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
Explain about the perfect competition according to economics theory. The procedure of testing and refining theories is the key to the development of modern economics like a sci


What is an optimization in the methods of mathematics of modern economics? Optimization is a basic tool for the development of modern microeconomics analysis. Many of economic

Neoliberalism So much thinking about the proper role of government in economic growth over the past 2 decades has tends to conclusions which are today known as neo-liberal. The

A tax imposed on a market with an inelastic demand and an elastic supply will cause



A firm has a short-run production function defined by:  Q = -. 02L 2 + 8L What  is  the short  run demand curve  for  labour  (L) in terms of  the market wage  rate  (w), if

Carmen, the Queen of Electra, is concerned over what she believes is an excessive consumption of electricity.  Consequently, she proposes an excise tax on electricity consumption w

Economies of Common Services: Through the concentration of firms in a particular industry in a given geographical location, the firms may enjoy certain commonservices.These