16.1 Internal Energy

2026 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Understand that internal energy is determined by the state of the system, and that it can be expressed as the sum of a random distribution of kinetic and potential energies associated with the molecules of a system.
  2. Relate a rise in temperature of an object to an increase in its internal energy.

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What is Internal Energy?

Every substance — whether it is a solid, liquid, or gas — is made up of tiny particles called molecules. These molecules are constantly moving and interacting with each other. Because of this, every molecule carries some amount of energy.

Internal energy is the total energy stored inside a substance due to the motion and position of all its molecules. It is given the symbol U.

Here is the key idea: internal energy is not just one type of energy. It is the sum (total) of two types of energy that every molecule has:

  • Kinetic energy — energy due to the movement (motion) of the molecules
  • Potential energy — energy stored due to the forces between molecules (called intermolecular forces)

Think of it this way: imagine you have a glass of water. Every water molecule inside is moving around and is also being pulled or pushed by nearby molecules. The total energy from all of that motion and all of those interactions, added together for every single molecule in the glass, gives you the internal energy of the water.

Kinetic Energy of Molecules

Molecules are always moving — even in a solid, they vibrate back and forth. This movement gives them kinetic energy (energy of motion).

  • In a solid, molecules vibrate in fixed positions.
  • In a liquid, molecules can move around more freely.
  • In a gas, molecules move very quickly and in all directions.

The faster a molecule moves, the more kinetic energy it has.

Potential Energy of Molecules

Molecules exert forces on each other — they attract or repel one another depending on how close together they are. This is similar to how a stretched spring stores energy. Because of these intermolecular forces, molecules also have potential energy.

The amount of potential energy depends on the separation (distance) between molecules:

  • When molecules are close together (as in solids and liquids), the intermolecular forces are strong, and so the potential energy is significant.
  • When molecules are far apart (as in gases), the forces are weaker, and the potential energy is different.

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