Editing Conservation of mass (section)

== Formulation and examples ==
The law of conservation of mass can only be formulated in [[classical mechanics]], in which the energy scales associated with an isolated system are much smaller than <math>mc^2</math>, where <math>m</math> is the mass of a typical object in the system, measured in the [[frame of reference]] where the object is at rest, and <math>c</math> is the [[speed of light]].

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 equation|differential form]] as <math display="block">\frac{\partial \rho}{\partial t} + \nabla\cdot(\rho \mathbf{v}) = 0,</math> where <math display="inline">\rho</math> is the [[density]] (mass per unit volume), <math display="inline">t</math> is the time, <math display="inline">\nabla\cdot</math> is the [[divergence]], and <math display="inline">\mathbf{v}</math> is the [[flow velocity]] field.

The interpretation of the continuity equation for mass is the following: For a given closed surface in the system, the change, over any time interval, of the mass enclosed by the surface is equal to the mass that traverses the surface during that time interval: positive if the matter goes in and negative if the matter goes out. For the whole isolated system, this condition implies that the total mass <math display="inline">M</math>, the sum of the masses of all components in the system, does not change over time, i.e. <math display="block">\frac{\text{d}M}{\text{d}t} = \frac{\text{d}}{\text{d}t} \int \rho \, \text{d}V = 0,</math> where <math display="inline">\text{d}V</math> is the [[Differential (infinitesimal)|differential]] that defines the [[integral]] over the whole volume of the system.

The continuity equation for the mass is part of the [[Euler equations (fluid dynamics)|Euler equations]] of fluid dynamics. Many other [[convection–diffusion equation]]s describe the conservation and flow of mass and matter in a given system.

In chemistry, the calculation of the amount of [[Reagent|reactant]] and [[Product (chemistry)|products]] in a chemical reaction, or [[stoichiometry]], is founded on the principle of conservation of mass. The principle implies that during a chemical reaction the total mass of the reactants is equal to the total mass of the products. For example, in the following reaction
{{block indent | em = 1.5 | text = {{chem|CH|4}} + 2&nbsp;{{chem|O|2}} → {{chem|CO|2}} + 2&nbsp;{{chem|H|2|O}},}}
where one [[molecule]] of [[methane]] ({{chem|CH|4}}) and two [[oxygen]] molecules {{chem|O|2}} are converted into one molecule of [[carbon dioxide]] ({{chem|CO|2}}) and two of [[water]] ({{chem|H|2|O}}). The number of molecules resulting from the reaction can be derived from the principle of conservation of mass, as initially four [[hydrogen]] atoms, 4 oxygen atoms and one carbon atom are present (as well as in the final state); thus the number water molecules produced must be exactly two per molecule of carbon dioxide produced.

Many [[engineering]] problems are solved by following the mass distribution of a given system over time; this methodology is known as [[mass balance]].