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The law can be formulated mathematically in the fields of fluid mechanics and continuum mechanics, where the conservation of mass is usually expressed using the continuity equation, given in differential form as + =, where is the density (mass per unit volume), is the time, is the divergence, and is the flow velocity field.
All of the conservation laws listed above are local conservation laws. A local conservation law is expressed mathematically by a continuity equation, which states that the change in the quantity in a volume is equal to the total net "flux" of the quantity through the surface of the volume. The following sections discuss continuity equations in ...
Noether's theorem: Any quantity with a continuously differentiable symmetry in the action has an associated conservation law. Conservation of mass was the first law to be understood since most macroscopic physical processes involving masses, for example, collisions of massive particles or fluid flow, provide the apparent belief that mass is ...
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes. In general, the conservation law states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.
The exact conservation law used in the analysis of the system depends on the context of the problem, but all revolve around mass conservation, i.e., that matter cannot disappear or be created spontaneously. [2]: 59–62 Therefore, mass balances are used widely in engineering and environmental analyses.
The most fundamental concept in chemistry is the law of conservation of mass, which states that there is no detectable change in the quantity of matter during an ordinary chemical reaction. Modern physics shows that it is actually energy that is conserved, and that energy and mass are related; a concept which becomes important in nuclear chemistry.
This quark–lepton definition of matter also leads to what can be described as "conservation of (net) matter" laws—discussed later below. Alternatively, one could return to the mass–volume–space concept of matter, leading to the next definition, in which antimatter becomes included as a subclass of matter.
Conservation law, principle that a particular measurable property of an isolated physical system does not change as the system evolves over time Conservation of energy, principle that the total energy of an isolated system remains constant over time; Conservation of mass, principle that the mass of any closed system must remain constant over time