Internal energy is the [[Energy|energy]] required to keep a [[Substance|substance]] or system in a certain [[State|state]]. Typically internal energy is used to describe the energy of a substance at a specific state point. Internal energy is defined as the product of the substance [[Mass|mass]]] and substance specific internal energy:
$U=mu$
Values for specific internal energy must be looked up in tables as it is a unique value based on the substance, [[Temperature|temperature]], [[Pressure|pressure]], and [[Specific Volume and Density|specific volume]]. The change in system internal energy will be the difference between final state internal energies and initial state internal energies.
$\Delta U=\sum m_eu_e−\sum m_iu_i$
For [[Ideal Gas|ideal gases]] the change in internal energy is found to be proportional to the change in temperature of the substance:
$\Delta u=C_{v0}\Delta T$
Likewise, for [[Solid|solids]] the change in internal energy can be found by:
$\Delta u=C\Delta T$