- #1
sai2020
- 26
- 0
The question:
In 1900, Planck used an abstract model consisting of harmonic oscillators with various frequency. Derive an average energy [tex]\bar{\epsilon}[/tex] of a single oscillator where the oscillators of frequency f can only take on discrete energies [tex]\epsilon[/tex][tex]_{n}[/tex] = nhf, n=0, 1, 2, ... and the Boltzmann probability distribution, P([tex]\epsilon[/tex][tex]_{n}[/tex]) = exp(-[tex]\epsilon[/tex][tex]_{n}[/tex] / k[tex]_{B}[/tex]T). (Note: Boltzmann showed that the probability for a system at equilibrium to have an energy E is proportional to exp(-[tex]\epsilon[/tex][tex]_{n}[/tex] / k[tex]_{B}[/tex] T, where k[tex]_{B}[/tex] is the Boltzmann constant.
I have no idea what he is talking about and my textbook doesn't say anything either. Can someone point me to a good book about these stuff?
In 1900, Planck used an abstract model consisting of harmonic oscillators with various frequency. Derive an average energy [tex]\bar{\epsilon}[/tex] of a single oscillator where the oscillators of frequency f can only take on discrete energies [tex]\epsilon[/tex][tex]_{n}[/tex] = nhf, n=0, 1, 2, ... and the Boltzmann probability distribution, P([tex]\epsilon[/tex][tex]_{n}[/tex]) = exp(-[tex]\epsilon[/tex][tex]_{n}[/tex] / k[tex]_{B}[/tex]T). (Note: Boltzmann showed that the probability for a system at equilibrium to have an energy E is proportional to exp(-[tex]\epsilon[/tex][tex]_{n}[/tex] / k[tex]_{B}[/tex] T, where k[tex]_{B}[/tex] is the Boltzmann constant.
I have no idea what he is talking about and my textbook doesn't say anything either. Can someone point me to a good book about these stuff?