Boyles Law: Verification of 1662 Data
By: Derrick Wood
Introduction Data Analysis Conclusions References
Introduction:
In 1662 Robert Boyle investigated what he termed the “spring of the air,”
a descriptive term for the relationship between pressure and volume (1).
In a physical sense, Boyle recognized that changing the volume of a volume of
air had an effect on the pressure exerted much like that of a spring: the further
it is stretched, the more it wants to return to its original state. By working
at a constant temperature, he was able to measure the change in volume incurred
by an increase in pressure (2).
The purpose of this exercise is to verify what is now known as Boyle’s
Law using his original 1662 data and modern graphical analysis.
Data: (2)
Graph 2: Pressure vs. 1/Volume
Analysis:
The data was first analyzed by a graphical plot of the pressure applied versus
the volume measured (Graph 1). The curve was not linear,
but rather showed an inverse proportion. For example, if the pressure was doubled,
the volume decreased by about half. As a result, a second curve was constructed
plotting the pressure versus the inverse of the volume (Graph
2). This curve was linear, with a correlation coefficient of 0.9999. The
correlation coefficient shows how close the data points are to one another when
a straight line is drawn through them, with complete correlation being 1.0000.
The small amount of error in Boyle’s original data set was likely due
to the decreased amount of precision or accuracy of his instrumentation. Even
by today’s standards, Boyle collected a respectable set of data that lends
itself to straightforward graphical results: the pressure is inversely proportional
to the volume at a constant temperature. This statement was also verified by
analyzing the product of the pressure and volume. When the products of the pressures
and volumes were calculated, a similar set of values was obtained: between 1396
and 1415. The small range between these numbers is indicative of the experimental
error. However, when analyzed from a relative perspective, the range is less
than 1 % of the mean value of 1408 thus demonstrating the high degree of accuracy.
Conclusions:
While the data obtained over 300 years ago does not contain any of the typical
units used in modern scientific experiments, the relationship between pressure
and volume from Boyle’s original data set could still be determined: the
pressure is inversely proportional to the volume at a constant temperature.
By analyzing Boyle’s data using graphical analysis, it was possible to
verify the accuracy of this “spring-like” relationship: P1V1 = P2V2.
References:
1.) Baldwin, W.G.; Boyle’s Law; http://www.umanitoba.ca/chemistry/staff/baldwin/002_130/addtl_reading/Boyle.html;
(Accessed July 26, 2005).
2.) Giunta, C.; Boyle’s Law: Verification; http://web.lemoyne.edu/~giunta/classicalcs/boyleverify.html; (Accessed July 26, 2005).
