## Graphing Example 6

It’s not enough to graph data. One has to know how to interpret the results. The graph below is a plot of air pressure in a sealed flask as a function of the air temperature. The best-fit line shows that as the temperature increases the pressure increases. But is there anything else to get from the graph?

We often teach our students to make sure the data fits as much of the page as possible. It usually isn’t a useful graph if all of the data is squashed into one, small area of the page. But this is where computers are useful. Instead of having the redraw the graph on paper (which can be difficult if there are numerous data points), one can quickly adjust parameters like the placement of the axes by just a few keystrokes. See how the y data, the air pressure, goes from 90 to 120 kilopascals? Press the “Shift Axis" button to see the y-axis scale change.

We can now get more information from this graph. Data is directly proportional if it's both linear, proportional, and if the line goes through the origin- (0,0). Think about what this means. If the pressure goes to 0 kilopascals, then shouldn't the temperature also go to 0? At least in some temperature units? This allows us to determine a value of 0 on the absolute temperature scale in terms of degrees Celsius. The equation y = mx + b can be rearranged to solve for x in terms of y (similar to what was done in example 4). If y, the pressure, is set 0 kPa, then the corresponding value for x is -301.6 °C.

Finally, what about these results? What is absolute 0 in degrees Celsius? It’s -273.15 and these results of -301.6 don’t appear to be too close. If you had obtained these results, then what would you conclude?

 Temperature (°C) Pressure (kPa) -0.1 92.17 0.6 92.39 3.2 93.24 10.1 95.40 16.5 97.44 19.0 98.12 34.9 103.01 61.3 111.29 72.5 114.58 81.4 116.85

Data collected 11/2007.

Uses the JSXGraph JavaScript libraries.