Particle model

Revision notes

The particle model describes matter as particles with spaces and interactions between them. Solids have particles vibrating about fixed positions, liquids have particles that remain close but move past one another, and gases have widely separated particles moving randomly. Density is ρ = \(\dfrac{m}{V}\).

Internal energy is the total kinetic and potential energy of particles in a system. Heating can raise temperature or cause a change of state. For a temperature change, E = mcΔT. During a change of state, energy changes particle potential energy without changing temperature; E = mL. Gas pressure results from particle collisions with container walls. Increasing temperature increases average kinetic energy and can increase pressure if volume is fixed.

Density and the particle model

Density is mass per unit volume, ρ = \(\dfrac{m}{V}\). A dense material has more mass packed into each unit volume; this does not necessarily mean each individual particle is larger. Solids usually have particles closely packed in fixed relative positions, liquids have closely packed particles that can move past each other, and gases have particles much farther apart moving randomly.

For density calculations, convert units before substituting. Common errors come from mixing grams with kilograms or cubic centimetres with cubic metres. For an irregular solid, volume can be found by displacement if the object can be safely submerged.

Internal energy and temperature

Internal energy is the total microscopic kinetic and potential energy of the particles in a system. Heating can increase internal energy, but temperature does not always rise. During a change of state, energy can change particle potential energy while average kinetic energy—and therefore temperature—remains approximately constant.

Specific heat capacity links energy transfer to temperature change: E = mcΔT. A high specific heat capacity means more energy is required for the same mass and temperature rise. Specific latent heat links energy to a change of state: E = mL. Latent heat is involved while state changes occur without the usual temperature rise or fall.

Gas pressure

Gas pressure results from particles colliding with container walls and changing momentum. Increasing temperature at fixed volume increases average kinetic energy, so particles move faster and produce more frequent and/or harder collisions; pressure rises. Reducing volume at constant temperature gives particles less distance to travel between wall collisions, so collision frequency rises and pressure increases.

For qualitative gas questions, connect the chain explicitly: temperature or volume changes → particle motion/collision rate changes → force on walls changes → pressure changes.

Changes of state

Melting, freezing, boiling, condensing and sublimation are physical changes. The material's particles remain the same substance; their arrangement and energy change. Evaporation can occur below boiling point because higher-energy particles at the surface can escape. Evaporation cools the remaining liquid because the average kinetic energy of the particles left behind decreases.

Exam technique

Microscopic explanations earn marks when they mention particles, movement, spacing, collisions or energy—not when they simply restate the observation. If temperature stays constant during melting or boiling, explain where the transferred energy goes rather than saying 'no energy is needed'.

Temperature in kelvin

At absolute zero (−273 °C) particles have the least possible kinetic energy. The kelvin scale starts at absolute zero: temperature in K = temperature in °C + 273. For example, 27 °C = 300 K. A change of 1 K is the same size as a change of 1 °C.

Gas pressure, volume and temperature

The pV relationship and work done on a gas are separate-physics content.

Gas particles move randomly at high speed. When they collide with the walls of a container they exert a force, which produces pressure. At constant volume, heating a gas makes its particles move faster, so they hit the walls more often and with more force, and the pressure increases. For a fixed mass of gas at constant temperature, pressure × volume = constant (pV = constant), so halving the volume doubles the pressure.

Worked example: a gas at 100 kPa is compressed at constant temperature from 3.0 × 10⁻³ m³ to 1.5 × 10⁻³ m³. p₂ = p₁V₁ ÷ V₂ = 100 × 3.0 ÷ 1.5 = 200 kPa.

Doing work on a gas, for example by pushing in a bicycle pump quickly, transfers energy to the gas. This increases its internal energy, so its temperature rises.