Internal Energy

All matter has internal energy – energy associated with molecular structure and activity. It includes all microscopic forms of energy such as kinetic energy of molecules, potential energy due to molecular interactions, and other forms of energy like vibrational and rotational energy of molecules.

$$\text{Chemical energy}\to \text{Atomic bonds in a molecule}$$

• Internal energy, $U[\text{kJ}]$, is an extensive property of a system
• Specific internal energy, $u\left[\frac{\text{kJ}}{\text{kg}}\right]$, is an intensive property of a system

The total energy of a closed system includes internal energy, such as:

$$\begin{array}{rl}E& =\frac{1}{2}m{v}^2+mgh+U\\ e& =\frac{E}{m}=\frac{1}{2}{v}^2+gh+u\end{array}$$

Internal energy is typically considered microscopic; thermal energy is a part of the internal energy of a system.