# Thread: Partial derivation issue

1. ## Partial derivation issue

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:

$P=\frac{RT}{v-b}-\frac{a(T)}{v(v+b)+b(v-b)}$

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 = $T*/frac{dP}{dT}v -P$
Guy sorry first time I'm using latex, with this $frac{dP} {dT}v$ (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:

$pi=\frac{a(T)}{v(v+b)+b(v-b)}(1+kTr^(^1^/^2^))$

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

2. Might be worth posting this one again, seems a little tricky to follow

under the "math" tags a fraction has the code \frac{RT}{v-b} giving, $\frac{RT}{v-b}$

Click on the code to see how!

3. Thanks pickslides,

but i do really do not succede to write the partial derivetion correctely. Do you have any tips for this.