Undergrad Planck had 2 definitions of energy in 1900, how?

[Cool4Kat]

TL;DR

Planck's 1900 paper appears to have two equations for the energy, hf, and hf/(e^(hf/kT)-1), how does that work?

So, I was looking into Einstein's 1907 paper where he derived the specific heat of solids using quantum mechanics and I found that Einstein just took the derivative of Planck's equation from 1900 for the average energy, U, as a function of time (and multiplied it by 3N for the three dimensions). Anyway, that makes sense for Einstein but then I got very confused about Planck in 1900.

This is the same paper that Planck said that light was created in little energy elements with energy equal to hf. So, how can the average energy = hf/(e^(hf/kT)-1)? I feel like that means that the energy has two definitions. I feel like I am missing something basic, what is it?

Thank you so much!

 

[atyy]

Summary: Planck's 1900 paper appears to have two equations for the energy, hf, and hf/(e^(hf/kT)-1), how does that work?

In Planck's proposal, there are many energy levels - the difference between each neighbouring pair of levels if hf.

When things are in equilibrium at temperature T, the probability with which the different energy levels are occupied is such that the average energy is hf/(e^(hf/kT)-1).

The derivation is given in http://galileo.phys.virginia.edu/classes/252/PlanckStory.htm.