PHYS 1401 – General Physics I

Boyle’s Law

 

Leader: ____________________                    Reporter: ___________________________

Skeptic: ___________________                     Encourager: _________________________

 

Materials

LabPro

Laptop

Pressure Sensor with Syringe

Digital Caliper

 

Introduction

      In this lab we will investigate one of the gas laws, namely Boyle’s Law.  Boyle’s law relates the pressure and volume of a gas.

 

Procedure

      We want to have a known volume of air in this experiment.  The volume we will use will consist of two pieces.  The first part of the volume is from the syringe and the second part is from the tube connecting the syringe to the gas pressure sensor (PS). 

      The contribution to the volume of air in the system from the plastic tubing will remain constant.  To determine the contribution, we will calculate the interior volume of the tube. 

 

Q1.  If you straighten the tube out, what is the shape of the volume interior to the tube? 

 

Q2.What measurements do you need to determine the volume?  Make these measurements and calculate the volume of the interior of the tube in units of cm3. 

 

 

Note:  The volume of the interior of the tube connecting the syringe to the pressure sensor is a fraction of a cm3.  If you got an appreciably bigger number, check your measurements and calculation.

 

We will read the volume for the syringe from the syringe, directly.

1.  Setup

      To set up the experiment, connect the plastic tube from the pressure sensor (PS) to the tip of the syringe as shown in figure 1.  Position the valve on the PS so that it is open to atmosphere as shown in figure 1.  This will make the pressure inside the syringe the same as that of the atmosphere.  Pull the syringe so that the tip sits at the 20 cm mark.  Then position the valve on the PS so that it reads the pressure inside the syringe as shown in figure 2.  Connect the PS to CH 1 on the LabPro.  Start LoggerPro and open the experiment file by following the path Probes & Sensors=>Pressure Sensors=>Pressure Sensor=>Boyle’s Law-PS.  When you open LoggerPro a box will appear asking you to confirm the sensor.  Click OK to proceed.

 

Figure 1 Position of valve so that syringe is open to the atmosphere

 

Figure 2 Position of valve when taking data

 

2.  Data Acquisition

      Click on the Collect button to start acquiring data.  The LabPro will read the pressure continuously until you click on the Keep button.  Once you click on the keep button the pressure will be recorded and a box will appear.  Record the volume of the syringe plus the tube in ml in the box that appears.   (Note 1 cm3 = 1 ml)

      Now decrease the volume in the syringe to 17.5 cm3, and repeat the data acquisition procedure.  Click on the Keep button when you are holding the syringe steadily at 17.5 cm3.  Repeat this procedure each time decreasing the volume by 2.5 cm3, until you reach a volume of 5 cm3.  Note:  Don't go beyond 5 cm3 as this can damage the pressure sensor.

Data Analysis and Questions

      We now wish to analyze our data.  Examine your graph of Pressure vs. Volume in LoggerPro.

 

Q3)  Do your data appear to lie on a straight line? 

 

Q4)  Add a best fit line through your data.  Do you see any systematic trends in the data? 

 

 

Q5)  May some other type of curve fit the data better?

 

 

      It turns out that the answer to the last question is yes.  Let us try and determine what type of curve will fit the data better. Our first volume was approximately 20 cm3 with its corresponding pressure.  A later data point had a volume of approximately 10 cm3 with the corresponding pressure.  Note here that the 10 cm3 volume is approximately 1/2 of the 20 cm3 volume. 

 

Q6)  Find the corresponding ratio of the pressures for these two volumes? 

 

Compare the original volume the volume of approximately 5 cm3.  Here the volume is 1/4 as much as the initial volume. 

 

Q7)  What is the ratio of the pressure at this volume to the initial pressure?

 

 

Q8)  Does there seem to be some kind of relationship between the ratio of volumes and the corresponding ratio of pressures?  Describe the type of relationship.

 

 

      You should have noticed that the ratios of the pressures and of the volumes are the reciprocals of each other.  This is the essence of Boyle’s law.  Boyle’s law states that if the temperature and the amount of gas are held constant, that the pressure is inversely proportional to the volume.

      This suggests to us a way that we should analyze our data to see the relationship between the points in a clear way.  Click on the curve fit button  in LoggerPro.  In the box that appears scroll down to the option Inverse  A/x and click on the radio button.  Click on the Try Fit button and then click on OK.  Print a copy of the graph and attach it to the report.

 

Q9)  Does the inverse relationship seem to fit the data well?  Explain.

 

 

Q10)  Record the value of A given by the fit for later reference. A is the proportionality constant between P and 1/V.

 

The Dependence of the proportionality constant on the amount of gas

      Open the valve on the pressure sensor so that the syringe is open to atmosphere as shown in figure 1.  Move the syringe at the 10 cm3 mark and position the valve again so that it reads the pressure in the syringe as shown in figure 2.  Collect Pressure vs. volume data as before except take into account your answer to the next question (Q11).

 

Q11)  What about your procedure do you need to modify, so that you end up with a total of six data points ending at a volume of 5 cm3? 

 

Once you’ve collected your new set of data, fit an Inverse A/x relationship to it like you did for the first graph.  Print and attach the graph to the report.

 

Q12)  Record the value of A given by the fit. 

 

 

Q13)  How does the value of A determined for the second set of data compare to the value determined from the first set of data? 

 

 

It should be about 1/2.  When you opened the valve you let air escape, thus the amount of air is less than when you started the syringe at 20 cm3. 

 

Q14)  If air has a constant density, by what factor is the amount of air reduced when the volume is reduced by half?

 

 

Q15)  How does this factor compare to the reduction in the value of A determined from your two experiments? 

 

 

Q16)  Based on these observations, what do you think is the relationship between the value of A and the amount of gas in the syringe?  

 

 

Q17)  Devise an experiment to test your answer to question 16.  Describe your procedure.  Be specific about details such as starting point, number of data points, changes between successive data points and so on.

 

 

 

 

P18)  Make a specific prediction about the value of A which will be found when you conduct your new procedure.

 

 

 

Q19)  Carry out your experiment and record the results below.  Print and attach the graph.

 

 

 

 

Q20)  Was your prediction correct?

 

 

Q21).  Summarize the experiment by completing the following with the appropriate type of mathematical relationship.  If the amount of gas and temperature are held constant, Pressure is ________ to Volume.  The proportionality constant of Pressure vs. 1/V is ___________ to the amount of gas.