Formula derivation, algebra

  1. I'm trying to derive a formula but can't seem to work the algebra.

    I need to combine these two:

    [tex]V_{1}p_{1} + V_{2}p_{2} = N[/tex]

    [tex]V_{1} + V_{2} = V[/tex]

    to get this:

    [tex]\frac{V_{1}}{V} = \frac{p-p_{1}}{p_{2}-p_{1}}[/tex]

    where [tex]p = N/V[/tex]

    If anyone could show me the steps that would be a huge help. Thanks in advance!
     
  2. jcsd
  3. Defennder

    Defennder 2,616
    Homework Helper

    Were you trying to obtain [tex]\frac{V_{1}}{V} = \frac{p-p_{2}}{p_{1}-p_{2}} [/tex] instead?

    With [tex]\frac{V_{1}}{V} = \frac{p-p_{1}}{p_{2}-p_{1}}[/tex], I got
    [tex]V_{2}p_{1} + V_{1}p_{2} = N[/tex] instead.
     
  4. Dang, that will teach me to copy and paste!

    I'm sorry, Defennder, here's the correct expressions:

    [tex]\frac{V_{2}}{V}=\frac{p-p_{1}}{p_{2}-p_{1}}[/tex]
     
  5. Defennder

    Defennder 2,616
    Homework Helper

    [tex]V_{1}p_{1} + V_{2}p_{2} = N[/tex]
    [tex](V-V_{2})p_{1} + V_{2}p_{2} = pV[/tex]
    Rearraging to get:
    [tex](p_{2}-p_{1})V_{2} = (p - p_{1})V[/tex]

    From here you just rearrange the terms and you'll get the answer.
     
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