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.
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.