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 sorbents for carbon capture adsorption for solids requires less energy for the CO to desorb from the material surface. Also, two primary or secondary amine molecules are generally required to absorb a single CO molecule in liquids. For solid surfaces, large capacities of CO can be adsorbed. For temperature swing adsorption processes, the lower heat capacity of solids has been reported to reduce the sensible energy required for sorbent regeneration. Many environmental concerns over liquid amines can be eliminated by the use of solid adsorbents. Manufacturing costs are expected to be significantly greater than the cost of simple amines. Because flue gas contains trace