Theme B · Particulate Nature of Matter · SL + HL · 6 hours
B.1 Thermal Energy Transfers
How do macroscopic observations reveal microscopic properties of matter?
Everything you observe about temperature — why coffee cools, why stars are different colours, why ice melts at a fixed temperature — is a macroscopic consequence of molecular behaviour. The kinetic theory connects these two levels: temperature is a measure of average molecular kinetic energy, internal energy is the total of all kinetic and potential energies of the molecules, and thermal processes are just energy moving between stores by conduction, convection, or radiation.
The Stefan-Boltzmann law turns thermal radiation into astrophysics: the luminosity of a star depends on its surface area and the fourth power of its temperature, and Wien's displacement law tells you the temperature from the peak wavelength of its spectrum. These are not separate facts but a single coherent model — the black body — that works from a candle flame to a neutron star.
The Sun has a surface temperature of approximately 5780 K and a radius of 6.96 × 10⁸ m. Using the Stefan-Boltzmann law, calculate the Sun's luminosity. (σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴)
Key equations
Specific heat capacity: Q = mcΔT
Latent heat: Q = mL
Average KE of a molecule: Ē_k = (3/2)kBT
Thermal conduction rate: ΔQ/Δt = kA(ΔT/Δx)
Stefan-Boltzmann (black body): L = σAT⁴
Apparent brightness: b = L / (4πd²)
Wien's displacement law: λmaxT = 2.9 × 10⁻³ m K
What students must understand
Molecular theory in solids, liquids, and gases — particle spacing, energy, and freedom of motion
Kelvin and Celsius scales; Kelvin temperature as a measure of average molecular KE
Internal energy = total molecular KE + total intermolecular PE
Temperature difference drives thermal energy transfer direction
Phase changes occur at constant temperature; energy goes to changing state, not temperature
Specific heat capacity and specific latent heat (fusion and vaporisation)
Conduction: kinetic energy passed between adjacent particles
Quantitative conduction: rate depends on material (k), area, and temperature gradient
Convection: qualitative — density differences drive fluid circulation
Radiation: black body model, Stefan-Boltzmann law, luminosity and apparent brightness
Wien's displacement law: peak wavelength determines temperature
Linking questions
How is the understanding of systems applied to thermodynamics? → B.4
What applications does the Stefan-Boltzmann law have in astrophysics? → E.5 Fusion and Stars
Where else do inverse square law relationships appear? → D.1 Gravitational Fields, D.2 Electric and Magnetic Fields