The Molecular Wind

NODE 01

Particle Picture

• Matter consists of microscopic particles.
• In continuous motion.
• Macro behaviour emerges from enormous numbers.

NODE 02

Atoms & Molecules

• Elements vs Compounds.
• Molecular mass, atomic mass.
• O₂, N₂, H₂O.

NODE 03

Mole Concept

N = nNₐ

• Bridge between particles and measurable quantities.
• Avogadro constant (Nₐ).
• Molar mass.

NODE 04

Ideal Gas Model

• Particles are tiny relative to volume.
• Random motion, elastic collisions.
• Negligible intermolecular attraction.

NODE 05

Microscopic Pressure

• Molecules move → collide with walls.
• Change momentum → transfer momentum.
• Micro collisions = Macro pressure.

NODE 06

Kinetic Theory of P

P = ⅓ρc²

• P = 1/3 ρ cᵣₘₛ².
• Equivalent: PV = 1/3 Nm cᵣₘₛ².
• Connects P & V to invisible motion.

NODE 07

Microscopic Temp

K_avg ∝ T

• Avg translational KE per particle = 3/2 kT.
• Higher T → greater avg molecular KE.
• Temperature has a microscopic meaning.

NODE 08

Boltzmann Constant

k = R/Nₐ

• The microscopic bridge.
• Connects particle-level Physics to mole-level Physics.

NODE 09

RMS Speed

vᵣₘₛ=√(3kT/m)

• Root-mean-square speed.
• Depends on Temperature and Molecular Mass.
• Lighter molecules move faster at same T.

NODE 10

Characteristic Speeds

V_pV_avgV_rms

• Most probable ≠ Average ≠ RMS speed.
• Gas molecules do not all travel at one speed.

NODE 11

Maxwell-Boltzmann

• Molecular speed distribution curve.
• T increases → curve broadens, shifts right.
• Mass increases → characteristic speeds decrease.

NODE 12

Molecular Collisions

• Elastic collisions in ideal gas.
• Momentum transfer.
• Produces stable macroscopic pressure.

NODE 13

Mean Free Path

• Average distance traveled between collisions.
• More crowded gas → shorter mean free path.
• Depends on density and molecular size.

NODE 14

Collision Frequency

1/τ

• Collision interval and frequency.
• Connects invisible world to transport properties.

NODE 15

Classical Gas Laws

Boyle: PV=CCharles: V/T=C

• Boyle's, Charles', Pressure, Avogadro's laws.
• Synthesize into PV = nRT.

NODE 16

Boyle's Law (Micro)

Vol↓ = Collisions↑

• Why P rises when V drops at constant T?
• Smaller volume → more frequent wall collisions → greater pressure.

NODE 17

Charles' Law (Micro)

Temp↑ = KE↑

• At constant P: T↑ means KE↑.
• Gas expands to keep pressure balanced.

NODE 18

Pressure-Temp Rel

P ∝ T

• At constant V: T↑ → molecular speeds ↑.
• → collision momentum transfer ↑ → P ↑.

NODE 19

Ideal Gas Eq

PV = nRTPV = NkT

• Both forms describe the same system.
• Macroscopic (moles) vs Microscopic (particles).

NODE 20

Univ Gas Constant

R ↔ k

• R operates per mole.
• k (Boltzmann) operates per particle.

NODE 21

Internal Energy (U)

U = 3/2 nRT

• Associated with microscopic molecular motion.
• For monatomic ideal gas, U ∝ T.
• Explains Realm 11 result.

NODE 22

Degrees of Freedom

TRV

• Translational, Rotational, Vibrational.
• Monatomic (mostly T). Diatomic (T+R).

NODE 23

Equipartition

½kT per DOF

• Classical thermal equilibrium.
• Each quadratic DOF contributes ~½kT.
• Explains heat capacities.

NODE 24

Molar Heat Caps

Cv = 3R/2Cp = 5R/2γ = 5/3

• Connects DOFs with Cv, Cp, γ.
• (Values for monatomic ideal gas).

NODE 25

Diatomic Gas

• Translational + Rotational modes.
• Vibrational modes active at higher T.
• Measured heat capacities vary with temp.

NODE 26

Graham's Law

rate ∝ 1/√M

• Molecular effusion/diffusion.
• Lighter gases diffuse faster.
• Connects mass to molecular speed.

NODE 27

Diffusion

• Spreading from high to low concentration.
• Random walks, concentration gradient.
• Intuitive entry into statistical physics.

NODE 28

Brownian Motion

• Visible particles exhibit irregular motion.
• Caused by countless invisible molecular collisions.
• Bridge between visible and invisible worlds.

NODE 29

Gas Mixtures

P_tot = ΣP_i

• Dalton's law of partial pressures.
• Mole fraction. Extends framework to mixtures.

NODE 30

Vapour & Partial P

• Connects gases with liquids.
• Saturated vapour, evaporation, condensation.
• Connects to Realm 10 phase changes.

NODE 31

Humidity (Micro)

RH %

• Water vapour, relative humidity, saturation.
• Dew point. Weather, cooling, comfort.

NODE 32

Atmospheric Gas

• Kinetic theory applied to Earth's atmosphere.
• Density/Pressure drops with altitude.

NODE 33

Barometric Idea

g (↓)vsP (↑)

• Balance: Gravity pulls molecules down vs Motion produces outward pressure.

NODE 34

Real Gases

NOT IDEAL

• Molecules have finite size.
• Experience intermolecular forces.
• Can condense, deviate from ideal behaviour.

NODE 35

Van der Waals Model

• (P + an²/V²)(V − nb) = nRT.
• 'a' corrects for attraction, 'b' for finite volume.

NODE 36

Real-Gas Deviation

HIGH P
LOW T

• Deviates most at High Pressure, Low Temp.
• Ideal behavior best at low density/high temp.

NODE 37

Compressibility (Z)

Z = PV/nRT

• Ideal gas: Z = 1.
• Real gases: Z ≠ 1. Quantitative measure of deviation.

NODE 38

Critical Phenomena

T_c, P_c

• Critical temp/pressure, critical point.
• Liquid-gas distinction blurs (Supercritical fluid).

NODE 39

Liquefaction

• Cooling + Compression → Intermolecular attraction wins.
• Phase transition to liquid. Cryogenics.

NODE 40

Transport Phenomena

• Viscosity (Momentum), Cond (Energy), Diff (Mass).
• Random motion → Macroscopic transport.

NODE 41

Viscosity (Micro)

Δp / layer

• Emerges from molecular momentum exchange between moving layers.
• Micro collisions → Macro resistance to flow.

NODE 42

Conduction (Micro)

ΔE / coll

• Molecules transport energy via collisions.
• Hotter → energetic particles → collisions → energy spreads.

NODE 43

Statistical Thinking

TRILLIONS OFRANDOM EVENTS= PREDICTABLE

• We cannot track every molecule.
• We use averages, probabilities, distributions.

NODE 44

Micro & Macrostate

MICRO: detailsMACRO: P,V,T

• Microstate: Detailed configuration.
• Macrostate: Bulk description.
• Huge # of microstates = same macrostate.

NODE 45

Entropy (Micro)

S=k ln Ω

• Ω = number of accessible micro-configurations.
• Entropy has both thermodynamic and statistical meaning.

NODE 46

Arrow of Time

▶

• Individual collisions are reversible.
• Macroscopic behaviour exhibits a strong statistical direction (mixing, expanding).

NODE 47

Gas Exp Lab

P-V-T LAB

• Boyle's, Charles', Pressure laws.
• Gas density, diffusion comparisons.

NODE 48

Brownian Lab

• Random particle paths, displacement, temp dependence.
• Random motion produces measurable patterns.

NODE 49

Graph Chamber

• Maxwell speed dist, P-V, P-T, V-T.
• Z vs P, Speed vs T, Mean free path vs density.

NODE 50

Misconceptions

X

• "All molecules move at same speed" → No.
• "Temp = speed" → It's avg kinetic energy.
• "Pressure = steady push" → It's collision momentum.

NODE 51

Solving Engine

MACRO ↔ MICROPV=nRT ↔ PV=NkT

• ID Macro Vars → Choose Model (Ideal/Real) → Connect to Micro (N, k).
• Interpret Microscopically.

NODE 52

Master Map

MOTION→P,T

• Matter → Atoms → Random Motion → Collisions.
• → Momentum/KE → Pressure/Temp → Gas Laws.
• → Speed Dist → Transport → Real Gases → Entropy.