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 environments. The surface to volume ratios of organisms of different sizes also leads to some biological rules such as Bergmann's rule and gigantothermy. In the context of wildfires, the ratio of the surface area of a solid fuel to its volume is an important measurement. Fire spread behavior is frequently correlated to the surface-area-to-volume ratio of the fuel (e.g. leaves and branches). The higher its value, the faster a particle responds to changes in environmental conditions, such as temperature or moisture. Higher values are also correlated to shorter fuel ignition times, and hence faster fire spread rates. A body of