A New Quantitative Pressure-Volume Experiment Based on the "Cartesian Diver" Judith U. S. ~ h o m ~ s o n ' Mt. Dora High School, Mt. Dora, FL 32757 Kenneth A. ~ o l d s b ~ ' The Florida State University, Tallahassee, FL 32306
The study of the physical properties of gases is a n important component of most high school and college chemistry courses. A wide variety of laboratory experiments and demonstrations have been developed to illustrate the physical properties of gases, generally in terms of one of the gas laws ( I ) . Unfortunately, most of the experiments involving pressure relationships use mercury mauometers, and many high schools and colleges are being asked to remove mercury from their laboratories. The Cartesian Diver is a classic exoeriment based on a device that dates to the 1600's and is generally credited to R e d Descartes (2.3). . Orieinallv. ". i t was used to amuse children and entertain house guests. I n its simplest form, a Cartesian Diver is constructed by placing a n inverted unstoppered vial in a glass of water, allowing enough water into the vial so that i t just floats. The glass is then filled one's hand comalmost to the brim with water. By pletely over the rim of the glass and pressing the palm into the gl.a&, the air trapped in the vial is compressed, drawing in more water and causing the vial to sink. Once the hand d P h is removed, the trapped air in the vial returns to its orieinal volume, a n d the vial flloats back to the top. Since its invention, the Cartesian Diver has experienced only modest changes. One simple modification is to place the inverted vial or a medicine dropper (3) in a capped plastic bottle of water, such t h a t when t h e s i d e s of t h e bottle a r e squeezed, the "diver" sinks. We h a v e modified t h e Cartesian Diver experiment to illustrate aualitativelv and quantitatively t h e inverse, nonlinear relationship between gas pressure and volume. The device is prepared by cutting t h e excess glass from a 10-mL graduated cylinder and inverting it in a l-L plastic soda bottle filled with water such that the cylinder just f l o a k 3 The plastic bottle is can -- fittad with - ~ -a -~ - 15 - - nsi full..~ Figure I . Amodified Cartesian scale pressure gauge (114.18 Diver consisting of: (A) 10-mL standard threadj that can be graduated cylinder with base removed. (B) water, ( C ) 15 psi phtained at any good plumbfull-scale pressure gauge, (D) lng supply house. A Pressureplastic cap, and (E) one-quart tlght seal was obtained by plastic soda bonle. punching a 0.5-in. hole in the
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Volume (mL) Figure 2. A graph of pressure. versus volume (average of three data sets). center of the cap, which was tightly screwed onto the gauge and sealed with a plumber's compound. The modified cap is then screwed onto the bottle tightly using Teflon tape (Fig. 1). The device functions a s a normal Cartesian Diver. When the bottle is squeezed, the graduated cylinder sinks, and when the bottle is released, the graduated cylinder returns to the surface. I t is easy to see that the volume of the trapped gas decreases when the bottle is squeezed; however, we have found that students often have a hard time understanding that the pressure of the trapped gas increases. By attaching the pressure gauge, the effect of squeezing the bottle on the pressure of a trapped gas can be observed and measured. Increasing the pressure beyond what it takes to make the maduated cvlinder sink gllows one to obtain pressure-vol;me data. Data acquisition is accomplished best bv two students: one to squeeze the bottle to integral units bf pressure and a secondto record the volume of the air trapped in the cylinder. With a little practice, it is easy to obtain good data. Absolute pressure can be obtained by adding atmospheric pressure to the gauge pressure read from the apparatus. The atmospheric pressure can be measured usine a manometer; however, thk average value of 14.7 psi is s u k cient for this experiment. Plots of pressure versus volume 'Young Scholars Program, The Florida State University, Summer 1007
'~uthorto whom correspondence should be addressed. 3~lternatively,an eudiometer of the appropriate size and mass could be used as the diver. While this would remove the oroblem associated with readina the inverted numbers. we have chosen this design because of t h e greater availability of graduated cylinders for most laboratories. Volume 71
Number 9 September 1994
801
Cartesian Diver typifies the ideal activity for this course. The apparatus is simple, and the experiment is engaging (consider that the Cartesian Diver was popular a s a toy long before it was used in the classroom). Furthermore, the experiment leads to important questions that can come from the students (ideally) or the instructor (if necessary). Examples include:
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Where dws the air go when the bottle is squeezed?
Why is it easier to compress air than water? What is pressure?
What is the difference between Eauge - -pressure and absolute pressure? What would a plat of pressure versus volume lwk like, and how could it be expressed mathematically?
1 1 Volume (mL-1) Figure 3. A graph of pressure versus l/volume (using data from Fig. 2).
and pressure versus llvolume for a typical data set are shown in Figures 2 and 3, respectively. A. expected, the relationship between pressure and volume is inverse and nonlinear. The plot of pressure versus llvolume is linear and gives the expected intercept based on the ideal gas law (or Boyle's Law). Amore detailed discussion of these plots in terms of the ideal gas law can be found in any good chemistry text. The modified Cartesian Diver experiment described here was developed in conjunction with a new college physical science course based on i n t e r a c t i v e l e a r n i n g . T h e
802
Journal of Chemical Education
All of these qualities, plus the ease and economy with which this apparatus can be constructed, make the modified Cartesian Diver a n excellent experiment for high school science courses. Acknowledgment We wish to acknowledge the National Science Foundation (under grant #RCD-9055146) for support of the Young Scholars Program a t Florida State U ~ v e r s i t yWe also acknowledge the National Science Foundation (under grant #TPE-9150031) for support of course development. We thank Craig Bowen for suggesting the use of the Cartesian Diver in the classroom. Literature Cited 1. Chrnirnl Demansfmtiona A Handbooh for k h e n o f c ~ r n i s t r yvo1me , 2. Ed. B. 2. Sh&as&. The University of Wiseonsin Press:Madison, 1985. 2. Swezey, K M.A,Qer Dinmr Science, Whifflesey House: New York,1948; p 28. 3. Swezw, K M. Science M d c . McGrsw-Hill: New York, 1952: p 57.
