The partition function for molecular gasses
The partition function for molecular gasses
It is common to assume that there are no intermolecular interactions between molecules when calculating the partition function for a molecular gas. Furthermore, it is also common to assume that the Hamiltonian for the molecules can be written as a sum of electronic, $H_e$, translational, $H_t$, rotational, $H_r$ and vibrational, $H_v$, parts as shown below: $$ H = H_e + H_t + H_r + H_v $$ as if the Hamiltonian can be written in this way the partition function can be written as a product of electronic, translational, rotational and vibrational parts: $$ Z = Z_e \times Z_t \times Z_r \times Z_v $$
Syllabus Aims
- You should be able to explain why the partition function can be written as a product of vibrational, electronic, translational and vibrational parts.
- You should be able to determine how many degrees of freedom a molecule contaning $N$ atoms possesses and how many of these degrees of freedom are translations, how many are rotational and how many are vibrational.
- You should be able to write an expression for the translational partition function based on your knowledge of the ideal gas model.- You should be able to derive an expression for the partition function of a harmonic vibrational degree of freedom.
- You should be able to derive expressions for the partition function of a rigid rotor, a symmetric top an assymetric top and a linear molecule.
- You should be able to explain what the equipartition principle tells us about the average energy of each degree of freedom of the molecule.
Description and link | Module | Author | ||
| A video describing how the partition function for a molecular gas can be decomposed in terms of translational, rotational and vibrational parts. | AMA4004 | G. Tribello |
Description and link | Module | Author | ||
| An exercise on deriving analytical expressions for the partition function of a harmonic oscillator and that introduces the notion of equipartition. | AMA4004 | G. Tribello |
Contact Details
School of Mathematics and Physics,
Queen's University Belfast,
Belfast,
BT7 1NN
Email: g.tribello@qub.ac.uk
Website: mywebsite