147-148 - Internal Energy and Absolute Zero

Internal Energy Is Molecular

Imagine a sealed metal canister sitting still on a bench. The canister has no obvious motion as a whole, but the molecules inside it are not still. They move randomly, collide, vibrate, rotate, and interact with neighbouring molecules.

Internal energy is the energy stored microscopically in a system.

The word random is doing real work. In a warm sample, not every molecule has the same speed or the same energy. Some molecules are moving faster than average and some slower; internal energy is spread across the whole molecular population.

Internal energy is not the kinetic energy of the whole object moving across the room. If the sealed canister is carried across the lab, it gains kinetic energy as a whole, but that is not internal energy. Internal energy is about the molecular-scale motion and interactions inside the sample.

Misconception contrast: it is tempting to say "internal energy is just the kinetic energy of the molecules". That misses half the definition. Molecular potential energy matters whenever the arrangement or separation of molecules matters, especially in liquids and solids.

For an Edexcel state or define item, a complete answer needs the molecular scale, random distribution, kinetic energy, and potential energy. A vague phrase such as "energy inside a substance" is not precise enough.

Temperature Is An Average

Now compare a mug of hot water with a bath of water at the same temperature. The molecules in the mug and the bath have the same average random kinetic energy if their temperatures are the same. The bath still has much more internal energy because it contains many more molecules.

That is the key separation:

Temperature is therefore not "the total energy in the object". It is an average molecular indicator. A tiny spark can be at a very high temperature while containing much less total internal energy than a warm bath.

The average matters because molecules have a spread of speeds. Heating a gas, for example, shifts the molecular population towards higher speeds on average. It does not make every molecule move at the same speed.

If a sample is heated and its temperature rises, the average random kinetic energy of its molecules increases. The internal energy also usually increases, but the reason must be stated carefully: internal energy increases because molecular kinetic energy, molecular potential energy, or both have increased.

Misconception contrast: "same temperature" does not mean "same internal energy". Same temperature means the same average random kinetic energy per molecule. The amount of substance and molecular potential energy still matter for internal energy.

The Absolute Temperature Scale

Celsius temperature is useful in everyday life, but its zero is not a zero of molecular kinetic energy. $0 {}^\circ\mathrm{C}$ is the freezing point of water under standard conditions. Water molecules at $0 {}^\circ\mathrm{C}$ still have random motion.

For molecular kinetic energy, the useful scale is kelvin. Absolute temperature, $T$, is measured in kelvin, K.

At A-level precision, $+273$ is often enough unless the question clearly needs more significant figures.

$0\,{}^\circ\mathrm C=273.15\,\mathrm K$ and $-273.15\,{}^\circ\mathrm C=0\,\mathrm K$.

$0\,\mathrm{K}$ is absolute zero. In the A-level molecular model, it is the temperature at which the average random kinetic energy of molecules has fallen to its minimum. It is not the same as $0 {}^\circ\mathrm{C}$, and kelvin temperatures do not use a degree sign.

The key relationship is:

So if the absolute temperature doubles, the average molecular kinetic energy doubles. If the absolute temperature halves, the average molecular kinetic energy halves.

Worked example: compare the average molecular kinetic energy of molecules in a gas at $27 {}^\circ\mathrm{C}$ and $127 {}^\circ\mathrm{C}$.

Decision point 1: use kelvin, not Celsius, because the relationship uses absolute temperature.