# How do you graph Boyle’s law?

Boyle’s Law examines the relationship between the volume of a gas and its pressure.
So you would do an experiment in which you measure the volume of a gas at various pressures.
Let’s assume you get the following data.
The best way to determine a relationship is to plot a graph that gives a straight line.
At this point we (theoretically) don’t know the relationship, so we plot ##V## vs. ##P## to see what the plot looks like.
We plot pressure as the independent variable (along the horizontal or ##x## axis) and volume as the dependent variable (along the vertical or ##y## axis).
You could do this by hand, but it is more convenient to use a computer to do the job for you.
Your graph, as in the figure, looks like a hyperbola.
The equation for a hyperbola is ##y = k/x##. It looks as if we should try a plot of ##V## vs. ##1/P##.
We calculate the values of ##1/P## and then plot ##V## vs. ##1/P##. We get the straight line plot shown above.
If you plot the data manually, you extend the line backwards until it reaches ##V ≈ “0 cm”^3##.
The graph of ##V## against ##1/P## is a straight line through the origin.
This means that the measured volume is INVERSELY PROPORTIONAL to its pressure — .
If you use a computer or a calculator, you can tell it to calculate the equation for the line that best fits all the points (the regression line). My computer tells me that the equation is
##V = 6185.8/P – 0.0827##
This says that when ##1/P = 0##, ##V = “-0.08 cm”^3##.
Since we measured the volumes only to the nearest cubic centimetre, ##”0.08 cm”^3## is negligible. Therefore, within experimental uncertainty,
##V = 6185.8/P##
This is Boyle’s Law, ##V = k/P##.
If ##V = k/P##, then ##PV = k##.
The graph of ##PV## against ##P## should be a straight line parallel to the ##P## axis. In other words, the product ##PV## is a constant at a fixed temperature.
We can test this by plotting ##PV## vs. ##P## as shown below.
The graph looks like a horizontal straight line.
The computer gives the equation for the best fit line as
##PV= -0.149P + 6192.8##
That means that the line starts at ##PV = 6183.8## at the left hand end and finishes at ##6163.0## at the right hand end.
However, since we are justified in using only two for the PV product, it starts and ends at ##6200##.
Therefore, within the limits of experimental uncertainty,
##PV = “constant”## → BOYLE’S LAW

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