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## Thermodynamics and Statistical Mechanics

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**Thermodynamics and Statistical Mechanics**Heat Capacities Thermo & Stat Mech - Spring 2006 Class 20**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**Partition Function**For one molecule, e = etrans + erot + evib Thermo & Stat Mech - Spring 2006 Class 20**Partition Function**Thermo & Stat Mech - Spring 2006 Class 20**Translational Motion**Thermo & Stat Mech - Spring 2006 Class 20**Vibrational Motion**Thermo & Stat Mech - Spring 2006 Class 20**High and Low Temperature Limits**Thermo & Stat Mech - Spring 2006 Class 20**Rotational Motion**Thermo & Stat Mech - Spring 2006 Class 20**Rotational Motion**Thermo & Stat Mech - Spring 2006 Class 20**Diatomic Gas Overall**Thermo & Stat Mech - Spring 2006 Class 20**Graph**Thermo & Stat Mech - Spring 2006 Class 20**Einstein Solid**Thermo & Stat Mech - Spring 2006 Class 20**Einstein Temperature**Thermo & Stat Mech - Spring 2006 Class 20**Einstein Heat Capacity**Thermo & Stat Mech - Spring 2006 Class 20**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**Density of States (Lec 17)**Thermo & Stat Mech - Spring 2006 Class 20**Transverse and Longitudinal**Thermo & Stat Mech - Spring 2006 Class 20**Density of States**Thermo & Stat Mech - Spring 2006 Class 20**Phonon Energy**Thermo & Stat Mech - Spring 2006 Class 20**Debye Cutoff**Thermo & Stat Mech - Spring 2006 Class 20**Debye Temperature**Thermo & Stat Mech - Spring 2006 Class 20**Energy**Thermo & Stat Mech - Spring 2006 Class 20**Heat Capacity**Thermo & Stat Mech - Spring 2006 Class 20**Debye Heat Capacity**Thermo & Stat Mech - Spring 2006 Class 20**High Temperature**Thermo & Stat Mech - Spring 2006 Class 20**Low Temperature**Thermo & Stat Mech - Spring 2006 Class 20