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!
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.
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]
[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.