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

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In summary, the conversation discusses an equation used to describe volume behavior at high pressures and the search for a derivation of the equation. A paper by Birch is suggested as a possible source for the derivation and it is noted that the equation is for isothermal conditions.
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Sylvester
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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.
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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.
 
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Frabjous said:
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!
 
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Sylvester said:
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.
 
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1. What is the Birch-Murnaghan equation?

The Birch-Murnaghan equation is an equation used in materials science to describe the relationship between pressure and volume at high pressures. It is often used to calculate the bulk modulus, which is a measure of a material's resistance to compression.

2. Who developed the Birch-Murnaghan equation?

The Birch-Murnaghan equation was developed by Francis Birch and Percy Murnaghan in the 1940s. They were both American physicists who studied the behavior of materials under high pressures.

3. How was the Birch-Murnaghan equation derived?

The Birch-Murnaghan equation was derived using the principles of thermodynamics and the assumption that the volume of a material changes linearly with pressure. The equation also takes into account the elastic properties of the material.

4. What is the significance of the Birch-Murnaghan equation?

The Birch-Murnaghan equation is significant because it allows scientists to accurately predict the behavior of materials under high pressures. This is important in fields such as geology and materials science, where high pressures are often encountered.

5. Are there any limitations to the Birch-Murnaghan equation?

Like any mathematical model, the Birch-Murnaghan equation has its limitations. It is most accurate for materials that have a linear volume-pressure relationship and do not undergo phase transitions at high pressures. Additionally, the equation does not take into account the effects of temperature on the material's behavior.

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