Thermal Physics

The kinetic particle model

All matter is built from tiny particles in constant motion. Whether a substance is a solid, a liquid or a gas comes down to three things: how its particles are arranged, how far apart they sit, and how freely they move.

The three states

In a solid, particles are packed in a regular pattern and held by strong forces. They can only vibrate about fixed positions, so a solid keeps its shape and volume and cannot be compressed.

In a liquid, the particles are still close together but no longer ordered. They can slide over one another, so a liquid flows and takes the shape of its container while keeping a fixed volume.

In a gas, particles are widely separated — roughly ten times further apart in each direction — and move randomly at high speed. A gas spreads to fill any container and is easily compressed.

Changing state

A substance moves between states when energy is added or removed. Melting turns a solid to a liquid and solidifying (freezing) reverses it; boiling turns a liquid to a gas and condensing reverses it. Throughout, the number of particles — and therefore the mass — stays the same; only the energy and arrangement change, which is why every change of state can be undone.

Temperature and motion

Raising the temperature of a substance increases the average speed of its particles, and so their average kinetic energy. Cooling it slows them down. There is a limit: at absolute zero, −273 °C, the particles have the least possible kinetic energy and cannot slow further. This is the starting point of the Kelvin scale.

ExtendedForces between particles

The forces and distances between particles, together with their motion, decide whether a substance is a solid, liquid or gas — and how it behaves. In a solid, strong forces hold particles in place, giving rigidity. In a liquid, the particles have enough energy to partly overcome these forces and slide past one another, so it flows. In a gas, the particles have largely escaped the forces altogether, so the gas expands to fill its container and is easily compressed.

Brownian motion and gas pressure

You cannot see a single air molecule, but you can see what it does. The jittering of smoke specks under a microscope, and the steady push of a gas on its container, are both fingerprints of particles in motion.

Brownian motion

Smoke or pollen grains suspended in a fluid, viewed through a microscope, are seen to jitter about in a random, erratic way. This Brownian motion is evidence for the kinetic particle model.

The motion is caused by collisions: light, fast-moving molecules of the surrounding gas or liquid strike the much larger visible particle from all sides. At any instant the collisions are uneven, giving the particle a small nudge that constantly changes its speed and direction.

Gas pressure

Gas particles move randomly and constantly collide with the walls of their container. Each collision exerts a tiny force on the wall; together, spread over the wall’s area, these collisions create pressure. Faster or more frequent collisions mean greater pressure.

Each particle rebounds from the wall, exerting a force at right angles to the surface. Since pressure is force per unit area, the combined effect of these collisions is the gas pressure on the wall.

Gases and absolute temperature

Squeeze a gas or heat it, and its pressure changes in ways the particle model predicts exactly. A new temperature scale, starting at absolute zero, makes those changes simple to describe.

Pressure changes in a gas

For a fixed mass of gas, the particle model explains two everyday changes in pressure. Heating at constant volume: the particles move faster, so they strike the walls harder and more often, and the pressure rises. Reducing the volume at constant temperature: the same particles are confined to a smaller space, so they hit the walls more often, and the pressure rises.

The Kelvin scale

The Kelvin (absolute) scale begins at absolute zero, so its values are never negative. A degree on each scale is the same size, so converting is a simple shift of 273: T = θ + 273.

Worked example: to convert 27 °C to kelvin, add 273 — T = 27 + 273 = 300 K. To convert 350 K to degrees Celsius, subtract 273 — θ = 350 − 273 = 77 °C.

The gas laws

The whole of this section is Extended — examined on Papers 2 and 4 only. For a fixed mass of gas at constant temperature, pressure and volume are locked together: squeeze the gas into half the space and the pressure doubles.

ExtendedPressure and volume

When a fixed mass of gas is compressed at constant temperature, its particles strike the walls more often, so the pressure rises. Pressure is inversely proportional to volume: halve the volume and the pressure doubles. Numerically, p₁V₁ = p₂V₂, with the same units used on both sides.

Worked example: a gas of volume 240 cm³ at 100 kPa is compressed to 60 cm³ at constant temperature. Applying p₁V₁ = p₂V₂ gives 100 × 240 = p₂ × 60, so p₂ = 24 000 / 60 = 400 kPa — four times smaller volume, four times the pressure.

Thermal expansion

Heat almost anything and it grows a little. The effect is small in solids and large in gases — and engineers must design for it, from railway lines to bridges.

Expansion of solids, liquids and gases

When a substance is heated at constant pressure it expands. Gases expand the most, liquids less, and solids least of all. Everyday uses and consequences include the bimetallic strip in thermostats, the rise of liquid in a thermometer, and the expansion gaps left in bridges and railway tracks.

ExtendedWhy gases expand most

Heating gives particles more kinetic energy, so they move more vigorously and push slightly further apart. In a solid, strong forces hold the particles in place, so the expansion is small. In a liquid, the weaker forces allow a larger expansion. In a gas, the particles are already free of these forces, so the same temperature rise produces by far the greatest expansion.

Specific heat capacity

Some materials soak up a great deal of energy for only a small rise in temperature; others heat up quickly. Specific heat capacity puts a precise number on that difference.

Heating and internal energy

Raising the temperature of an object increases its internal energy. At the level of particles, this is an increase in their average kinetic energy.

The specific heat capacity c measures how much energy each kilogram of a material needs to warm by one degree: E = mcΔθ.

Worked example: to raise the temperature of 2.0 kg of water by 20 °C, with c = 4200 J/(kg·°C), E = mcΔθ = 2.0 × 4200 × 20 = 168 000 J = 168 kJ.

Measuring it

To find the SHC of a metal block, an electrical heater warms a block of known mass. The energy supplied is found from the heater (E = power × time), and a thermometer gives the temperature rise. Then c = E / (mΔθ). Insulating the block reduces energy lost to the surroundings, which would otherwise make c appear too large.

Melting, boiling and evaporation

Heating a substance does not always raise its temperature. At a melting or boiling point, the energy goes into pulling particles apart instead — the temperature holds steady until the change of state is complete.

Energy without a temperature rise

When a solid melts or a liquid boils, energy is supplied but the temperature stays constant, because the energy separates the particles rather than speeding them up. For water at standard atmospheric pressure, melting happens at 0 °C and boiling at 100 °C. The reverse changes — condensation (gas to liquid) and solidification (liquid to solid) — release energy as particles move closer and slower.

Evaporation

Evaporation happens when the most energetic particles near the surface of a liquid have enough energy to escape into the air. Because the fastest particles leave, the average energy of those remaining falls, so the liquid cools.

ExtendedBoiling versus evaporation

Boiling and evaporation both turn a liquid into a gas, but they are not the same process, and the distinction is a frequent source of lost marks. Boiling occurs at the boiling point only, throughout the liquid, with bubbles forming, and is rapid. Evaporation occurs at any temperature below the boiling point, at the surface only, with no bubbles, and is slower.

Evaporation is faster when the temperature is higher, the surface area is larger, or there is more air movement over the surface carrying escaped particles away. An object in contact with an evaporating liquid is cooled: the liquid loses its most energetic particles, so its average kinetic energy — and temperature — fall, and it then draws thermal energy from the object.

Conduction

Hold a metal spoon in hot soup and the handle soon warms. Conduction is thermal energy passing through a material, particle to particle, without the material itself moving.

Good and bad conductors

Metals are excellent thermal conductors; non-metals such as wood, plastic and most liquids and gases are poor conductors, or insulators. This can be shown by heating one end of rods of different materials, each with a small object held on by wax — the wax melts first on the best conductor.

ExtendedHow conduction works

In every solid, heated particles vibrate more and pass energy to their neighbours through the lattice vibrations. In metals there is a second, much faster route: free (delocalised) electrons gain kinetic energy at the hot end and carry it quickly through the metal — which is why metals conduct best. Gases and most liquids conduct poorly because their particles are far apart, so energy-sharing collisions are rare.

Convection

In liquids and gases, energy can travel a second way: the warm fluid itself moves. Heated fluid rises, cool fluid sinks, and the resulting loop carries energy through the whole fluid.

Convection currents

When a fluid is heated, it expands and becomes less dense, so it rises. Cooler, denser fluid sinks to take its place, is heated in turn, and also rises. This circulation is a convection current, and it carries thermal energy throughout the fluid. It can be shown by dropping a coloured crystal into water above a gentle heat source and watching the colour rise and circulate.

Radiation

The third route needs no particles at all. Thermal radiation is infrared travelling as a wave, which is how the Sun’s energy crosses the vacuum of space to reach us.

Infrared and surfaces

All objects emit thermal radiation as infrared, and unlike conduction and convection it needs no medium — it crosses empty space. A surface’s appearance decides how well it radiates and absorbs: dull black surfaces are good emitters and good absorbers, while shiny white or silver surfaces are poor emitters and absorbers but good reflectors. This can be tested by comparing how quickly black and shiny containers of hot water cool, or warm in front of a heater.

ExtendedEnergy balance

An object stays at a constant temperature when it emits energy at the same rate as it absorbs it. If it absorbs faster than it emits, it warms up; if it emits faster, it cools. The Earth’s temperature is set by this balance between incoming radiation from the Sun and radiation emitted back into space. The rate of emission rises with a higher surface temperature and a larger surface area.

Everyday consequences

Most real objects use more than one kind of thermal transfer at once. Knowing which mechanism dominates where is exactly what the exam rewards — and what good design exploits.

Single and combined transfers

Many objects are designed around one mechanism: a saucepan conducts heat through its metal base while its plastic handle insulates, and a heater warms a room by convection. More complex cases combine all three — a fire radiates heat to the room, drives convection currents of hot gas up the chimney, and conducts through its grate; a car radiator conducts heat through its metal fins and loses it by convection to the passing air.

The vacuum flask

A vacuum flask keeps drinks hot or cold by defeating all three transfers at once: the vacuum between its double walls stops conduction and convection, the silvered surfaces reflect radiation back, and an insulating stopper seals the top.