Solid angle to the unit sphere with center P, which can be calculated as the surface integral: where formula_5 is the unit vector corresponding to formula_6, the position vector of an infinitesimal area of surface with respect to point P, and where formula_7 represents the unit normal vector to . Even if the projection on the unit sphere to the surface S is not isomorphic, the multiple folds are correctly considered according to the surface orientation described by the sign of the scalar product formula_8. Thus one can approximate the solid angle subtended by a small facet having flat surface area ,
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