This thermodynamic quantity equals what?

[M. next]

I am trying to use thermodynamics manipulations in order to find $\partial$P/$\partial$V (at constant entropy) I tried replacing P by T($\partial$S/$\partial$V)(at constant Energy) and then differentiated that by V but didn't help me. Do you have any idea where I can get around with this? Just throw in any formula!

Thanks!

 

[rude man]

Well, there's k_s = adiabatic compressibility (= reciprocal of the adiabatic bulk modulus):

k_s = - (1/v)(∂v/∂p)|_s,
s = sp. entropy.

It's related to C_p/C_V = γ = k/k_s

where k = the reciprocal of the isothermal bulk modulus = (-1/v)(∂v/∂p)|_T.

Made your day, eh?