# Question with respect to a Max Planck article

• Phillip
In summary, the conversation discusses the book "The Dreams that Stuff is Made of" by Stephen Hawking and the first article by Max Planck titled "On the Distribution of Energy in the Normal Spectrum." The article introduces the concept of entropy and the formula SN = k log W + constant, where S represents the average entropy of a single resonator and N is the set of identical resonators. The constant k is Boltzmann's constant and serves as a proportionality constant to make the statistical and thermodynamic formulations of entropy equivalent. The conversation also includes a request for references to better understand the concept of probability and the elements in the formula. The recommended resource is Kittel and Kroemer's "Thermal Physics."

#### Phillip

This is not a homework problem, this is a question borne out of self-interest.

I picked up the book "The Dreams that Stuff is Made of" by Stephen Hawking:
(https://www.amazon.com/dp/0762434341/?tag=pfamazon01-20 )

and read the first article by Max Planck: "On the Distribution of Energy in the Normal Spectrum."
(The article can be found here: http://theochem.kuchem.kyoto-u.ac.jp/Ando/planck1901.pdf )

Just reading this article without understanding the formulas is surely not enough and my question is what all of the symbols mean in (3) of the article: SN = k log W + constant

S -> the average entropy of a single resonator
Subscript N -> the set of identical resonators

Now, log W is supposed to denote the probability of a set system of entropy existing if I understood this part correctly. My specific questions are:

What purpose does the k serve in front of log W?
What purpose does the +constant serve?
Why use log W to denote the probability of a set system of entropy existing?

If anyone has read this article, or chooses to do so before responding, could you please point me towards some references that might assist me in understanding probability and the rest of the elements in this formula?

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W is the number of "ways" or elementary configurations the system of resonators can be in (i.e., the number of ways the energy quanta can be distributed among all the N rasonators).

k is Boltzmann's constant. It serves as a constant of proportionality so that the statistical formulation of the entropy and the thermodynamic formulation of the entropy are equivalent.

As far as useful references go, I think pretty much any upper-level undergraduate textbook on statistical mechanics and thermodynamics will cover how to derive the blackbody spectrum. I am particularly partial to Kittel and Kroemer's "Thermal Physics".

• vanhees71
Thank you very much for your response as I now know where and what to look for in my university library. I checked the reference website and we have this text by Kittel and Kroemer. Thank you once again for the response.