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
Vapor–liquid–solid method the metal droplet). More specifically, Δµ is the difference between the chemical potential of the depositing species (Si in the above example) in the vapor and solid whisker phase. Δµ is the initial difference proceeding whisker growth (when formula_7), while formula_8 is the atomic volume of Si and formula_9 the specific free energy of the wire surface. Examination of the above equation, indeed reveals that small diameters (formula_10100 nm) exhibit small driving forces for whisker growth while large wire diameters exhibit large driving forces. Involves the removal of material from metal-containing solid targets by irradiating the surface with high-powered (~100