Internal Energy

Definition

Internal Energy ($U$) represents the sum of all microscopic forms of energy within a system. This includes:

• Kinetic: Translational, rotational, and vibrational motion of molecules.
• Potential: Intermolecular forces and chemical bonds.

It is a state function and extensive property.

Formula

$U = E_{total} - E_{kinetic} - E_{potential}$ (General definition as intrinsic energy)

Relationships

• Related: [[first-law|First Law of Thermodynamics]]
• Relation: $c_v = (\partial u / \partial T)_V$

Ideal Gases

Internal energy depends only on temperature (Joule’s Law): $du = c_v(T)\,dT$ $\Delta u = \int_{T_1}^{T_2} c_v\,dT$