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The law of conservation of mass and the analogous law of conservation of energy were finally generalized and unified into the principle of mass–energy equivalence, described by Albert Einstein's equation =. Special relativity also redefines the concept of mass and energy, which can be used interchangeably and are defined relative to the frame ...
The continuity equation says that if charge is moving out of a differential volume (i.e., divergence of current density is positive) then the amount of charge within that volume is going to decrease, so the rate of change of charge density is negative. Therefore, the continuity equation amounts to a conservation of charge.
A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity ...
Mass–energy equivalence states that all objects having mass, or massive objects, have a corresponding intrinsic energy, even when they are stationary.In the rest frame of an object, where by definition it is motionless and so has no momentum, the mass and energy are equal or they differ only by a constant factor, the speed of light squared (c 2).
The term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The invariant mass is another name for the rest mass of single particles. The more general invariant mass (calculated with a more complicated formula) loosely corresponds to the ...
In this form, it is apparent that in the assumption of an inviscid fluid – no deviatoric stress – Cauchy equations reduce to the Euler equations. Assuming conservation of mass, with the known properties of divergence and gradient we can use the mass continuity equation, which represents the mass per unit volume of a homogenous fluid with ...
The general form quoted for a mass balance is The mass that enters a system must, by conservation of mass, either leave the system or accumulate within the system. Mathematically the mass balance for a system without a chemical reaction is as follows: [2]: 59–62
Classically, conservation of energy was distinct from conservation of mass. However, special relativity shows that mass is related to energy and vice versa by =, the equation representing mass–energy equivalence, and science now takes the view that mass-energy as a whole is conserved. Theoretically, this implies that mass can itself be ...