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Lecture 6 ： Imperfect Gases

Statistical Thermodynamics. Lecture 6 ： Imperfect Gases. Dr. Ronald M. Levy ronlevy@lutece.rutgers.edu. 1. 2. 3. 4. 5. Pair potential. Mayer F function. 6. Mayer F function. In terms of Mayer f function, the first 2 Virial coefficient:. 7. Cluster diagram and star diagram. 3. 3.

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Lecture 6 ： Imperfect Gases

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  1. Statistical Thermodynamics Lecture 6： Imperfect Gases Dr. Ronald M. Levy ronlevy@lutece.rutgers.edu

  2. 1

  3. 2

  4. 3

  5. 4

  6. 5

  7. Pair potential Mayer F function 6

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

  9. Cluster diagram and star diagram 3 3 3 3 3 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. 1 2 1 1 1 1 1 2 2 2 2 2 Cluster diagrams Not doubly connected Not star diagram Doubly connected Star diagram Note: There are 2 topologically distinct cluster diagrams for 3 particles, there us 1 star diagram and 3 which is not 8

  10. 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 1 1 1 2 2 4 4 3 4 2 3 3 2 4 4 9

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

  12. Square well potential For square well potential: 11

  13. Lennard-Jones potential. 12

  14. 12

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