Thermal Energy

physics

Definition

Thermal Energy

Thermal energy is the energy contained in the disordered microscopic motion of the particles of a physical system. It is the internal energy associated with random translations, rotations, and vibrations of atoms and molecules, as opposed to the ordered motion of the whole body.

Formally, for a system of $N$ particles with total kinetic energy $K_{\text{tot}}$, the thermal energy is the kinetic energy measured in the centre-of-mass frame,

$$E_{\text{thermal}}=\sum _{i=1}^N\frac{1}{2}{m}_i⟨{\mathbf{v}}_i^{\prime }\cdot {\mathbf{v}}_i^{\prime }⟩,$$

where ${\mathbf{v}}_i^{\prime }={\mathbf{v}}_i-{\mathbf{v}}_{\text{cm}}$ is the velocity relative to the centre of mass. Flow of thermal energy between systems is heat.