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Background:
Gases havevarious properties that can be observed in the laboratory, includingtemperature, pressure, mass and volume.With experimentation, scientists have found that these variables arerelated to each other. Robert Boyle isa scientist known for studying the relationship between pressure and volume ofa confined gas held at constant temperature.Boyle found that when he manipulated the pressure, the volumeof the gasresponded in the opposite direction.Today, Boyle’s Law states that pressure of a gas is inverselyproportional to its volume. Themathematical expression for this relationship is P1V1= P2V2,assuming temperature to be constant.
Purpose:
The purpose ofthis exercise is to verify that pressure and volume indeed are inverselyrelated through graphical analysis based on data collected by Robert Boyle in1662.
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Analysis:
In order toanalyze a table of data presented by Robert Boyle in 1662, a graph has beenconstructed using Excel to demonstrate his findings. According to this graph, shown in Figure 1, as volume increases,pressure decreases. The R2value of 0.9999 indicates the power trendline fits the regression almostperfectly, showing that there is a precisely inverse relationship between thepressure and volume of a gas at constant temperature. The equation of the trendline, y=1400.9x-0.996xindicates that indeed the relationship observed is a constant of 1400.9 timesapproximately 1/x, reinforcing the inverse relationship between temperature andvolume of a gas.
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Secondly, tosee the inverse relationship more clearly, a second graph was constructed. This graph of pressure versus inverse volumeshould demonstrate a linear relationship, if indeed the two variables, pressureand volume, are inversely related. As the graph in Figure 2 illustrates, therelationship between pressure and inverse volume is linear, with high certaintyillustrated by the R2 of 0.9999.The relationship is approximately equal to y = 1403x, a linearrelationship.
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To furtheranalyze this finding, a last graph was constructed to demonstrate therelationship between the inverse of pressure versus volume. The expected linear relationship wasdemonstrated with high certainty again with an R2 approximatelyequal to 1. The trend is linear, withan equation of about y = 0.0007x, as shown in Figure 3.
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Figure 1: Boyle’s Law:Pressure vs. Volume Graph
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Figure2: Pressure vs. InverseVolume Graph
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Figure 3: Inverse Pressureversus Volume
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Conclusions:
Asdemonstrated by this report, the graphical analysis of Robert Boyle’s datasupports his findings that the pressure of a gas is inversely proportional tothe volume at constant temperature.This is illustrated by the graph in Figure 1 above that indicates thatas volume increases, pressure decreases.It is further confirmed by the following two graphs, Figures 2 and 3,which both demonstrate that the relationship between one variable and the inverseof the other is indeed a linear function.Each graph has a high correlation efficient, at about 1, whichdemonstrates with certainty that there is truly an inverse relationship betweenvolume and pressure.
