Internal energy

Physics A2 · Thermodynamics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

The molecules of any substance move at random, so they have kinetic energy. Forces act between them, so they also have potential energy. The internal energy of a system is the sum of the randomly distributed kinetic and potential energies of all its molecules.

Internal energy depends only on the state of the system (its pressure, volume, temperature and phase), not on how it reached that state. If a system returns to its starting state, its internal energy is back to the starting value.

A rise in temperature means a greater mean kinetic energy of the molecules, so the internal energy rises. Melting and boiling raise the potential energy at constant temperature. An ideal gas has no intermolecular forces, so its internal energy is kinetic only.

Rules to remember

Common mistake

Students say internal energy cannot change if the temperature stays the same. During melting or boiling the temperature is constant but the potential energy of the molecules increases, so the internal energy increases.

Worked example

A sample of an ideal gas contains 3.0 × 1022 molecules at 27 °C. What is the total random kinetic energy of its molecules?

  1. Change to kelvin: T = 27 + 273 = 300 K.
  2. Mean kinetic energy of one molecule = (3/2)kT = 1.5 × 1.38 × 10−23 × 300 = 6.21 × 10−21 J.
  3. Total = 3.0 × 1022 × 6.21 × 10−21 = 186 J.
  4. An ideal gas has no potential energy, so this is also its internal energy.

Answer: About 190 J.

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