AQA A-Level Physics: Thermal Physics and Fields Revision Guide

Thermal Physics and Fields are two of the most demanding sections of the AQA A-Level Physics specification. They sit at the heart of Paper 2, which accounts for 34% of the overall A-Level grade. Both topics build heavily on the mathematical and conceptual foundations established in Paper 1, so a strong grasp of mechanics, electricity, and periodic motion is essential before you tackle them.

What makes these topics particularly challenging is the depth of mathematical reasoning required. You will need to work fluently with exponential functions, inverse-square laws, and calculus-based arguments. The reward is that once you understand the underlying principles, the topics become highly interconnected -- the same mathematical structures reappear across gravitational, electric, and magnetic fields, and the statistical approach underpinning kinetic theory connects to thermodynamic ideas in a satisfying way.

This guide works through the specification content for both topics, explains the key concepts and equations at A-Level depth, and offers practical advice on how to approach exam questions.

Thermal Physics

Thermal Physics is Section 6.2 of the AQA specification. It covers thermal energy transfer, the ideal gas laws, molecular kinetic theory, and the relationship between microscopic particle behaviour and macroscopic quantities like pressure and temperature.

Internal Energy

Internal energy is the sum of the random kinetic energies and potential energies of all the particles in a substance. The kinetic component relates to particle motion -- translational, rotational, and vibrational. The potential component relates to the forces between particles, which depend on their separation.

Temperature measures the average kinetic energy of particles. When you heat an object and its temperature rises, you are increasing the average kinetic energy of its particles. However, internal energy can also increase without a temperature change -- during a change of state, energy goes into breaking intermolecular bonds (increasing potential energy) rather than increasing kinetic energy. This distinction is examined frequently.

Specific Heat Capacity and Latent Heat

Specific heat capacity (c) is the energy required to raise the temperature of 1 kg of a substance by 1 K. The equation is E = mc(delta T).

In the required practical, you measure c using an electrical heater. The energy supplied is E = VIt, equated to mc(delta T). A common error source is heat loss to the surroundings, which causes measured values to exceed accepted values.

Specific latent heat (L) is the energy required to change the state of 1 kg of a substance without changing its temperature: E = mL. There are two types -- latent heat of fusion (solid to liquid) and latent heat of vaporisation (liquid to gas). Vaporisation always requires more energy than fusion for the same substance, because completely separating particles demands more energy than partially overcoming intermolecular forces.

The Gas Laws and the Ideal Gas Equation

Three empirical gas laws describe the behaviour of gases when one variable is held constant:

• Boyle's law: At constant temperature, pV = constant.
• Charles's law: At constant pressure, V/T = constant.
• The pressure law: At constant volume, p/T = constant.

These combine into the ideal gas equation:

pV = nRT

where p is pressure (Pa), V is volume (m cubed), n is the number of moles, R is the molar gas constant (8.31 J per mol per K), and T is absolute temperature (K). An equivalent form uses the Boltzmann constant: pV = NkT, where N is the number of molecules and k = R/N_A. You should be comfortable using either form.

An ideal gas perfectly obeys these laws. Real gases approximate ideal behaviour at low pressures and high temperatures, where particles are far apart and intermolecular forces are negligible.

Molecular Kinetic Theory

The kinetic theory model derives macroscopic gas properties from microscopic molecular behaviour. The key assumptions are: a very large number of molecules in constant random motion; negligible molecular volume compared to the container; perfectly elastic collisions; negligible collision duration compared to time between collisions; and no intermolecular forces except during collisions.

From these assumptions, the derivation produces:

pV = (1/3)Nm(c_rms) squared

The derivation considers a single molecule bouncing between walls of a cubic container. By calculating the change in momentum at each collision and the rate of collisions, you derive the pressure from one molecule, then scale up to N molecules moving in three dimensions (hence the factor of 1/3). You must be able to reproduce this derivation -- it is a favourite of examiners.

Combining pV = NkT with pV = (1/3)Nm(c_rms) squared yields a profoundly important result:

(1/2)m(c_rms) squared = (3/2)kT

This tells you that the average kinetic energy of a gas molecule depends only on absolute temperature, linking the microscopic world to the macroscopic. The Boltzmann constant (k = 1.38 x 10 to the power of -23 J per K) bridges energy at the molecular scale and temperature at the macroscopic scale.

Note that c_rms (root-mean-square speed) is not the same as mean speed. It is calculated by squaring all individual speeds, taking the mean, and then taking the square root -- giving a higher value than the simple mean because it weights faster molecules more heavily.

Fields

The Fields section spans Sections 7.1 to 7.5 of the specification, covering gravitational, electric, and magnetic fields. The mathematical treatment is demanding but highly structured -- once you understand one field type, many ideas transfer to the others.

Gravitational Fields

Gravitational field strength at a point is the force per unit mass on a small test mass: g = F/m (units: N per kg).

Newton's law of gravitation gives the force between two point masses: F = -GMm / r squared, where G = 6.67 x 10 to the power of -11 N m squared per kg squared. The negative sign indicates attraction. The field strength at distance r from mass M is therefore g = -GM / r squared -- an inverse-square law.

Gravitational potential (V) is the work done per unit mass bringing a test mass from infinity to that point: V = -GM / r. It is always negative because work is needed to move a mass back to infinity. The field strength is the negative gradient of potential: g = -dV/dr.

Orbits: For a circular orbit, gravitational force provides centripetal force: GMm / r squared = mv squared / r, giving v = (GM/r) to the power of 1/2. Orbital speed decreases with increasing radius. Geostationary orbits require T = 24 hours, an equatorial orbit, and rotation in the same direction as the Earth. Kepler's third law, T squared = (4 pi squared / GM) r cubed, lets you calculate orbital radius. The total energy of an orbiting satellite (kinetic plus potential) is negative, meaning it is gravitationally bound.

Electric Fields

Electric fields exert forces on charges, with mathematics closely paralleling gravitational fields but with a key difference -- electric forces can be attractive or repulsive.

Coulomb's law: F = (1 / 4 pi epsilon_0) Qq / r squared, where epsilon_0 = 8.85 x 10 to the power of -12 F per m. The field strength from a point charge Q is E = (1 / 4 pi epsilon_0) Q / r squared. For a uniform field between parallel plates: E = V / d.

Electric potential is the work done per unit positive charge bringing a test charge from infinity: V = (1 / 4 pi epsilon_0) Q / r. Equipotential surfaces are perpendicular to field lines. As with gravity, E = -dV/dr.

Capacitance

Capacitance is charge stored per unit potential difference: C = Q / V (farads). Energy stored: E = (1/2)QV = (1/2)CV squared = (1/2)Q squared / C.

Charge and discharge through a resistor follow exponential curves. During discharge: Q = Q_0 e to the power of (-t / RC), and similarly for V and I. The time constant RC determines the rate -- after one time constant, the quantity falls to about 37% of its initial value. During charging: Q = Q_0 (1 - e to the power of (-t / RC)). You should be able to interpret exponential curves and use logarithmic plots (ln Q against t) to determine RC from the gradient.

Magnetic Fields

Magnetic fields are produced by moving charges. The force on a current-carrying conductor is F = BIl sin(theta), where B is magnetic flux density (tesla), I is current, l is length in the field, and theta is the angle between conductor and field.

For a moving charged particle: F = Bqv sin(theta). This force is always perpendicular to velocity, so it changes direction without changing speed. A charged particle moving perpendicular to a uniform field follows a circular path with radius r = mv / Bq.

Magnetic flux through a surface is phi = BA cos(theta), measured in webers (Wb). Flux linkage for N turns is N phi = BAN cos(theta).

Faraday's law states that induced EMF equals the rate of change of flux linkage: EMF = -d(N phi) / dt. The negative sign is explained by Lenz's law -- the induced EMF opposes the change producing it, a consequence of conservation of energy. For a coil rotating in a magnetic field, flux linkage varies as BAN cos(omega t), giving EMF = BAN omega sin(omega t).

Lenz's law has practical consequences that are frequently examined. When a magnet falls through a copper tube, induced currents oppose the magnet's motion, slowing it dramatically. Practise determining induced current direction using Lenz's law with the right-hand rule until it is second nature.

Alternating current varies sinusoidally. Root-mean-square values are the effective DC equivalents: V_rms = V_0 / (square root of 2) and I_rms = I_0 / (square root of 2). Average power is P = I_rms x V_rms.

Transformers use electromagnetic induction to change voltage. For an ideal transformer: V_s / V_p = N_s / N_p, and input power equals output power. The national grid uses step-up transformers for efficient long-distance transmission (reducing current and therefore I squared R losses) and step-down transformers for safe domestic use.

Exam Strategy for Paper 2

Paper 2 is 2 hours long and worth 85 marks, containing short-answer questions, longer calculations, and extended writing.

Show every step of your working. In multi-step calculations, marks are awarded for method even if you make an arithmetic error. Write down your equation, substitute values clearly, and present working logically.

Check your units. Ensure distances are in metres, pressure in pascals, and temperature in kelvin. A quick unit check catches errors before you move on.

Know your derivations thoroughly. The kinetic theory derivation and orbital equations from Newton's law of gravitation are classic exam questions. Practise writing them out under timed conditions.

Use the formulae booklet efficiently. Know which equations are given and which you must memorise. Equations like pV = nRT and Coulomb's law are provided, but you need to know when and how to apply them.

Prepare with LearningBro

Thermal Physics and Fields are topics where understanding must run deep. Memorising equations is not enough -- you need to know the derivations behind them, understand the physical reasoning, and practise applying them to unfamiliar problems under timed conditions.

LearningBro offers structured courses to support your revision across these topics:

• AQA A-Level Physics: Thermal Physics in Depth -- covers the ideal gas equation, kinetic theory derivation, internal energy, specific heat capacity, and latent heat with detailed questions at A-Level depth.
• AQA A-Level Physics: Fields in Depth -- works through gravitational, electric, and magnetic fields, including Coulomb's law, capacitance, Faraday's law, and AC circuits.
• AQA A-Level Physics: Thermal Physics and Fields -- a combined course covering the full Paper 2 content for these topics, ideal for comprehensive revision.

Final Thoughts

Thermal Physics and Fields are among the most intellectually rewarding parts of the A-Level Physics course. They connect the behaviour of invisible molecules to the temperature you can feel, and explain how forces act across empty space through fields that permeate the universe. The mathematics is demanding, but it provides precise, quantitative predictions that match experimental observations.

Build your revision around understanding, not memorisation. If you understand why pV = nRT works, you can derive it. If you understand why gravitational potential is negative, you will not make sign errors. If you understand Lenz's law as a consequence of energy conservation, you can apply it to any situation.

Work through past paper questions methodically, check your units at every step, and practise your derivations until they flow naturally. These topics reward the students who put in the time to truly understand the physics -- and that understanding will serve you well beyond the exam hall.