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Lavoisier's system was based largely on the quantitative concept that mass is neither created nor destroyed in chemical reactions (i.e., the conservation of mass). By contrast, Priestley preferred to observe qualitative changes in heat, colour, and particularly volume.
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.
These equations were found by d'Alembert from two principles – that a rectangular canal, taken in a mass of fluid in equilibrium, is itself in equilibrium, and that a portion of the fluid, in passing from one place to another, preserves the same volume when the fluid is incompressible, or dilates itself according to a given law when the fluid ...
Again, the derivation depends upon (1) conservation of mass, and (2) conservation of energy. Conservation of mass implies that in the above figure, in the interval of time Δt, the amount of mass passing through the boundary defined by the area A 1 is equal to the amount of mass passing outwards through the boundary defined by the area A 2: = =.
Mass continuity (conservation of mass) The rate of change of fluid mass inside a control volume must be equal to the net rate of fluid flow into the volume. Physically, this statement requires that mass is neither created nor destroyed in the control volume, [2] and can be translated into the integral form of the continuity equation:
Antoine-Laurent de Lavoisier (/ l ə ˈ v w ɑː z i eɪ / lə-VWAH-zee-ay; [1] [2] [3] French: [ɑ̃twan lɔʁɑ̃ də lavwazje]; 26 August 1743 – 8 May 1794), [4] also Antoine Lavoisier after the French Revolution, was a French nobleman and chemist who was central to the 18th-century chemical revolution and who had a large influence on both the history of chemistry and the history of biology.
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 respect to space and time (i.e., material derivative) of any finite volume (V) to represent the change of velocity in fluid media ...
Earlier references of the law of conservation of mass and its use were made by Jean Rey in 1630. [13] Although the law of conservation of mass was not explicitly discovered by Lavoisier, his work with a wider array of materials than what most scientists had available at the time allowed his work to greatly expand the boundaries of the principle ...