Internal energy and absolute zeroEdexcel A-Level Physics: Revision notes

The molecules of any substance move randomly and exert forces on each other. The internal energy is the sum of the random distribution of kinetic and potential energies of all the molecules.

• Kinetic energy: the random motion of molecules (vibration in solids, translation and rotation in liquids and gases).
• Potential energy: due to the forces between molecules, which changes when their separation changes.

For an ideal gas there are no intermolecular forces, so there is no potential energy and the internal energy is just the total kinetic energy.

Internal energy depends on the amount of substance as well as the temperature: it is a total, not an average.

Molecules in a substance have a range of kinetic energies. The absolute temperature T, in kelvin, is proportional to the mean kinetic energy of the molecules.

T (K) = θ (°C) + 273, and a change of 1 K is the same as 1 °C.

Because mean kinetic energy ∝ T, the ratio of the mean kinetic energies equals the ratio of the kelvin temperatures.

Worked example: the mean kinetic energy of molecules at 127 °C compared with 27 °C is 400 K ÷ 300 K = 1.33, not 127 ÷ 27.

Absolute zero is the temperature at which the molecules have the minimum possible internal energy. For an ideal gas this means zero kinetic energy.

It is 0 K, or about −273 °C. Because kelvin temperature is proportional to mean kinetic energy, no lower temperature is possible and there are no negative kelvin temperatures.

Worked example: at 300 K the mean kinetic energy of a molecule is 6.2 × 10⁻²¹ J. At 75 K it is 6.2 × 10⁻²¹ × 75 ÷ 300 = 1.6 × 10⁻²¹ J.

There are two ways internal energy can increase.

• Heating at constant state: the mean kinetic energy rises with temperature. Heating raises the temperature.
• Changing state: the temperature is constant, so the mean kinetic energy is constant. The energy increases the potential energy as molecules move apart (melting, boiling).

This is why the temperature of ice stays at 0 °C while it melts, although its internal energy increases.

Temperature tells you the mean kinetic energy per molecule. Internal energy tells you the total over all the molecules.

Two blocks of the same material at the same temperature have the same mean kinetic energy per molecule, but the larger block has more molecules and so more internal energy.

A swimming pool at 25 °C has far more internal energy than a cup of tea at 80 °C, because it contains vastly more molecules, even though the tea has a higher temperature. Energy flows from the tea to the pool, because of the temperature difference, not the total internal energy.