(f) increase in the internal energy of a body as its temperature rises

The idea

Internal energy is the sum of the random kinetic and potential energies of the particles of a body. When a body's temperature rises, the average random kinetic energy of its particles increases, so its internal energy increases. For a fixed mass with no change of phase, the rise is linked to the temperature change by E = mcΔθ, where c is the specific heat capacity.

For example: Heating 2.0 kg of water by 10 K transfers about 8.4 × 10⁴ J, since 2.0 × 4200 × 10 = 8.4 × 10⁴ J. A question may ask what happens to internal energy as temperature rises, or which quantity increases.

What earns the marks

• Internal energy is the sum of the random kinetic and potential energies of the particles.
• A rise in temperature increases the average random kinetic energy of the particles.
• Therefore the internal energy of the body increases as its temperature rises.
• For a fixed mass with no phase change, E = mcΔθ links energy transfer to temperature change.
• Specific heat capacity c is the energy needed per unit mass per unit temperature change.

Common mistakes and how to put them right

• Saying internal energy is the same as temperature.

  Put it right: Temperature relates to average random kinetic energy, while internal energy includes potential energy too.

• Thinking only kinetic energy changes.

  Put it right: Potential energy can also change, especially during a phase change.

• Using E = mcΔθ during a change of phase.

  Put it right: At constant temperature Δθ = 0, so a different energy relationship applies.

• Forgetting to convert mass to kilograms or temperature change to kelvin before substituting into E = mcΔθ.

Exam tips

• Check whether the question involves a temperature change or a phase change before choosing an equation.
• Use Δθ in kelvin or degrees Celsius; a temperature difference is the same in both scales.
• Substitute values with units and check that the energy answer is in joules.