Lab 1-Boyle's Law

UIC Physics Department Physics 132 Laboratory Manual Boyle’s Law Page 1 of 6 Boyle’s Law You have probably been well-acquainted with Boyle's law for most of your life without realizing it. As long as the air temperature remains the same, w e experience examples of this law on a regular basis. This law explains the science behind tires, balloons, bubbles, spray paint, plane travel etc. Another example of Boyle’s law in action is in a syringe. In a syringe, the volume of a fixed amount of gas is increased by drawing the plunger back, thereby lessening the pressure. The blood in a vein has higher pressure than the gas in the syringe, so it flows into the syringe, equalizing the pressure differential. Boyle’s law is one of three gas laws which describe the behavior of gases under varying temperatures, pressures and volumes. Together, they form the ideal gas law. Objectives  Determine the relationship between pressure and volume at constant temperature of an ideal gas ሺairሻ and compare the experimental results with theoretical prediction. Introduction Boyle's Law gives the relation between the pressure and volume of a given amount of gas at constant temperature. It states that the volume is inversely proportional to the pressure of the gas. 𝑃 ∝ ଵ ௏ ሺ1ሻ where V is the volume of the gas and P is the pressure. This can also be written as 𝑉𝑃 ൌ constant ሺ2ሻ The ideal gas law PV ൌ nRT ሺ3ሻ states that this constant ሺ nRT ሻ is proportional to the amount of ideal gas in the sample ሺthe number of moles, n ሻ and the absolute temperature, T . The constant R in this equation is the universal gas constant which has a value of R ൌ 8.31 J/ሺmole  Kሻ in SI units. Note that if T is held constant throughout the experiment, then the ideal gas law reduces to Boyle’s law. Equipment  Pasco Absolute Pressure/Temperature Sensor  60 mL Syringe  Silicone tubes  Two-way valve  Pasco 850 Universal Interface  Computer

UIC Physics Department Physics 132 Laboratory Manual Boyle’s Law Page 2 of 6 Boyle’s Law ሺExperimental Procedure and Data Analysisሻ This part of the lab must be completed entirely independently of your lab partnerሺsሻ or other students. Make sure that you avoid unauthorized collaboration and plagiarism. All suspected violations of the Standards of Conduct will be referred to Student Judicial Affairs. Lab Section ሺDay & Timeሻ: ________________________________ Name: ________________________________________________________________________ Station #: ___________ 1. Make sure that the power for the Pasco Interface 850 is turned on. 2. Check that the Pressure Sensor is plugged into the Pasport Sensor 1 port on the interface and the 60 mL syringe is connected via silicone tubing to the pressure sensor and two-way valve as shown in Figure 1. 3. Open Pasco Capstone software from the desktop. 4. Click Hardware Setup under Tools on the left and check that the pressure sensor is recognized by the interface . 5. Drag “Digits” dispay into the center of the workspace. On the display, click ൏Select Measurement൐ and choose “Absolute Pressure ሺkPaሻ”. The computer screen should look something like Figure 2. 6. Turn the two-way valve to the open position. The diagram below shows what this looks like. 7. To measure atmospheric pressure click “Record” button in “Control” menu. The atmospheric pressure value measured by the sensor will appear on display. Figure 2 Figure 1

UIC Physics Department Physics 132 Laboratory Manual Boyle’s Law Page 4 of 6 Note: Measure the volume at the position of black rubber seal marked with red arrows as shown in the figure to the right, not at the inverted V-shaped projection. The syringe barrel has major scale divisions marked every 5 milliliters ሺ1mL ൌ 1 cm 3 ሻ, and minor scale divisions every 1.0 mL. The volume should be estimated to within േ0.5 mL. 11. click “Record” button and slowly push the plunger in to 38 cm 3 position. 12. When you reach the the plunger final position, record the pressure, P , in Table 1 and then click “Stop” and open two-way valve and set the syringe plunger back to the 40 cm 3 mark. 13. Calculate the total volume 𝑉 ൌ 𝑉 ௦௬௥௜௡௚௘ ൅ 𝑉 ௧௨௕௘ and record the result in Table 2. Repeat steps 10 – 13 for the final syringe volumes listed in Table 1 ሺthree times for each volumeሻ. 14. Estimate the uncertainties in volume measurements, 𝜎 ௏ and record the values in Table 2. Explain your reasoning. _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _________________________________________________________________________________________________________________________ 15. Calculate 1/𝑉 and the uncertainties in these values, 𝜎 ଵ/௏ , and record the results in Table 2. 16. Calculate the average pressure, 〈𝑃〉, for each volume and record the results in Table 2. 17. Make a reasonable estimate of uncertainty in pressure measurements, 𝜎 〈𝑷〉 , and record its values in Table 2. _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ 𝑉 ௦௬௥௜௡௚௘ ሺcm 3 ሻ Trial #1 Trial #2 Trial #3 𝑃 ሺkPaሻ 𝑃 ሺkPaሻ 𝑃 ሺkPaሻ 40 38 36 34 32 30 Table 1

UIC Physics Department Physics 132 Laboratory Manual Boyle’s Law Page 5 of 6 18. For each volume, V , calculate PV and record its values in Table 2. 19. Calculate the average value , 〈𝑃𝑉〉 and its uncertainty, and write its value below 〈𝑃𝑉〉 ൌ ______________________  _________________ kPa  cm 3 20. Calculate the uncertainties associated with PV , 𝜎 ௉௏ , and record the results in Table 2. 21. Use the graph paper on page 7 ሺlabeled with “ P vs 1/V graph”ሻ to plot a graph of pressure on the y-axis versus 1/V on the x-axis. Add error bars on the graph and draw a best-fit line through the data. Note: The origin of the graph should be ሺ0,0ሻ. Choose a suitable scale for each axis so that the data points fill the graph as completely as possible. 𝑉 ሺcm 3 ሻ 𝜎 ௏ ሺcm 3 ሻ 1/𝑉 ሺcm  3 ሻ 𝜎 ଵ/௏ ሺcm  3 ሻ 〈𝑃〉 ሺkPaሻ 𝜎 〈௉〉 ሺkPaሻ 𝑃𝑉 ሺkPa  cm 3 ሻ 𝜎 ௉௏ ሺkPa  cm 3 ሻ Table 2 P vs 1/V graph