Formula derivation, algebra

raintrek

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!

Defennder

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.

raintrek

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]

Defennder

[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.