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

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

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Answer 1 · 2017-03-20T07:51:05

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

$P V = n R T$ $PV = nRT$

Solving for pressure we get:

$P = (n R T) \cdot \frac{1}{V}$ $P = (nRT)*1/V$

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

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

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

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If we plot PP vs. 1/V1//V, then do we get a straight line?

1 Answer

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