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
Solid nitrogen of Pluto. The thermal conductivity of solid nitrogen is 0.7 W m K. Thermal conductivity varies with temperature and the relation is given by "k" = 180.2×T watts per kelvin. Specific heat is given by 926.91×e joules per kilogram per kelvin. Its appearance at 50 K is transparent, while at 20 K it is white. Nitrogen frost has a density of 0.85 g cm. As a bulk material the crystals are pressed together and density is near that of water. It is temperature dependent and given by ρ = 0.0134"T" − 0.6981"T" + 1038.1 kg/m. The volume coefficient of expansion