# The Conservation Law

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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