How was the Birch-Murnaghan equation derived for high pressure volume behavior?

[Sylvester]

Hello, physicists! Does anyone know how was this equation (below) mathematically derived? It is basically used to describe the behavior of volume at very high pressures (above 1 GPa). Vo designates the volume at ambient pressure. Bo is the bulk modulus and B’ its pressure derivative. I can't find anything in the literature where there is a step-by-step or at least a clue on how to come up with this expression.

 

[Frabjous]

I found this with google
https://mcbrennan.github.io/BMderivation.pdf

I would guess that Birch‘s paper has a derivation
Birch,F., “Finite Elastic Strain of Cubic Crystals,” Physical Review 71 (11),809–824 (1947).

Notice that it is isothermal.

 

[Sylvester]

I found this with google
https://mcbrennan.github.io/BMderivation.pdf

I would guess that Birch‘s paper has a derivation
Birch,F., “Finite Elastic Strain of Cubic Crystals,” Physical Review 71 (11),809–824 (1947).

Notice that it is isothermal.

Hey Frabjous! Thanks for the material. Just now, I briefly checked the pdf file and I think that's more than enough. Again, thank you so much for the help!

 

[Frabjous]

Hey Frabjous! Thanks for the material. Just now, I briefly checked the pdf file and I think that's more than enough. Again, thank you so much for the help!

You are welcome.

BTW, I could be wrong, but I think F is the Helmholtz free energy, not force.