Internal Energy

Quantity
Symbol$U$
UnitJoule (J)
Dimension$ML^2T^{-2}$
AliasesU

Definition

Internal Energy (UU) 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=Etotal−Ekinetic−EpotentialU = E_{total} - E_{kinetic} - E_{potential} (General definition as intrinsic energy)

Relationships

Ideal Gases

Internal energy depends only on temperature (Joule’s Law): du=cv(T) dTdu = c_v(T)\,dT Δu=∫T1T2cv dT\Delta u = \int_{T_1}^{T_2} c_v\,dT