The pressure inside an ideal spherical bubble can be derived from thermodynamic free energy considerations. The above free energy can be written as:
where  is the pressure difference between the inside (A) and outside (B) of the bubble, and  is the bubble volume. In equilibrium, , and so,
For a spherical bubble, the volume and surface area are given simply by
and
Substituting these relations into the previous expression, we find
which is equivalent to the Young–Laplace equation when .