N = n × NA
N = number of molecules, n = number of moles
  • One mole holds NA identical particles.
  • NA ≈ 6.02 × 1023 mol−1 (Avogadro constant).
Equation of State

One law links pressure, volume and temperature for an ideal gas. T must be the absolute temperature in kelvin.

pV = nRT = NkT
k = R / NA
R = molar gas constant
k = Boltzmann constant
Kinetic Theory: Pressure from Motion

Pressure is molecules drumming on the walls. Each wall bounce reverses momentum, and that rate of change of momentum is the force.

  • Many tiny molecules in random motion; no forces between them; elastic collisions.
  • Time in a collision is negligible compared with time between collisions.
pV = ⅓Nm<c²>
N molecules, mass m, mean-square speed <c²>
wall feels pressure p
Molecular Energy & Temperature

Compare pV = ⅓Nm<c²> with pV = NkT: temperature is a measure of mean molecular kinetic energy.

½m<c²> = &frac32;kT
mean translational KE per molecule
  • Mean KE depends only on T in kelvin, not on the kind of gas.
  • Heating raises <c²>, so molecules move faster.
mean KE T / K slope = &frac32;k
BUILDS ON · Temperature · Particle model → IDEAL GASES → LEADS TO · Thermodynamics
thelucidstem.com · Cambridge AS & A Level Physics 9702 · TheLucidSTEM revision map