Thermal energy transfers

📚The physics

Three words that are not synonyms. Temperature is proportional to the average random kinetic energy of the molecules. Internal energy is the total of all the molecular kinetic energies plus all the intermolecular potential energies. Thermal energy (heat) is energy in transit from hotter to colder. A bathtub of warm water has far more internal energy than a spark, while the spark has the far higher temperature. Examiners test this distinction constantly.

Absolute temperature. \( T(\text{K}) = \theta(^\circ\text{C}) + 273 \). Kelvin is not an alternative unit of convenience: average kinetic energy is proportional to the absolute temperature, so doubling from 20 °C to 40 °C does not double anything. Doubling from 293 K to 586 K does. Every proportionality in this theme requires kelvin.

Specific heat capacity \(c\) is the energy needed to raise 1 kg by 1 K. Specific latent heat \(L\) is the energy needed to change the phase of 1 kg with no temperature change.

Water’s specific heat capacity is unusually large, about 4200 J kg\(^{-1}\) K\(^{-1}\), which is why coastal climates are mild and why water is the coolant of choice. Fusion is solid–liquid, vaporisation is liquid–gas, and for water the latter is roughly seven times larger — separating molecules entirely costs far more than merely loosening them.

Why the temperature stops during a phase change is the question most worth being able to answer in words. The energy supplied goes into potential energy, breaking the intermolecular bonds, not into kinetic energy. Since temperature tracks average kinetic energy, and that is not changing, the thermometer sits still even though energy is pouring in. On a temperature–time graph this is the flat plateau, and a longer plateau simply means a larger latent heat.

The three transfer mechanisms. Conduction passes energy through a material by molecular collision and, in metals, by free electrons — which is why metals conduct so much better. It needs a medium. Convection moves energy by bulk motion of a fluid: warmed fluid expands, becomes less dense, and rises. It needs a fluid. Radiation transfers energy as electromagnetic waves and is the only one that works through a vacuum, which is how the Sun’s energy reaches us at all.

Black-body radiation. A black body is a perfect absorber and a perfect emitter. Two laws describe what it emits.

That fourth power does a great deal of work: a modest rise in temperature produces a dramatic rise in power. Wien’s displacement law says hotter bodies peak at shorter wavelengths — the reason a heated metal glows dull red, then orange, then white, and the reason blue stars are hotter than red ones.