Thermal Physics and Graph of PV against Temperature Lab Report 5

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Lab 5 - Thermal Physics Objectives • • Understand the ideal gas law Determine the value of Boltzmann’s constant Writeup Requirements Overview - 4 pts, Data & Analysis - 6 pts, Questions - 8 pts, Lab 5 Survey - 2 pts Part 1: Boyle’s Law Preparation View the lecture video linked here. Boyle’s law is an empirical law which states that the pressure (P) of a gas is inversely proportional to its volume (V) : (5-1) where C is a constant. The value of C is only constant if the temperature of the gas (T) and the number of gas molecules (N) are both held constant as well. 1. What unit do physicists use to measure temperature, and why does that make the most sense with the definition of temperature described in the prelab lecture? Procedure First, we will test Boyle’s law by varying the volume of a gas container, measuring the pressure. Please open the following simulation, which will help illustrate ideal gas behavior: Gas Properties - Ideal Gas Law | Kinetic Molecular Theory | Diffusion 1. Open the simulation, and select “Ideal” from the main menu. 2. You will see a gas pump, a thermometer, a pressure gauge, and a heater/cooler (for now, we want the temperature constant, so leave this alone). 3. Inject some gas by depressing the pump a few times. (Note: there are two different types of molecules to choose from, a heavier one and a lighter one.) 4. Once you have injected the gas, you can expand the Particles parameter and see the number of molecules currently in the container. 5. Give the particles a little time to spread throughout the container, than answer the following: 2. Carefully observe how the particles are moving, and try to describe the motion of a single particle. (Consider its position and velocity). 3. Do all the particles share the same speed? 6. The handle on top can vent the gas. (For now, make sure this stays closed.) 7. The handle on the left can be used to vary the volume of the gas container. Try compressing and expanding the volume a few times. 4. As you make the volume smaller and larger, what happens to the pressure? Pressure has units of force per area (Newtons per meter squared), and the SI unit for pressure is the pascal (Pa). (The gauge reads in standard atmosphere (atm), and 1 atm is equal to 101,325 Pa.) 5. Show that, in SI units, pressure times volume has units of joules (J). Now, we will vary the volume and measure the pressure systematically. 8. Prepare a table like Table 5-1: 9. Check the width box, which will make visible the width of the box, in nm. 10. Also check the Collision Counter box. This opens a counter that will count the number of collisions between a gas molecule and the container’s walls over a fixed time interval (leave this as 10 ps). 11. Record the temperature (in kelvin) and the number of molecules. These values are to remain constant during this experiment. 12. Record the width of the container in your table (start with a width of 15 nm). 13. Using the width, calculate the volume of the box. This can be calculated as: V = Aw, where w is the width of the box in meters, and A = 3.5✕10-17 m2. (It is a very small container.) 14. Start the collision counter, and let it run until the end of its time interval. Record the total count under “Wall Collisions”. 15. Record the pressure (in atm), and convert to Pa. 16. Compress the container (do this in increments of ~3 nm) and repeat these measurements (4 times total). 17. In the last column, calculate the product of volume and pressure (the constant C in Boyle’s law). 18. Find the average value of C and record it in your table. 19. Calculate the standard deviation of C and record it in your table. Table 5-1. Testing Boyle’s law. N= Width (nm) T= K Volume (m3) Wall Collisions Pressure (atm) Pressure (Pa) C = PV (J) Caverage= Cstd= 6. What is the relationship you observed between the number of wall collisions per time interval and the pressure. Part 2: The Ideal Gas Law Preparation The ideal gas law relates the pressure and volume of a gas to the amount of gas and its temperature. The ideal gas law is stated as: (5-2) where P is the pressure in pascals, V is the volume in m3, T is the temperature of the gas in kelvin (K), N is the number of gas molecules, and k is the Boltzmann constant: Note that the ideal gas law is an approximation, and is valid when the distance between gas molecules is much larger than the size of the molecules, and collisions between molecules can be treated as perfectly elastic collisions between point-like particles (with no long-range interactions or intermolecular forces). 7. Verify that the units on both sides of Equation 5-2 match. 8. Compare the average value of C that you found in Part 1 to the quantity NkT (using your previous measurements of N and T). 9. Are your results from Part 1 consistent with the ideal gas law? Explain your reasoning. Procedure We will use the same simulation as in Part 1 to test the ideal gas law. First we will keep the number of molecules constant and vary the temperature in order to find the constant k. Table 5-2. N= V= Pressure (atm) Pressure (Pa) PV (J) Temperature (K) 1. 2. 3. 4. 5. 6. 7. 8. 9. Prepare a table like Table 5-2. Reset the simulation by pressing the “eraser” button. Set the container width to 10 nm, and record the volume. Before injecting any particles, select the lighter (brown) particle below the pump. Inject at least 300 particles (note: you can also set the particle number using the arrows under the Particles drop-down menu). Record this value. Record the pressure, once the particles are well-distributed through the container. Heat the container using the Heat/Cool bucket, and repeat these measurements for 5 different temperatures. For each temperature, calculate the product of volume and pressure. Once these measurements have been made, create a plot of PV vs T, and find the equation of the linear best-fit line. 10. Looking at Eq. (5-2), what quantity does the slope of the best-fit line represent? 11. From your slope, determine the value of the Boltzman constant, k. Compare this value to the accepted value of k = 1.380649x10-23 J/K with a percent error. Complete the Post Lab 5 Survey on D2L once you have submitted your report. This is located in the Quizzes section. N
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Explanation & Answer


Lab 5: Thermal Physics
Data and Analysis
Table 5-1. Testing Boyle’s law.
N = 100
Width (nm)
Volume (m )
Wall Collisions


5.25 × 10
4.2 × 10−25
3.15 × 10−25
2.1 × 10−25

Pressure (atm)



Pressure (Pa)

C = PV (J)
4.9472 × 10−19
4.8940 × 10−19
4.9791 × 10−19
5.0429 × 10−19
4.9658 × 10−19

Cstd= 6.2243 × 10−21

Table 5-2.
N = 350
Pressure (atm)

V = 3.5× 10−25
Pressure (Pa)


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