LucidSTEM
A-LEVEL 9702 · A2 · TOPIC 15
Ideal gases
The chain of the topic: the mole counts molecules through the Avogadro constant, the equation of state pV = nRT = NkT links pressure, volume and temperature, and kinetic theory derives that pressure from molecular motion, ending at the average kinetic energy per molecule. Around the hexagon are the three ideas; above is what it builds on, below is where it leads.
TOPIC 15: IDEAL GASES
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T14 Temperature: the kelvin and absolute zero T11 Particle physics: atoms and molecules T3 Dynamics: force as rate of change of momentum 15.1
15.2
15.3
15.3
TOPIC 15
IDEAL
GASES
1 · THE MOLE
Count molecules, do not weigh them.
Amount of substance is an SI base quantity, unit mole.
One mole contains N = n × N_A particles.
The Avogadro constant fixes how many that is.
N_A = 6.02 × 10²³ mol−¹
particles per mole (the Avogadro constant)
n moles hold n N_A identical molecules
2 · EQUATION OF STATE
One law links pressure, volume and temperature.
An ideal gas obeys pV ∝ T at all p and V.
Use n and R for moles, or N and k for molecules.
T must be the absolute temperature, in kelvin.
pV = nRT = NkT
k = R / N_A
Boltzmann constant
p
V
higher T
isotherms: pV = constant at fixed T
3 · KINETIC THEORY: PRESSURE FROM MOTION
Pressure is molecules drumming on the walls.
Assume many tiny molecules, random motion, no
forces between them, elastic collisions, time in
collision negligible compared with time between.
Each wall bounce reverses momentum: that rate of
change of momentum is the force, hence pressure.
pV = ⅓ N m ‹c²›
N molecules, mass m, mean-square speed ‹c²›
c_rms = √‹c²›
v
wall feels pressure p
collisions push outward on every wall
4 · MOLECULAR ENERGY & TEMPERATURE
Temperature is average molecular kinetic energy.
Compare pV = ⅓Nm‹c²› with pV = NkT.
The mean translational KE depends only on T,
not on the kind of gas.
Heating raises ‹c²›, so molecules move faster.
½ m ‹c²› = ₃⁄₂ kT
E = ₃⁄₂ kT ∝ T
mean KE per molecule, T in kelvin
E
T / K
slope = ₃⁄₂ k
mean KE is proportional to absolute T
LEADS TO
T16 Thermodynamics: internal energy as total molecular KE T14 Temperature: a microscopic meaning for kelvin T25 Astronomy: hot gas in stars and nebulae Each reuses one idea: a gas of moving molecules carries energy set by its absolute temperature.
← Builds on IGCSE: Particle model of matter