# If we plot P vs. 1//V, then do we get a straight line?

Mar 20, 2017

We don't, unless the temperature is fixed. For simplicity, this is certainly true for ideal gases. The ideal gas law is:

$P V = n R T$

Solving for pressure we get:

$P = \left(n R T\right) \cdot \frac{1}{V}$

Since mols $n$, the universal gas constant $R$, and $T$ are held fixed intentionally, if we chose to make a graph of $P$ vs. $\frac{1}{V}$, it is linear. That's a mathematical result of forcing $n R T$ to be a constant.

It is of the form $y = m x + b$ where $x = \frac{1}{V}$, $b = 0$, and $m = n R T$. Mind you, if you chose to plot $P$ vs. $V$ you would not see a straight line. What would you see instead?