Internal energy
The internal energy of a system is the total energy stored by all its particles. It is the sum of:
- the kinetic energy of every particle (vibrational, rotational, translational), and
- the potential energy stored in the bonds between particles.
The internal energy is the proper name for the "thermal store" introduced in P1.
What heating does
Heating a substance transfers energy to the internal energy store. This can:
- Raise temperature — by increasing the average kinetic energy of particles.
- Change state — by overcoming the potential energy of bonds, with no change in temperature.
Most of the time both happen in succession (heating ice → warmer ice → melting → warmer water → boiling → hotter steam).
Temperature is the average KE
Crucially, temperature is a measure of the average kinetic energy of particles. A hotter object has faster-vibrating particles (in a solid) or faster-moving molecules (in a gas).
Two objects can have the same temperature but very different total internal energies — a swimming pool at 20 °C contains far more internal energy than a cup of water at the same temperature, because there are more particles.
Specific heat capacity (preview)
Different substances need different amounts of energy to raise their temperature by 1 °C per kg. This is the specific heat capacity $c$:
$\Delta E = mc\Delta\theta$
Water has unusually high $c$ (4200 J/kg/K) — that's why coastal climates are mild and water is used as a coolant.
During a phase change
When ice melts, energy supplied is going into the potential part of internal energy (separating particles in the lattice), so kinetic energy (and therefore temperature) does not rise. This explains the plateau on a heating curve.
✦Worked example
A 2.0 kg block of aluminium ($c = 900$ J/kg/K) is heated from 20 °C to 80 °C. How much energy is transferred?
- $\Delta\theta = 60$ K.
- $\Delta E = mc\Delta\theta = 2.0 \times 900 \times 60 = 108,000$ J = 108 kJ.
⚠Common mistakes
- Confusing internal energy with temperature — temperature is average KE, not total energy.
- Forgetting that PE matters during phase change.
- Saying "heat" is a substance contained in objects — heat is transfer of energy, not a stored quantity.
- Using $\Delta\theta$ in degrees Celsius vs Kelvin — for differences, both give the same number.
AI-generated · claude-opus-4-7 · v3-deep-physics