Question #8ea79

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Question #8ea79

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Answer 1 · 2015-03-17T21:02:03

You have three variables, $P$ $P$ , $V$ $V$ , and $T$ $T$ , so you need a three-dimensional graph with $P$ $P$ , $V$ $V$ , and $T$ $T$ axes.

You get a 3D surface that looks like the middle graph in the image below.

![Graph of a 3D surface from http://web.inc.bme.hu.](http://web.inc.bme.hu/csonka/csg/oktat/english/gaslaws_elemei/image001.gif)

If the temperature is constant and you look at the graph in a $P V$ $PV$ plane, you see the blue line hyperbola of Boyle's Law, $P V = k$ $PV = k$ .

If the pressure is constant and you look at the graph in a $V T$ $VT$ plane, you see the straight black line of Charles' Law, $V = k T$ $V= kT$ .

If the volume is constant and you look at the graph in a $P T$ $PT$ plane, you see the straight red line of Amontons' Law (often called Gay-Lussac's Law), $P = k T$ $P= kT$ .

Put them all together, and the 3D surface is a graph of the Combined Gas Law, $\frac{P V}{T} = k$ $(PV)/T = k$ .

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Question #8ea79

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