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 their biology, including their physiology and behavior. For example, many aquatic microorganisms have increased surface area to increase their drag in the water. This reduces their rate of sink and allows them to remain near the surface with less energy expenditure. An increased surface area to volume ratio also means increased exposure to the environment. The finely-branched appendages of filter feeders such as krill provide a large surface area to sift the water for food. Individual organs like the lung have numerous internal branchings that increase the surface area; in the case of the lung, the large surface supports gas