B.1 Thermal energy transfersIB Physics HL: Revision notes

In the molecular model of matter:

• solids: particles vibrate about fixed positions, held by strong intermolecular forces
• liquids: particles are close together but can move past one another
• gases: particles are far apart, move randomly at high speed and interact only in collisions

Density $\rho = \frac{m}{V}$ (kg m⁻³). Gases have much lower densities than solids and liquids because their particles are far apart.

Temperature is measured in degrees Celsius or kelvin: T(K) = θ(°C) + 273. A change in temperature has the same value on both scales. The Kelvin temperature is a measure of the average random kinetic energy of the particles:

$\bar{E}_k = \frac{3}{2}k_B T$

The internal energy of a system is the total intermolecular potential energy (from the forces between molecules) plus the total random kinetic energy of the molecules.

Thermal energy flows from a region of higher temperature to one of lower temperature; the temperature difference sets the direction of the resultant transfer.

During a phase change (melting, boiling) energy is transferred at constant temperature. The average kinetic energy does not change; the energy increases the intermolecular potential energy as particles are separated.

Energy to change temperature: $Q = mc\Delta T$, where c is the specific heat capacity (J kg⁻¹ K⁻¹).

Energy to change phase: $Q = mL$, where L is the specific latent heat of fusion (melting) or vaporization (boiling) (J kg⁻¹).

For a heater of power P running for time t, the energy supplied is Q = Pt. Multi-stage problems (ice → water → steam) are solved stage by stage and the energies added.

Conduction: particles with more kinetic energy collide with neighbours, passing energy along the material from hot to cold. In metals, free electrons also carry energy, making them good conductors. The rate of conduction is

$\frac{\Delta Q}{\Delta t} = kA\frac{\Delta T}{\Delta x}$

where k is the thermal conductivity of the material, A the cross-sectional area and ΔT/Δx the temperature gradient. Still air has a very low k, so trapped air is an excellent insulator.

Convection occurs in fluids: warmer fluid expands, becomes less dense and rises, while cooler, denser fluid sinks, setting up convection currents that carry energy.

All bodies emit thermal radiation (electromagnetic waves) from their surfaces. A black body is a perfect absorber and emitter. Its power output, the luminosity L, is given by the Stefan–Boltzmann law:

$L = \sigma A T^4$

The apparent brightness b is the power received per unit area at a distance d:

$b = \frac{L}{4\pi d^2}$

The black-body spectrum has a peak wavelength that shortens as temperature rises — Wien's displacement law:

$\lambda_{max} T = 2.9 \times 10^{-3}$ m K

So a red star is cooler than a blue one. Combining these, a star's temperature (Wien), luminosity (b and d) and radius (Stefan–Boltzmann) can all be found.