Partial derivative of pure substance thermodynamic properties

[satheeshsg]

I'm trying to solve the following equation:

 

 

 

using the following properties available in RefProp (specifically the derivatives of pure substance):

 

 

 

Could anyone tell me how to modify the equation from being partial derivative with respect specific volume to partial derivative with respect to density (which can be easily obtained from RefProp). Thank you

[paulhorth]

Satheeshsg,

 

Your equations are not displayed in the post. Nevertheless, though I am not a calculus expert, i think the manipulation below is correct:

 

for any x, dx/da =dx/db. db/da

 

so, whatever x is, dx/d (rho) = dx/dv . dv/d(rho) I think this is true for partial derivatives also

 

then since v = 1/ (rho), dv/d (rho) = -1/(rho)^2

 

so dx/d(rho) = - (dx/dv)/(rho)^2

 

Paul.