Mass conservation and transfer

For a closed system, the total mass of the system is conserved. For a component that is made of nonradioactive and nonradiogenic nuclides, the concentration of the component in the whole system can increase or decrease only through chemical reactions. The mass of a radioactive component decreases with time due to decay, whereas that of a radiogenic component increases with time (nuclear reaction). On the basis of mass conservation, some relations can be derived 

We first derive a relation for total mass conservation. Consider an arbitrary volume V enclosed in a surface Q. The mass inside the volume is JpdV, where p is density (in kg/m ) and dt is an infinitesimal volume in the volume V. The time derivative of the mass in the volume (i.e., the rate of the variation of the mass with time) is 

This is the differential form of the mass balance equation in three dimensions. Since J can be written as pu, where u is the flow velocity of the fluid, the above equation can also be written as 

we treat the case of mass conservation of a species. The difference between the conservation of total mass and the conservation of the mass of a species is that other species may react to form the species under consideration. Hence, the reactions must be included. The conservation equation for a species k can be written as 

One example is mass conservation of in a mineral (such as hornblende). Because decays to °Ar at a rate of where °Kq is the initial 

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