Variable-mass system events. The following derivation is for a body that is gaining mass (accretion). A body of time-varying mass "m" moves at a velocity v at an initial time "t". In the same instant, a particle of mass dm moves with velocity u. The initial momentum can be written as Now at a time "t" + d"t", let both the main body and the particle accrete into a body of velocity v + dv. Thus the new momentum of the system can be written as Since d"m"dv is the product of two small values, it can be ignored, meaning during d"t"
Law of mass action formula. The law of mass action also has implications in semiconductor physics. Regardless of doping, the product of electron and hole densities is a constant at equilibrium. This constant depends on the thermal energy of the system (i.e. the product of the Boltzmann constant, formula_20, and temperature, formula_21), as well as the band gap (the energy separation between conduction and valence bands, formula_22) and effective density of states in the valence formula_23 and conduction formula_24 bands. When the equilibrium electron formula_25 and hole formula_26 densities are equal, their density is called the "intrinsic" carrier density formula_27 as this would be