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-area-to-volume ratio very large surface area for a given volume. The surface-area-to-volume ratio has physical dimension L (inverse length) and is therefore expressed in units of inverse distance. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm and a volume of 1 cm. The surface to volume ratio for this cube is thus For a given shape, SA:V is inversely proportional to size. A cube 2 cm on a side has a ratio of 3 cm, half that of a cube 1 cm on a side. Conversely, preserving SA:V as size increases