My Math Forum How to graph an equation with highly varied data points

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 July 2nd, 2017, 05:49 AM #1 Newbie   Joined: Feb 2017 From: USA Posts: 28 Thanks: 1 How to graph an equation with highly varied data points Hello all, I have a small challenge that I want to understand better. I need to graph some data points we produced in lab. It is a measure of pressure versus temperature given by the equation: $\displaystyle P=((nR)/V)*T+((273*nR)/V)$. My scale is very large and I would like to make it more manageable. On the one extreme, I have -273 degrees C at 0 Pa and on the opposite end ~100 degrees C and 140k Pa. Most of my data points are at 0-100 degrees C and between 100k Pa - 140k Pa. Is there a way to do a logarithmic plot that will contain most of the data in the largest section? Would that be considered an inverse log plot? I am not well versed in logarithms.... I thought perhaps the following would be the log, but was not sure about the inverse: log P = [((log n + log R)- log V)+log T] + (273[log n + log R])- log V Thanks for any assistance.
 July 2nd, 2017, 05:56 AM #2 Senior Member   Joined: Jun 2015 From: England Posts: 740 Thanks: 208 Is this a 2 axis (P and T) or three axis graph (P,T and V)? IOW is V constant? Also what about plotting PV against T? That would have a straight line form PV = aT + b with your equation of state. Last edited by studiot; July 2nd, 2017 at 05:59 AM.
 July 2nd, 2017, 06:00 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,959 Thanks: 801 The very first thing I would do is combine the two fractions: P= (nRT+ 273nR)/V. That could also be written PV= nRT+ 275nR and, if you are varying only P and V to graph one against the other, nRT+ 275nR is a constant: PV= c, a hyperbola.
July 2nd, 2017, 06:23 AM   #4
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Hello gents and thank you for the quick replies!

Yes, this is a 2 axis plot with volume being fixed.

The graph that I produced is in a straight line already. The equation as stated is in the form of graph of a line, y = mx+b. The professor has us write the equations in this format so that we can graph them easier.

My only problem is with the fact that one data point, absolute zero and zero pressure is on the far left while the remainder of the data points are on the far top right. Because the scale is so large, it is hard to represent the data accurately on the top right side. I have done a graph in excel, but we are to hand create this as a challenge. I thought perhaps some type of log scale was the answer.
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July 2nd, 2017, 06:43 AM   #5
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Quote:
 Originally Posted by chopnhack My scale is very large and I would like to make it more manageable.
From the figures you gave, it's already manageable and you don't need to do anything special. Are your experimental values unusually accurate (or at least consistently accurate)? How many different temperatures were used?

The plot you posted suggests your data aren't particularly accurate. Was the straight line drawn in by hand or calculated to fit your data as well as possible? If the latter, is the line affected much if you don't use the point at the lower left (corresponding to zero pressure)?

July 2nd, 2017, 07:10 AM   #6
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Quote:
 My only problem is with the fact that one data point, absolute zero and zero pressure is on the far left
My problem is imagining how you managed to obtain measurements at absolute zero temperature or zero pressure in your experiment.

 July 2nd, 2017, 07:49 AM #7 Newbie   Joined: Feb 2017 From: USA Posts: 28 Thanks: 1 The values are fairly accurate, but the line was chosen to fit the data as best as possible. Absolute zero was extrapolated from the slope of the line. Any further thoughts on how to graph differently?
 July 2nd, 2017, 07:58 AM #8 Senior Member   Joined: Jun 2015 From: England Posts: 740 Thanks: 208 So the point that was a long way off was derived by extrapolation from the real measured experimental data. So why include it? Thanks from JeffM1
 July 2nd, 2017, 08:03 AM #9 Senior Member   Joined: May 2016 From: USA Posts: 904 Thanks: 359 First, if you insist on including a point that was not in fact observed, I'd suggest a graph of the line without ANY data points with an insert showing the data points in a more appropriate scale. Otherwise, your graph is dishonestly implying that you observed something you did not. Second, I would not extend my graph far beyond what I observed. You do not have evidence to support that extension.
 July 2nd, 2017, 02:27 PM #10 Newbie   Joined: Feb 2017 From: USA Posts: 28 Thanks: 1 Because the professor requested. Thanks all.

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