Surface tension gases. The pressure inside an ideal (one surface) soap bubble can be derived from thermodynamic free energy considerations. At constant temperature and particle number, , the differential Helmholtz energy is given by where is the difference in pressure inside and outside of the bubble, and is the surface tension. 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 . For real soap bubbles, the pressure is doubled due to the presence of two
Surface energy number of atoms at the surface and in the bulk of the solid. Calculating the surface formation energy of a crystalline solid In density functional theory, surface energy can be calculated from the following expression where formula_17 is the total energy of surface slab obtained using density functional theory. formula_18 is the number of atoms in the surface slab. formula_19 is the bulk energy per atom. formula_6 is the surface area. For a slab, we have two surfaces and they are of the same type, which is reflected by the number 2 in the denominator. To guarantee this, we need