Origin to the 'virial theorem' by Clausius

[pandabear]

Hello,
I wonder if there is a common origin to the 'virial theorem' by Clausius and the 'virial expansion' or equation of state used to express the compressibility of a gas. I am just wondering about this because the two concepts do not seem to have a common mathematical origin (that I can see), and upon searching for the etymology of the the word, "virial", I am lead back to the definition of these two concepts. I am just curious and would appreciate any leads you might have. Thank you!

 

[DaTario]

I had discussed this issue here in the forum and according to what was said then virial can be understood as each one of the three terms that constitutes the total energy.

E = (1/2)(mv_x^2) + (1/2)(mv_y^2) + (1/2)(mv_z^2)

for instance.

In the case above, the term E_x = (1/2)(mv_x^2) is a virial.

I would appreciate also to have here confirmations of this notion if it is possible.

Best regards

DaTario