# Rearrange the Equation

#### Tekker

Joined Apr 22, 2005
33
This is actually a chemistry problem, but I'm stuck on the math. :huh:

Rearrange this equation and solve for "V".

Rich (BB code):
      RT         a
P = -----  -  -----
V-b       V^2
I imagine I need to somehow rearrange this so that V^2 is over V which would result in just V, but I cannot figure out how to get it to end up like that. I've tried a few different methods and all I seem to do is scatter V throghout the equation, which makes it much harder to isolate it. LOL

Thanks,
-tkr

#### CoulombMagician

Joined Jan 10, 2006
37
Multiply everything by V^2 and by (V-B). You'll end up with a quadratic equation.

#### hgmjr

Joined Jan 28, 2005
9,027
Rich (BB code):
                RT           a    ab
V^3  - (b  + -----) V^2  + ---- V - -----  =  0
P            P     P
The above expression is in the general form of a 3rd order equation.

hgmjr

EDIT: Amended equation.

#### Tekker

Joined Apr 22, 2005
33
Originally posted by CoulombMagician@Mar 5 2006, 05:37 PM
Multiply everything by V^2 and by (V-B).  You'll end up with a quadratic equation.
[post=14696]Quoted post[/post]​
I tried that and I can't get it into a quadratic equation:

This is what I get

Rich (BB code):
      RT         a
P = -----  -  -----
V-b       V^2

RT         a
0 = -----  -  -----  -  P  * (V^2) ( V-b)
V-b       V^2

0 = V^2 * RT  (aV  ab)  (V^3 * P  V^2 * bP)

0 = V^2 * RT - aV + ab - V^3 * P + V^2 * bP)
Now I have no idea where to go.... And where did that V^3 come from??? There has to be something Im missing, because this makes absolutely no sense to me.

hgmjr I cannot figure out how you got yours setup like that, would you mind breaking it down?

Thanks,
-tkr

#### Tekker

Joined Apr 22, 2005
33
I guess my horrible algebra skills scared everyone off....  -tkr

#### hgmjr

Joined Jan 28, 2005
9,027
Greetings Tekker,

I composed this step by step derivation last night but I hesitated to post it until I had a chance to review it.

My earlier attempt to simplifiy the equation had a flaw in it. I plan to go back and edit the original to correct the error.

In the meantime, for what its worth here is my latest effort.

Rich (BB code):
   RT     a
P = ----- - -----
V-b    V^2

Here it goes.......

V^2RT
V^2P = --------  - a (multiply both sides by V^2)
V-b

V^2(P)(V-b) = V^2(RT) - a(V-b)

V^3(P) - V^2(Pb) = V^2(RT) - Va + ab

(P)V^3 - (Pb)V^2 - (RT)V^2 + aV - ab = 0

(P)V^3 - (Pb + RT)V^2 + aV - ab = 0

RT      a    ab
V^3 - (b + ----) V^2 + --- V - --- = 0
P      P    P
It has been a while since I tackled solving a third-order equation. Your best bet may be to graph the equation with EXCEL.

hgmjr

Oh wow, now I don't feel so bad that I couldn't figure it out. I thought I was just over-complicating it and it was actually simpler than I was making it out to be. LOL 