Diffusion

Unit 1 Micro Displacement

Diffusion

Juan Juan
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Diffusion is the spontaneous, linear movement of gas molecules from a region of higher concentration to a region of lower concentration. It is the Micro Displacement force in Superphysics’ Gas Relationalities — the linear, translational action of individual gas particles through the aetherspace.

Unlike turbulence (rotational/chaotic), diffusion is directional and linear — molecules march from dense to sparse until equilibrium is reached.

The Equation: Fick’s Law

Fick’s First Law (Steady-State)

[ J = -D \frac{dC}{dx} ]

Where:

Symbol Meaning Unit
( J ) Diffusion flux (amount flowing per area per time) ( \text{mol}/(\text{m}^2 \cdot \text{s}) )
( D ) Diffusion coefficient (depends on gas, temperature, pressure) ( \text{m}^2/\text{s} )
( \frac{dC}{dx} ) Concentration gradient (change in concentration over distance) ( \text{mol}/\text{m}^4 )
( - ) Negative sign = flow is down the gradient (high → low) —

Fick’s Second Law (Time-Dependent)

[ \frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2} ]

This predicts how concentration changes over time as diffusion proceeds.

Key Properties of Gas Diffusion

Property Explanation
Passive No external energy needed — driven by entropy
Linear Molecules move in straight paths between collisions
Random walk Each molecule zigzags, but net flow is directional
Temperature-dependent Higher ( T ) → faster diffusion
Inversely pressure-dependent Higher ( P ) → slower diffusion
Mass-dependent Lighter gases diffuse faster (Graham’s Law)

Graham’s Law of Effusion/Diffusion

[ \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} ]

Lighter gas diffuses faster. Example: helium ( (M = 4) ) diffuses ~2.6× faster than oxygen ( (M = 32) ).

Real-Life Examples

Example How Diffusion Works
1. Perfume in a room Fragrance molecules spread from the bottle (high concentration) to the entire room (low concentration)
2. Oxygen entering blood ( O_2 ) diffuses from lung alveoli (high ( O_2 )) into capillaries (low ( O_2 ))
3. Carbon dioxide leaving blood ( CO_2 ) diffuses from blood (high ( CO_2 )) into lungs (low ( CO_2 ))
4. Natural gas leak Methane spreads through air from the leak point outward
5. Ammonia and HCl experiment Two gases in a tube meet and form a white ring — closer to the heavier gas (HCl)
6. Aerosol spray Propellant gas diffuses into surrounding air
7. Plant respiration ( CO_2 ) diffuses into leaves through stomata; ( O_2 ) diffuses out
8. Helium balloon deflating Helium atoms diffuse through the balloon’s microscopic pores
9. Smell of cooking Aroma molecules diffuse from kitchen to other rooms
10. Landfill methane Methane diffuses through soil and into the atmosphere

Diffusion vs. Other Gas Forces

Force Type Direction Scale
Diffusion Displacement (linear) High → low concentration Micro
Turbulence Cohesion (rotational) Chaotic, swirling Micro
Convection Displacement (linear) Hot → cold (buoyancy-driven) Mid
Vortex Cohesion (rotational) Spiral, wrapping Mid
Air Pressure Displacement (linear) High → low pressure Macro
Coriolis Cohesion (rotational) Deflecting, wrapping Macro

Summary

Question Answer
What is gas diffusion? Linear movement of gas molecules from high to low concentration
What law describes it? Fick’s Law: ( J = -D \frac{dC}{dx} )
What type of force? Micro Displacement (linear, Rule 1 + 3)
What drives it? Concentration gradient (entropy)
Real examples? Perfume spreading, ( O_2 ) into blood, gas leaks, cooking smells
What’s its rotational counterpart? Turbulence (Micro Cohesion)

Bottom line: Gas diffusion is the linear, invisible marching of molecules from dense to sparse — the Micro Displacement force that pairs with turbulence’s rotational chaos in Superphysics’ Gas Relationalities.

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