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

    Moderator

    Jan 28, 2005
    9,030
    214
    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.... :eek:

    :D

    -tkr
     
  6. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    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 :D

    Thanks a lot.

    -tkr
     
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