The internal energy of a system of a system is the microscopic energy associated with the particles in the system. This includes the translational, rotational, vibrational energy of these particles, the inter-particle potential energy, as well as the energy of their electrons and their nuclei.
– It does not include the macroscopic kinetic energy associated with the translation or rotation of the centre-of-mass of the system, or any potential energy the system may have as a result of it being in a field, e.g. the gravitational potential energy associated with the height of the system above some reference frame.
Consider a glass of water sitting on a table. It has no apparent energy. But on the microscopic scale, it comprises high speed molecules moving and vibrating and rotating. It has internal energy. If the water were tossed across the room, the system will of course gain macroscopic translational kinetic energy, but its microscopic internal energy remains largely unchanged.
Internal energy = thermal energy + chemical energy + nuclear energy + …
– Thermal energy is the energy of vibrations, internal rotation, intermolecular bond, etc, that can be changed by changing the temperature.
– Chemical energy is the energy stored in chemical bonds (in the electrostatic energy of the electrons and nuclei).
– Nuclear energy is the energy stored in the nuclei.
– It is not possible to list down all the energies that contribute to the internal energy.
For ideal gases:
– Mono-atomic gases: The thermal energy is stored as the translational kinetic energy of the atoms.
– Polyatomic gases: The thermal energy is stored as the sum of translational kinetic energy of the molecules, their rotational kinetic energy and vibrational energies.
The internal energy of an ideal gas depends only on its temperature: ΔE = nCvΔT.
For liquids and solids: There is a large contribution from the potential energy of the intermolecular forces. In these states, it is possible for the internal energy to change without changing the temperature. For example, this can occur when the material changes its state, or when the material is stretched/compressed. The change in intermolecular energy causes a change in the ΔE due to the latent heat.