Number of bonds in a substance giving us an approximation of Ebond
The concept of modes as independent places to put energy
The idea of equipartition: thermal energy gets spread out evenly
Deriving relationships between the microscopic PE and KE to the macroscopic quantities Ebond and Ethermal.
Specific concepts introduced in this section
Lennard-Jones potential
The potential energy between atoms or molecules. The Lennard-Jones potential requires two parameters: the "size" of the bond (&sigma) and the well-depth (&epsilon).
Nearest neighbours
The average number of atoms that are closest to an atom. Essentially the same as the number of bonds per atom.
The generalisation of next-to-nearest neighbours should be obvious. Note that even though there are (typically) no bonds between NNN that they still contribute to the potential energy.
Thermal energy Ethermal
In this section meaning is given to Ethermal, rather than just ΔEthermal. Note that this energy is derived from the microscopic KE and PE of atoms/molecules. Does not depend on the number of nearest neighbours!
Bond energy Ebond
Bond energy is made up of all the microscopic PE that is not associated with random motion. Does not depend on the number of modes!
Equipartition of energy
Once a mode becomes active, the amount of energy in the mode is kBT/2.