Beaker of Water

The internal energy is the sum of the kinetic and potential energies associated with the molecules and atoms that make up an object. The energy that an object possesses due to its macroscopic motion does not contribute to its internal energy. For example, a beaker of water has the same internal energy whether it is sitting stationary on a lab bench or being carried across a room.


Water Molecules

Water molecules in ice vibrate in relatively fixed positions. These vibrations contribute to the kinetic energy portion of the internal energy and involve the bending and stretching of bonds. [Zoom in for a more detailed view.] The potential energy components of internal energy, when viewed at the mesoscopic level, include the attractions and repulsions between molecules. These interactions are called intermolecular attractions.

Kinetic Energy

Rotational motion

Unlike vibrational motion, which involves the motion of the hydrogen and oxygen atoms within a water molecule, rotational motion involves the rotation of the entire molecule as a group around an axis in three-dimensional space.

Kinetic Energy

Translational motion

Like rotational motion, translational motion involves the movement of the entire molecule in three-dimensional space. In the liquid phase translational motion is somewhat restricted as water molecules are very close to each other.

Potential Energy

Intermolecular forces

Intermolecular forces are electrostatic attractions and repulsions that occur between molecules that are close to each other. These interactions contribute to the potential energy component of internal energy and are relatively weak compared to the covalent bonds that hold the atoms together. As the temperature rises, molecules move faster and the number of intermolecular interactions decreases.


Atoms of a water molecule

At the molecular level of liquid water, molecules are free to move past each other and flow. They have vibrational motion that involves the stretching and bending of bonds, are able to rotate around an axis and translate in three dimensional space. As the water cools down to form a solid, rotational and translational motion becomes restricted. Select each type for an illustration and description.

Kinetic Energy

Vibrational motion

All stretching vibrations involve a change in bond length, while all bending vibrations involve a change in bond angles.

Kinetic Energy

Vibrational motion - Symmetric stretch

A symmetric stretch is a vibration that occurs as bonds are stretched in the same manner simultaneously. In a water molecule, a symmetric stretching vibration occurs when the hydrogen atoms are either both moving away from the oxygen atom or both moving toward the oxygen atom.

Kinetic Energy

Vibrational motion - Asymmetric stretch

An asymmetric stretch is a vibration that occurs when bonds are stretched in different manners. In a water molecule, an asymmetric stretching vibration occurs when one hydrogen atom moves away from the oxygen atom while the other moves toward the oxygen atom.

Kinetic Energy

Vibrational motion - Bending vibrations

Bending vibrations involve a change in bond angles. In a water molecule, a bending vibration occurs when the two hydrogen atoms move toward each other or away from each other. This type of vibration is called scissoring.

Potential Energy

Intramolecular forces

Intramolecular forces are the forces that occur between atoms in the same molecule and include covalent bonds. These forces constitute a potential energy contribution for internal energy.

Potential Energy

Electrostatic interactions

Electrostatic interactions contribute to the potential energy component of internal energy and include the attraction between nuclei and the electrons in bonds, the interactions between protons and neutrons, and the repulsions between different electrons.


Atomic nucleus

The nuclear force binds protons and neutrons together in the nucleus of an atom. The energy needed to bind nucleons is formed from the mass of the nucleons themselves and results in a phenomenon known as the mass defect (discussed further in chapter 20). Overall, this small amount of stored energy makes up only a minor component of the internal energy.