# Internal Energy

Internal energy is the sum of the kinetic and potential energies of the particles in a system.

In a thermodynamic system, internal energy (U) is the sum of all kinetic energy and potential energy of the particles in a system. Kinetic energy arises from the motion and vibration of particles, and potential energy arises from particle interactions such as chemical bonds, lattice energy in solids, and attraction and repulsion between gas particles. Internal energy is often shown by the letter U.

The internal energy of a system usually cannot be measured, with ideal gases being an exception. For ideal gases, particle interactions are considered to be completely elastic—the particles can return to their regular form after being deformed. This makes the internal energy of an ideal gas directly proportional to its temperature. In most systems, internal energy cannot be easily determined.

However, it is easier to detect changes in internal energy. For example, consider 100.0 g of water at 20.0°C. If the temperature of the water reaches 25.0°C, it is possible to determine how much the internal energy has changed by using the formula $Q=mc\Delta T$. How much the internal energy changed (or thermal energy) is Q, m is the mass, c is specific heat, and T is temperature in kelvins. For this example, the internal energy increases by $(100.0\;\rm{g})(4.186\;\rm{J/g}{\cdot}\degree\rm{C})(5.0\degree\rm{C})= 2\rm{,}100\;{J}$.

Internal energy changes when heat moves into and out of a system. Internal energy also changes when a system does work, or when work is done on a system.