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Every object around you — a cup of tea, a block of iron, even the air in the room — is made up of an enormous number of particles (atoms or molecules) that are constantly in motion. These particles have kinetic energy because they are moving, and they have potential energy because of the forces between them. The internal energy of a system is the sum of the randomly distributed kinetic and potential energies of all the particles within it.
This is one of the most fundamental ideas in thermodynamics, and it underpins everything from heating a saucepan of water to understanding how engines work.
The particles in any substance are in constant, random motion. In a gas, this motion is primarily translational — the molecules fly around in straight lines between collisions. In solids, the particles vibrate about fixed positions. In liquids, the behaviour is somewhere in between.
Kinetic energy of particles depends on their speed. At higher temperatures, the particles move faster on average, so their mean kinetic energy increases. This is a crucial link: temperature is a measure of the average kinetic energy of the particles in a substance.
Potential energy of particles arises from the intermolecular forces (bonds) between them. In a solid, particles are held close together in a regular arrangement by strong forces, and they sit in potential energy "wells." In a liquid, the particles have enough energy to partially overcome these forces but remain loosely bound. In a gas, the particles have largely overcome the intermolecular forces and the potential energy contribution is very different from that in a solid or liquid.
Therefore:
Internal energy = total kinetic energy of all particles + total potential energy due to intermolecular forces
When you heat a substance and its temperature rises, you are increasing the average kinetic energy of its particles. The particles move faster (or vibrate more vigorously), and the internal energy of the system increases.
However — and this is a critical distinction — internal energy is not the same as temperature. Temperature only reflects the average kinetic energy component. Internal energy also includes the potential energy between particles. Two objects at the same temperature can have very different internal energies if they contain different amounts of substance or are in different phases.
For example, 1 kg of water at 100 °C and 1 kg of steam at 100 °C are at the same temperature, but the steam has significantly more internal energy because additional energy was needed to break the intermolecular bonds during the change of state.
When a substance changes state — for example, ice melting to water, or water boiling to steam — something remarkable happens: the temperature stays constant even though energy is being supplied.
Where does the energy go? It goes into increasing the potential energy of the particles. During a change of state, the energy supplied is used to overcome the intermolecular forces that hold the particles in their current arrangement, rather than increasing their kinetic energy.
Consider ice at 0 °C being heated:
The same principle applies at 100 °C when water boils to steam: the temperature remains constant while the energy input increases the potential energy of the molecules as they break free from the liquid.
This is worth emphasising because it is frequently examined. During a change of state:
A heating curve illustrates this clearly:
| Phase | What happens | Temperature |
|---|---|---|
| Solid being heated | KE increases | Rises |
| Solid → Liquid (melting) | PE increases, bonds broken | Constant |
| Liquid being heated | KE increases | Rises |
| Liquid → Gas (boiling) | PE increases, bonds broken | Constant |
| Gas being heated | KE increases | Rises |
The flat sections of a heating curve correspond to changes of state, where all the supplied energy increases potential energy rather than kinetic energy.
The total internal energy differs between phases even at the same temperature:
This explains why steam burns are more severe than boiling water burns — the steam carries additional internal energy (the latent heat) that is released when it condenses on the skin.
A 2 kg block of ice at 0 °C is heated until it has completely melted into water at 0 °C. The specific latent heat of fusion of ice is 334 000 J kg⁻¹. What happens to the internal energy?
The energy supplied is:
Q = mL = 2 × 334 000 = 668 000 J
This 668 kJ of energy has increased the internal energy of the water compared to the ice. Since the temperature has not changed, the kinetic energy of the particles is the same. All 668 kJ has gone into increasing the potential energy of the particles — breaking the hydrogen bonds in the ice lattice so the water molecules can move more freely.