Physics Notes Wizard

Comprehensive A-Level Physics Notes on Gas Laws

Gas Laws Satellites Thermal Physics

1. Avogadro's Number and the Mole

Macroscopic vs. Microscopic

  • Macroscopic: Observable properties (e.g., pressure, volume)
  • Microscopic: Molecular-level behavior (e.g., particle motion)

Mole Definition

  • 1 mole = Avogadro's number (6.022 × 10²³ particles)
  • Molar mass = mass of 1 mole of substance (g/mol)

Molar Mass (M) = mass (m) / number of moles (n)

Example Calculations

Helium (He): M = 4 g/mol (monatomic)

Oxygen (O₂): M = 32 g/mol (diatomic)

2. Kinetic Theory of Gases

Five Key Assumptions

  1. Gases consist of small particles in random motion
  2. Particles have negligible volume compared to container
  3. Collisions are perfectly elastic
  4. No intermolecular forces except during collisions
  5. Average kinetic energy ∝ absolute temperature

Ideal Gas Definition

A hypothetical gas that perfectly follows these assumptions under all conditions of temperature and pressure.

3. Pressure of a Gas

Pressure from Collisions

Gas pressure results from molecules colliding with container walls, transferring momentum.

Δp = 2mv (momentum change per collision)

Pressure Derivation

  1. Calculate momentum change per collision
  2. Determine collision frequency
  3. Relate force to rate of momentum change
  4. Pressure = Force/Area

4. Boyle's Law

Law Statement

For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume.

P ∝ 1/V or PV = constant

Experimental Setup

• Trapped gas in glass tube
• Mercury column varies pressure
• Measure volume changes

Graphical Representation

• P vs V: Hyperbolic curve
• P vs 1/V: Straight line through origin

5. Pressure vs Temperature

Key Relationship

For a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature.

P ∝ T (in Kelvin)

Experimental Setup

• Sealed gas in constant volume
• Heat bath varies temperature
• Measure pressure changes

Absolute Zero

• Extrapolate P-T graph to P=0
• Intersects at -273.15°C (0 K)
• Theoretical minimum temperature

6. Ideal Gas Equation

pV = nRT

Variables

  • p = pressure (Pa)
  • V = volume (m³)
  • n = moles of gas
  • R = 8.314 J/mol·K
  • T = temperature (K)

Example Problem

Weather Balloon:
V₁=1m³ at 20°C → V₂=? at -30°C
(Assume constant pressure)