The Conservation Law

Topics: Atom, Chemistry, Molecule Pages: 11 (336 words) Published: October 11, 2014






For each problem (momentum, energy & mass),
we will start with an initial chapter dealing with
some results of the molecular theory of the
transport phenomena (viscosity, thermal
conductivity & diffusivity)
Then, proceed to microscopic level and learn how
to determine the velocity, temperature and
concentration profiles in various kinds of
systems.
Then, the equations developed at microscopic
level are needed in order to provide some input
into problem solving at macroscopic level.



At all three levels of description (molecular,
microscopic & macroscopic), the conservation
law play a key role.









Conservation law – keeping from change or to
hold ( a property) constant during an interaction
or process.

We consider two colliding diatomic molecules
system.
For simplicity we assume that the molecules do
not interact chemically and that each molecule is
homonuclear (molecules composed of only one
type of element).
The molecules are in a low-density gas, so that
we need not consider interactions with other
molecules in' the neighborhood.



In Fig. 0.3-1 we show the collision between
the two homonuclear diatomic molecules, A
and B, and in Fig. 0.3-2 we show the notation
for specifying the locations of the two atoms
of one molecule by means of position vectors
drawn from an arbitrary origin.





Total mass of the molecules entering and
leaving the collision must equal.

Here mA and mB are the masses of molecules
A and B. Since there are no chemical
reactions, the masses of the individual
species will also be conserved, so that





the sum of the momenta of all the atoms
before the collision must equal that after the
collision, so that

in which rA1 is the position vector for atom 1
of molecule A, and rA1 is its velocity.



We now write rA1 = rA + RA1, so that rA1 is
written as the sum of the position vector for
the center of mass and RA2 = -RA1.



Rewrite the equation to:



Given,



the energy of the colliding pair of molecules
must be the same before and after the
collision



Rewrite the equation to:



Given,

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