Thermodynamics and Statistical Mechanics

Thermodynamics and Statistical Mechanics

Thermodynamics and Statistical Mechanics

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Presentation Transcript

1. Thermodynamics and Statistical Mechanics Heat Capacities Thermo & Stat Mech - Spring 2006 Class 20

2. Diatomic Gas • A gas of diatomic molecules can have translational, rotational and vibrational energy. Because of the spacing of the energy levels of each type of motion, they are not all equally excited. This shows up in the heat capacity. Thermo & Stat Mech - Spring 2006 Class 20

3. Partition Function For one molecule, e = etrans + erot + evib Thermo & Stat Mech - Spring 2006 Class 20

4. Partition Function Thermo & Stat Mech - Spring 2006 Class 20

5. Translational Motion Thermo & Stat Mech - Spring 2006 Class 20

6. Vibrational Motion Thermo & Stat Mech - Spring 2006 Class 20

7. High and Low Temperature Limits Thermo & Stat Mech - Spring 2006 Class 20

8. Rotational Motion Thermo & Stat Mech - Spring 2006 Class 20

9. Rotational Motion Thermo & Stat Mech - Spring 2006 Class 20

10. Diatomic Gas Overall Thermo & Stat Mech - Spring 2006 Class 20

11. Graph Thermo & Stat Mech - Spring 2006 Class 20

12. Einstein Solid Thermo & Stat Mech - Spring 2006 Class 20

13. Einstein Temperature Thermo & Stat Mech - Spring 2006 Class 20

14. Einstein Heat Capacity Thermo & Stat Mech - Spring 2006 Class 20

15. Debye Model of Solid • The solid is treated as a continuum, calculating the number of standing wave states in the frequency range between w and w + d w, and Bose-Einstein statistics is used to determine the number of phonons in each state. Then the energy can be calculated. Thermo & Stat Mech - Spring 2006 Class 20

16. Density of States (Lec 17) Thermo & Stat Mech - Spring 2006 Class 20

17. Transverse and Longitudinal Thermo & Stat Mech - Spring 2006 Class 20

18. Density of States Thermo & Stat Mech - Spring 2006 Class 20

19. Phonon Energy Thermo & Stat Mech - Spring 2006 Class 20

20. Debye Cutoff Thermo & Stat Mech - Spring 2006 Class 20

21. Debye Temperature Thermo & Stat Mech - Spring 2006 Class 20

22. Energy Thermo & Stat Mech - Spring 2006 Class 20

23. Heat Capacity Thermo & Stat Mech - Spring 2006 Class 20

24. Debye Heat Capacity Thermo & Stat Mech - Spring 2006 Class 20

25. High Temperature Thermo & Stat Mech - Spring 2006 Class 20

26. Low Temperature Thermo & Stat Mech - Spring 2006 Class 20