Effective mass (solid-state physics) from both sides gives where is the th element of , is the th element of , and are the th and th elements of , respectively, and is the total energy of the particle according to the Planck–Einstein relation. The index is contracted by the use of Einstein notation (there is an implicit summation over ). Since Newton's second law uses the inertial mass (not the gravitational mass), we can identify the inverse of this mass in the equation above as the tensor This tensor expresses the change in group velocity due to a change in crystal momentum. Its
Mass balance stoichiometric mass of air is , so AFR = 14.56. The combustion product mass is then . At exact stoichiometry, should be absent. At 15 percent excess air, the AFR = 16.75, and the mass of the combustion product gas is , which contains of excess oxygen. The combustion gas thus contains 2.84 percent by mass. The relationships between percent excess air and % in the combustion gas are accurately expressed by quadratic equations, valid over the range 0–30 percent excess air: In the second example we will use the law of mass action to derive the expression for a