Statistical Thermodynamics Lecture 6 Imperfect Gases Dr Ronald

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Statistical Thermodynamics Lecture 6: Imperfect Gases Dr. Ronald M. Levy ronlevy@temple. edu

Statistical Thermodynamics Lecture 6: Imperfect Gases Dr. Ronald M. Levy ronlevy@temple. edu

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 remainder 1 1 -0. 00064 0. 00000 100 1 -0. 06754 +0. 02127

remainder 1 1 -0. 00064 0. 00000 100 1 -0. 06754 +0. 02127 -0. 00036 1000 1 -0. 38404 +0. 68788 +0. 37237 2

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 Pair potential Mayer F function 6

Pair potential Mayer F function 6

Mayer F function In terms of Mayer f function, the first 2 Virial coefficient:

Mayer F function In terms of Mayer f function, the first 2 Virial coefficient: 7

Cluster diagram and star diagram Numbered circles represent particles whose coordinates we integrate over

Cluster diagram and star diagram Numbered circles represent particles whose coordinates we integrate over the bond between pairs of circles means particles are connected by a Mayer f function. All the Virial coefficients can be expressed in terms of a special set of cluster, These are called doubly connected, or star diagram. 3 1 2 Cluster diagrams 3 1 3 2 Doubly connected Star diagram 1 3 2 1 2 Not doubly connected Not star diagram Note: There are 2 topologically distinct cluster diagrams for 3 particles, there us 1 star diagram and 3 which is not 8

 All star diagram for j+1 particles. (The sum of all products of f

All star diagram for j+1 particles. (The sum of all products of f functions that connect 1, 2, …, j+1 molecules such that the cluster are connected so that the removal of any point, along with all lines to that point, still results in a connected graph) Star diagram for 4 particles: 1 2 2 3 4 4 3 1 1 4 2 4 3 2 9

 A. Hard sphere potential: Very important theoretically, can get exact results! Starting point

A. Hard sphere potential: Very important theoretically, can get exact results! Starting point for ##### very important for liquids �� /2 10

B. Square well potential For square well potential: 11

B. Square well potential For square well potential: 11

C. Lennard-Jones potential. 12

C. Lennard-Jones potential. 12

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