The internal energy of a thermodynamic system is the sum of the kinetic and potential energies of all the molecules or entities in the system. The kinetic energy of an individual molecule includes contributions due to its rotation and vibration, as well as its translational energy. The potential energy is associated only with the interactions between one molecule and the other molecules of the system. Neither the system's location nor its motion is of any consequence as far as the internal energy is concerned.

Consider an ideal monatomic gas. Here, each molecule is a single atom. Consequently, there is no rotational or vibrational kinetic energy. Furthermore, there are no interatomic interactions, so potential energy is assumed to be zero. The internal energy is, therefore, a result of translational kinetic energy only. Therefore, the internal energy of ideal gas is just the number of molecules multiplied by the average kinetic energy per molecule. Thus, for n moles of an ideal monatomic gas, the internal energy is given by

It can be seen that the internal energy of a given quantity of an ideal monatomic gas depends on the temperature and is independent of the pressure and volume of the gas. For other systems, the internal energy cannot be expressed so simply. However, an increase in internal energy can often be associated with an increase in temperature.

In general, when a quantity of heat Q is added to a system, and the system does no work during the process, the internal energy increases by an amount equal to Q. When a system does work W by expanding against its surroundings, and no heat is added during the process, energy leaves the system and the internal energy decreases. While Q and W depend on the path, the change in internal energy of a system during any thermodynamic process depends only on the initial and final states, not on the path leading from one to the other.