Energies of the diametric molecules of a gas, chemistry, Microeconomics

Energies of the diametric molecules of a gas, chemistry assignments

The analysis basis for treating these different types of motion can be seen by describing the motion of a diametric molecule of a gas. Here we describe the potential and kinetic energy components of a freely moving gas phase molecule treated as if it were a ball and spring system.

The only potential energy contribution arises from variations in the distance between the atoms of the molecule. If the variable intermolecular distance is represented by, then the energy U can be shown to be a function of r by writing U(r).

The kinetic energy depends on the motion of the two atoms of the molecule dx1/dt, dy1/dt and dz1/dt, respectively, of one of the atoms. The symbols x2y2 and z2 represent the velocity components of the second atom.

The total mechanical energy ε of the diatomic molecule is given by;

Separate translational, rotational and vibrational components of this energy can be recognized if a different coordinate system is introduced.

The center of mass of the molecules can be located by coordinates represented by X, Y and Z. the center of the mass, as is illustrated in two dimensions in fig. is related to the atomic pressure by the expressions:

ε = ½ m1 (x21 + y21 + z21) + ½ m2(x22 + y22 +z22) + U (r)

(m1 + m2)X = m1x1 + m2x2

(m1 +m2)Y = m1y1 + m2y2

(m1 + m2)Z = m1z1 +m2z
2

The orientation of the molecule is expressed by the polar angular coordinate's θ and Ø. These angular coordinates and the internuclear distance r lead to the relations:

x2 - x1 = r sinθ cos∅, y2 - y1 = sinθ cosØ, z2 - z1 = r cosθ

These relations can be used to eliminate the coordinates for one or the other of the two atoms. We can, for example, use the first to write x2 = x1 +r sinθ cos Ø. Substitution in the first step of eq.  eliminates the x2term. This procedure leads to:

x1 = X - m2/m1 + m2 r sinθ cos Ø 

y1 = Y- m2/m1 + m2 r sinθ cos Ø 

z1 = Z - m2/m1 + mr cos θ 

and, x2 = X - m2/m1 + m2 r sinθ cos Ø 

y2 = Y - m2/m1 + m2 r sinθ cos Ø 

z2 = Z - m2/m1 + m2 r cos θ 


the derivates of expressions with respect to time can be taken if we recognize that X, y, X, r, θ and Ø are all time dependent. The results for x1, y1, z1 and x2, y2z2 can be substituted to give, after rearrangement:

ε = ½ (m1 + m2) (X2 + Y2 +Z2) + ½ m1m2/m1 +m2 [r2 + r2 θ2 + r2 (sin2θ) Ø2] +U (r) 

Posted Date: 2/15/2012 10:01:55 AM | Location : United States







Related Discussions:- Energies of the diametric molecules of a gas, chemistry, Assignment Help, Ask Question on Energies of the diametric molecules of a gas, chemistry, Get Answer, Expert's Help, Energies of the diametric molecules of a gas, chemistry Discussions

Write discussion on Energies of the diametric molecules of a gas, chemistry
Your posts are moderated
Related Questions
Use of Income elasticity of demand: Income elasticity of demand on the other hand, has the following uses (i) Income elasticity of demand shows how the pattern of consumer de

WHAT ARE THE PRACTICAL IMPORTANCE OF INCOME ELASTICITY OF DEMAND?

The accountants keep all the business transactions and records of a sole proprietorship separate from the business owner''s personal transactions and For legal purposes a sole prop


Discriminatory Fee Structure This method discriminates between courses and the economic condition of the family to which the student belongs. The cost of providing the educati

Employer’s Estimates of Future Manpower Requirements One of the parameters of demand for employment in a firm or a factory or an establishment is the level of capital investme

could the village prepare 14 campsites and grow 350 pawpaws?explain your answer.

Capital Gain: A capital gain is a form of profit which is earned on an investment by re-selling an asset for more than it cost to buy. Assets that can be purchased for this purpose


When Alex's income increased from $3,000 to $5,000, he increased his consumption of bagels from 4 to 8 a month and decreased his consumption of donuts from 12 to 6 a month. Calcula