Internal energy is the sum of the randomly distributed kinetic energies…

The idea

Internal energy is a property of a body arising from its particles. It is the total of two contributions: the kinetic energies associated with random motion of particles, and the potential energies associated with forces between particles. Random means there is no net bulk motion; individual particles have a distribution of speeds. For an ideal gas, potential energy is negligible, so internal energy depends only on total kinetic energy and therefore on temperature and number of particles. For a real substance, potential energy changes during changes of state at constant temperature, so internal energy changes even when kinetic energy does not.

For example: Melting ice at 0 °C increases internal energy because energy is used to break intermolecular bonds, increasing potential energy while temperature stays constant.

What earns the marks

• Internal energy is the total of the kinetic and potential energies of all particles in a body, not an average per particle.
• Kinetic energy contribution arises from random motion of particles; random means no net movement of the body as a whole.
• Potential energy contribution arises from forces between particles and their separations.
• For an ideal gas, intermolecular potential energy is negligible, so internal energy is the total random kinetic energy of its particles.
• During a change of state at constant temperature, kinetic energy stays constant but potential energy changes, so internal energy changes.
• Internal energy is not the same as temperature: temperature relates to average random kinetic energy per particle, while internal energy is a total over all particles.

Common mistakes and how to put them right

• Treating internal energy as only kinetic energy.

  Put it right by including potential energy for real substances, while noting it is negligible for an ideal gas.

• Confusing internal energy with temperature.

  Put it right by stating that temperature is related to average random kinetic energy per particle, whereas internal energy is the total for all particles.

• Assuming internal energy always rises when temperature rises.

  Put it right by recognising that during a change of state at constant temperature, internal energy can change because potential energy changes.

• Using the term 'heat' for internal energy.

  Put it right by using 'internal energy' for the energy stored in a body and 'heating' for a transfer process.

Exam tips

• Define internal energy in one sentence that includes both kinetic and potential contributions and the word 'random'.
• When explaining a change of state, state explicitly that kinetic energy remains constant while potential energy increases.
• Use the ideal gas case to show understanding: if potential energy is negligible, internal energy depends on total kinetic energy, so it depends on temperature and number of particles.
• Avoid saying 'heat energy inside a body'; refer to internal energy stored and energy transferred by heating.