213_Ideal Gas Law and Thermodynamic Cycles Lab-Fall2023

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 1 of 16 Physics 213 --- Lab The Ideal Gas Law and Thermal Cycles (Using the new PasPort Sensors) Name: ________________________________________________________ Lab Partner(s): __________________________________________________ (indicate who has plots) _________________________________________________ _________________________________________________ Section: __________________ TA: _____________________________ Lab Date: _______________________________ Key Concepts: • The Ideal Gas Law • The Absolute Temperature Scale • Absolute Zero • Pressure • Thermal Cycles • First Law of Thermodynamics Handy numbers you may need: • Boltzmann’s constant, k B = 1.381 x 10 -23 J/K • Avagadro’s Number, N A = 6.022 x 10 23 molecules/mol • 1 mol of gas (@STP) = 22.4 L P: /5 L: /15 T: /20

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 2 of 16 Making measurements with the Physics 213 Measurement System In this course, most of the measurements will be taken with a computer-interfaced measurement system. This system consists of three basic components: • Measurement sensors – a collection of sensors for measuring temperature, pressure, force, motion, etc. • A computer interface box – for connecting the sensors to the computer. • A computer – for collecting and analyzing data. • Lab files – A lab file is used to record data for each lab. Experiment # 1 The Ideal Gas Law: Boyle's Law Measure the variation of the pressure with the volume of a fixed quantity of an ideal gas at constant temperature. 1. Connect The Absolute Pressure & Temperature Sensor into PasPort1. Also, be sure to plug the temperature sensor into the Absolute Pressure sensor jack. 2. Open up the file: “ P213-Ideal Gas Law and Thermodynamic Cycles Lab Experiment 1-PasPort Sensors.cap ” found in the “ Lab 213 Lab Files Using PasPort Sensors” folder on the desktop . 3. Click on the 1 st window tab, Room Temp Measurement. Syringe V = 0 - 30mL Pressure sensor The Temperature sensor contains a semiconductor integrated circuit whose output voltage is linearly proportional to its temperature. The circuit is fabricated on a silicon chip and encapsulated at the end of the probe. What is the Temperature sensor we are using?

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 4 of 16 Predictions: How do you expect the pressure to change with decreasing volume? In particular, with what functional dependence do you expect the pressure to vary with volume (i.e., linear, quadratic, etc.)? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ 10. Decrease the syringe volume by 4 mL, to 26 mL. Hold the syringe steady at 26 mL and click on the “Keep Sample” button again to record the pressure. Decrease the syringe volume by 4 mL, to 22 mL, then click on “Keep Sample” button again.

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 5 of 16 11. Continue decreasing the syringe volume by 4 mL for each row in the 2 nd column of Absolute Pressure until you get to 6 mL. Click on the “Keep Sample” button to save each sample in the table. After getting sample for 4 mL, click on the “Stop” button to stop the data recording. 12. If needed, drag the graph towards the left with the cursor to pull the plot graph into the center of the graph. THEORY: For an ideal gas, pV = N k B T. In an isothermal expansion (T constant), V ∝ 1/p. In our setup, in addition to the volume of the syringe V S , there is some volume V' in the tubing and inside the pressure sensor so that V = V S + V'. To find N and V', plot V S vs. 1/p : V S = N k B T (1/p) - V' Thus, a plot of V S vs. 1/p should be linear with slope = N k B T and y-intercept = -V'.

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 7 of 16 5. Make graph plot data visible. Use mouse wheel to zoom out data in graph plot. Left click, hold, and move mouse to move data in graph plot. Move the linear fit box to a place where the graph data can be easily seen. 6. Using the room temperature (in K) value from the 1 st window tab (and what was written down in this experiment, calculate the number of air molecules N, the number of moles of air n = N/N A , and the excess volume V'. Play close attention to the units. Slope = Nk B T [kPa-mL] Slope = Nk B T [Pa-m 3 ] N [# air molecules] n = N/N A [moles] V' = - Intercept [mL] 7. Then print a copy of the data by selecting “Print” in the File Menu. Make sure that the Page Range in the print menu specifies “All”. (Make sure to indicate on the first page which team member has the printouts). 8. Click on top right “X” to close the Ideal Gas Law and Thermodynamic Cycles Lab Experiment 1 experiment. DO NOT SAVE YOUR CHANGES! TA Check #1

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 8 of 16 Questions: How do your results compare with your predictions? What were the chief surprises in your results? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ Experiment # 2 The Ideal Gas Law: Charles's Law Measure the variation of the volume with the temperature of an ideal gas at constant pressure. 1. Locate the piston assembly (Heat Engine/Gas Law Apparatus) and place it on its side. Slide the piston to its minimum volume (with the bottom of the plunger at 0 mm). 2. Locate the copper ball mounted in the ring stand clamp (yes, it's a toilet float). Connect the tube from the copper ball to one of the inlets on the piston assembly. Connect the other piston inlet to the pressure sensor input. 3. Fill the large glass beaker with ~ 1000mL water (a bit less than half full) and place it on the hot plate. Put the magnetic stir rod in the water (the stir rod is a magnet encased in a white plastic cylinder about 2" long). Submerse the copper ball in the water, covering it completely. Turn on the magnetic stirrer to circulate the water gently. 4. Insert the temperature sensor into the bath next to the copper ball. It should be suspended in the water, not touching the bottom. 5. Open the file: “P213-Ideal Gas Law and Thermodynamic Cycles Lab_Experiment 2 - PasPort Sensors.cap”. A table and graph plot has been created, including the volume calculation. Pressure sensor Temperature sensor bath copper ball piston hot plate Important Note: The piston assembly is delicate and expensive -- please handle it gently and carefully!

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 10 of 16 7. Make sure the data is now on the 2 nd row of the temperature column, where Position is 4mm. Turn the hotplate to high and heat the bath. Watch the piston. When the piston position has expanded to 4 mm, click on the “Keep Sample” button. 8. As the volume expands, continue clicking on the next row down on the temperature column. Take readings in 4-mm increments. Continue to click the “ Keep Sample” button , and then click on the next temperature row . Continue stirring the water bath with the stir bar to maintain a uniform temperature. 9. When the volume reaches 36 mm, click the “ Stop” button.

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 11 of 16 10. To get ready for the next part, add some ice to the bath to cool it down. [In fact, you may want to start in on the next activity before crunching through the numbers on this one – just make sure you have saved your data!] THEORY: For an ideal gas, pV = Nk B T. In an isobaric expansion (p constant), V ∝ T. In our setup, if the piston is level and frictionless, the pressure inside the piston will be constant and equal to the atmospheric pressure. The volume V is the volume of the copper ball (plus attachment tube) V ball plus the measured piston volume V piston , V = V ball + V piston . To find N and V ball , you will plot V piston vs. T: V piston = (Nk B /p) T – V ball Thus, a plot of V piston vs. T should be linear, with slope (N k B /p) and y-intercept (-V ball ). [Note: you can also get V ball directly in terms of N, P, and T when V piston = 0.] ANALYSIS: 1. As before , let’s first roughly estimate V’ and N. Specifically, first estimate the ball volume V ball (show your work): V ball ≈ ____________mL Now use the fact that at STP, 1 mole of a gas occupies 22.4 L to estimate N: N ≈ ___________ 2. Add recorded data to graph plot. Re-select the Volume data on the right side of the graph. Then re-select the Absolute Pressure data on the left side of the graph. The new data will now show up in the graph. 3. Make graph plot data visible. Use mouse wheel to zoom out data in graph plot. Left click, hold, and move mouse to move data in graph plot. The linear fit for both curves has already been created. Move the linear fit boxes to a place where the graph data can be easily seen.

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 13 of 16 Questions: How do your results compare with your predictions? Is the pressure constant? Is V ∝ T? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ 6. Delete the data for this run by clicking on the “Delete Last Run” button. 7. Close the graph and the table. DO NOT SAVE THE FILE! Experiment # 3 Constant Volume Gas Thermometer Measure pressure vs. temperature of a constant volume of an ideal gas and identify the absolute zero of temperature. 1. Plug the tube from the copper ball directly into the pressure sensor input (remove the piston). 2. The ball should be completely submersed in cool (20-30°C) water. 3. Insert the temperature sensor into the bath. 4. Open the file: “P213-Ideal Gas Law and Thermodynamic Cycles Lab_Experiment 3 - PasPort Sensors.cap”. A table has been created to record temperature and pressure every 10 sec. 5. Turn on the magnetic stirrer to obtain a uniform temperature in the 20-30°C range. Predictions: If you gradually heat the water around the copper ball, how do you expect the pressure in the ball to vary as a function of temperature? ______________________________________________________________ ______________________________________________________________ What should the pressure be at a temperature of absolute zero? ______________________________________________________________ Pressure sensor Temperature sensor bath copper ball hot plate

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 14 of 16 6. Test your predictions. Start the data acquisition by clicking on the “Record” button. Data will be recorded every 10 sec. 7. Turn the hotplate to high. Record data every 10 sec, stirring continuously, until the water temperature reaches 40-50°C. Click the “Stop” button to stop the data acquisition . Turn off the hotplate. THEORY: For an ideal gas, pV = Nk B T. In an isochoric process (V constant), p ∝ T. If the gas inside the volume is at uniform temperature, the pressure will vary linearly with temperature, with slope = (N k B /V) = (n k B ), where n = N/V is the number density of air molecules (# molecules/m 3 ): p = (Nk B /V) T = (n k B ) T The temperature at which the pressure vanishes (p = 0) is absolute zero, T = 0 K. ANALYSIS: 1. A graph has been created with Pressure on the vertical axis, Temperature on the horizontal axis and a linear fit the curve to a straight line. 2. Make graph plot data visible. Use mouse wheel to zoom out data in graph plot. Left click, hold, and move mouse to move data in graph plot. As stated above,

The Ideal Gas Law and Thermal Cycles Physics 213 Lab Fall 2023 Edition Page 16 of 16 4. Delete the data for this run by clicking on the “Delete Last Run” button. 5. Close the graph and table. DO NOT SAVE THE FILE!! FINISHING UP: When you are finished with the lab, please carry out the following clean-up steps. 1. Empty all water containers and dry up any spills or drops. 2. Make absolutely certain that the hot plate is completely turned off !!! 3. Stack all equipment, samples, and tools neatly on your table. 4. Close the PASCO interface window by going to the File menu and clicking “Exit”. 5. Turn in your lab write-up. Attach the (3) graphs that you have plotted. Experiment 1. p vs. V and V vs. 1/p Experiment 2. V, p vs. T Experiment 3. p vs. T In short, leave the lab as you found it -- or would have wanted to find it.