# Substituting values and solving for an unknown

• Apr 27th 2009, 12:35 PM
self_shattered
Substituting values and solving for an unknown
i need to find the value of V in the following equation
(p+(a/V^2))*(V-b)=RT
where
P=9500KPa
R=.2968Kj/k/kg
T=175 K
a=27R^2*Tcr^2?(64*Pcr)
b=(R*Tcr)/(8Pcr)
Tcr=136.2 K
Pcr=3.39MPa
• Apr 28th 2009, 12:09 AM
Numerical solution of equations
Hello self_shattered
Quote:

Originally Posted by self_shattered
i need to find the value of V in the following equation
(p+(a/V^2))*(V-b)=RT
where
P=9500KPa
R=.2968Kj/k/kg
T=175 K
a=27R^2*Tcr^2?(64*Pcr)
b=(R*Tcr)/(8Pcr)
Tcr=136.2 K
Pcr=3.39MPa

$(p+(a/V^2))(V-b)=RT$

$\Rightarrow (pV^2+a)(V-b)=RTV^2$

$\Rightarrow pV^3-(b+RT)V^2+aV-ab=0$

The best advice I can give now is to use a numerical method; e.g. Newton-Raphson, with $f(V)= pV^3-(b+RT)V^2+aV-ab$ and $f'(V) = 3pV^2-2(b+RT)V+a$.

I'm not sure what the numerical values are, especially
Quote:

a=27R^2*Tcr^2?(64*Pcr)
What does ? mean?

If you don't know how to use Newton-Raphson, work out the numerical values of
$p, a, b, R, T$ (don't bother with the units, they only confuse things); post them here, and I'll do it for you.