I got this problem with a simple partial derivation that is driving me crazy, since the solution I obtain is different from the one published in the article, in which I believe.

Basically I got this equation:

Where:

P= pressure

R=Gas constant

T= temperature

V= molar volume

And

a(T) = a(Tc)*( 1+ k( 1-Tr^(1/2) ) )^2

a(Tc) = 0.45724 * R^2 * Tc^2 / Pc

Tc & Pc are the critical temperature & pressure respectively

k = 0.37464 + 1.54226*w - 0.26992*w^2

b=0.0778*R * Tc / Pc

Tr = T / Tc

w is the acentric factor.

Now I need to make this partial derivation:

pi = internal pressure =

Guy sorry first time I'm using latex, with this (if some one can show me the code please) I mean the partial derivation of P respect to T at constant volume.

The solution on the article is:

Could you please help me to understand how to arrive there.

Thanks