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
i have 40cm3 of hcl of 1 molarity i want to dilute it to 0.2m can yo please help

what to produce? how to produce? for whom to produce

Uses and Habit Forming Commodity -price elasticity of demand: The number of possible uses : A commodity has high price elasticity of demand (or elastic demand) if it can be p

I need help finding the future worth given the initial investment, MARR, and profit over a period of time.

Wage Differentials: Market structure alone does not account for all of the differences in wages and employment. Market wage differentials arise from various other sources, includin

Public Expenditure Trends: The expenditure pattern of the Government sector has been generally guided by the concern about the role of the State in the economy, both as invest

Two firms produce a pollutant called Q. The total costs of reducing emissions of Q are as follows for Firm 1 and Firm 2, respectively: TC1=10+100Q12 TC2=20 + 50Q22. This means tha

americana is a small country that produces and consumes jelly beans. The world price of jelly beans is $1 per bag, americana''s demand and supply for jelly beans are governed by th


STRATEGIES AND POLICIES FOR ADMINISTRATIVE REFORMS: As stated in a United Nation's Publication, following strategies and policies are necessary to bring about administrative i