Rearrange the Equation

Discussion in 'General Science' started by Tekker, Mar 5, 2006.

1. Tekker Thread Starter Active Member

Apr 22, 2005
33
0
This is actually a chemistry problem, but I'm stuck on the math. :huh:

Rearrange this equation and solve for "V".

Code ( (Unknown Language)):
1.
2.       RT         a
3. P = -----  -  -----
4.       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

2. CoulombMagician Active Member

Jan 10, 2006
37
0
Multiply everything by V^2 and by (V-B). You'll end up with a quadratic equation.

3. hgmjr Retired Moderator

Jan 28, 2005
9,029
219
Code ( (Unknown Language)):
1.
2.
3.                 RT           a    ab
4. V^3  - (b  + -----) V^2  + ---- V - -----  =  0
5.                 P            P     P
6.
7.
The above expression is in the general form of a 3rd order equation.

hgmjr

EDIT: Amended equation.

4. Tekker Thread Starter Active Member

Apr 22, 2005
33
0
I tried that and I can't get it into a quadratic equation:

This is what I get

Code ( (Unknown Language)):
1.       RT         a
2. P = -----  -  -----
3.       V-b       V^2
4.
5.       RT         a
6. 0 = -----  -  -----  -  P  * (V^2) ( V-b)
7.       V-b       V^2
8.
9. 0 = V^2 * RT  (aV  ab)  (V^3 * P  V^2 * bP)
10.
11. 0 = V^2 * RT - aV + ab - V^3 * P + V^2 * bP)
12.
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

5. Tekker Thread Starter Active Member

Apr 22, 2005
33
0
I guess my horrible algebra skills scared everyone off....  -tkr

6. hgmjr Retired Moderator

Jan 28, 2005
9,029
219
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.

Code ( (Unknown Language)):
1.
2.    RT     a
3. P = ----- - -----
4.    V-b    V^2
5.
6. Here it goes.......
7.
8.      V^2RT
9. V^2P = --------  - a (multiply both sides by V^2)
10.      V-b
11.
12. V^2(P)(V-b) = V^2(RT) - a(V-b)
13.
14. V^3(P) - V^2(Pb) = V^2(RT) - Va + ab
15.
16. (P)V^3 - (Pb)V^2 - (RT)V^2 + aV - ab = 0
17.
18. (P)V^3 - (Pb + RT)V^2 + aV - ab = 0
19.
20.          RT      a    ab
21. V^3 - (b + ----) V^2 + --- V - --- = 0
22.          P      P    P
23.
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

7. Tekker Thread Starter Active Member

Apr 22, 2005
33
0
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 Thanks a lot.

-tkr