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This is an accepted version of this page This is the latest accepted revision, reviewed on 31 December 2024. Law of physics and chemistry This article is about the law of conservation of energy in physics. For sustainable energy resources, see Energy conservation. Part of a series on Continuum mechanics J = − D d φ d x {\displaystyle J=-D{\frac {d\varphi }{dx}}} Fick's laws of diffusion ...
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 ...
The global versions can be united into a single global conservation law: the conservation of the energy-momentum 4-vector. The local versions of energy and momentum conservation (at any point in space-time) can also be united, into the conservation of a quantity defined locally at the space-time point: the stress–energy tensor [ 11 ] : 592 ...
The first law of thermodynamics states that, when energy passes into or out of a system (as work, heat, or matter), the system's internal energy changes in accordance with the law of conservation of energy. The second law of thermodynamics states that in a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic ...
The first law is the law of conservation of energy. The symbol δ {\displaystyle \delta } instead of the plain d, originated in the work of German mathematician Carl Gottfried Neumann [ 1 ] and is used to denote an inexact differential and to indicate that Q and W are path-dependent (i.e., they are not state functions ).
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Other equations in physics, such as Gauss's law of the electric field and Gauss's law for gravity, have a similar mathematical form to the continuity equation, but are not usually referred to by the term "continuity equation", because j in those cases does not represent the flow of a real physical quantity.
where: is the rate of change of the energy density in the volume. ∇•S is the energy flow out of the volume, given by the divergence of the Poynting vector S. J•E is the rate at which the fields do work on charges in the volume (J is the current density corresponding to the motion of charge, E is the electric field, and • is the dot product).