Assignment lab 4

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Lab: Gas Properties Phys 242

In this lab we will study several macroscopic quantities that can be used to describe a gas and explore the relationships among these quantities. using a simulation from the PhET team: https://phet.colorado.edu/sims/html/gas-properties/latest/gas-properties_en.html The simulation can be run in a browser. If you have issues with the simulation, try using another browser. If you are unable to run the simulation, your TA will provide you with remote assistance. When you run the simulation, choose the “Ideal” option. At the very bottom of the screen you will see the other options for the simulation, including a home button, “Ideal,” “Explore,” “Energy,” and “Diffusion.” If you accidentally navigate to another area, you can return to the Ideal option by clicking the button. The simulation shows a preset volume. In its initial configuration the box is empty. On the right side of the screen there is a menu labelled “Particles.” By expanding this menu, you can choose to add so many heavy or light particles. These particles will enter the volume at a temperature of 300 K in the initial setup. Once there are particles in the box, the temperature and pressure in the box can be read off the scales on the right corner of the box. The units can be changed for these values. To adjust the temperature of the particles in the box, move and hold the slider bar below the box. On the left there is a handle to change the size of the box. There is also a lever at the top of the box that can be lifted to open the box, allowing particles to escape. Particles can also be removed from the box by reducing the number of particles in the “Particles” menu.

Finally, to refresh the simulation to the initial point, click the arrow in the bottom right.

Handle to

adjust volume

Dial to adjust

temperature

Restart simulation

Show the width

measurement

Add heavy particles 50 at a time

Lab: Gas Properties Phys 242

I. Volume A. Refresh the simulation so that you begin with an empty box. Add 100 heavy particles to the box.

Which of the quantities in the ideal gas law, P, V, N, kB, or T, does “100 heavy particles” describe?

B. Select the width option in the right panel. This will put a scale bar on the bottom of the box. Assuming the box is a cube, what is the volume of the box?

C. Keep the box closed and use the handle on the side to make the box smaller. 1. Did the volume of gas change? Explain.

2. Did the number of molecules of gas enclosed in the system change? Explain.

D. Consider the following statement made by a student in an introductory physics class. “As I pushed the handle inward, no air entered or left the system, so the volume did not change.” Explain what is incorrect about this student’s statement.

II. Measuring the Pressure A. Refresh the simulation. What is the pressure in the box when 100 heavy particles have been added?

Note that this value fluctuates, so you will have to estimate a value.

B. Atmospheric pressure is about 101 kPa (or 1 atm). How does the reading you obtained compare to atmospheric pressure?

Lab: Gas Properties Phys 242

C. Suppose you were to change the volume of the box. 1. Predict whether the pressure reading would be greater than, less than or equal to the value

you measured in Part A if the volume were decreased?

2. Predict whether the pressure reading would be greater than, less than or equal to the value you measured in Part A if the volume were increased?

D. Check your predictions by changing the volume of the box. 3. Decrease the volume of the box. Is the pressure reading greater than, less than or equal to

the value you measured in Part A?

4. Increase the volume of the box. Is the pressure reading greater than, less than or equal to the

value you measured in Part A?

E. Now, for each volume in the table at right, record

the value of the pressure of the gas.

Width (nm)

Volume (nm3)

Pressure (atm)

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

14.0

Lab: Gas Properties Phys 242

F. Once you have obtained your entire data set, create a graph showing the relationship between the pressure and the volume using your data.

G. As the volume increases, does the pressure increase, decrease, or remain the same?

H. Does the pressure change linearly with the volume? Explain how you know.

I. Is your data consistent with the Ideal Gas Law? Explain

Lab: Gas Properties Phys 242

III. Forces exerted by a gas Refresh the simulation and add 100 heavy particles to the box. A. Draw a free-body diagram for the top of the box (i.e., draw vectors representing the forces exerted on

the box). For each force: • indicate the type of force, and • identify the object on which the force is exerted and the object exerting the force.

B. Is your free-body diagram consistent with the fact that a gas can only push (and not pull) on other objects?

C. Does your free-body diagram include any forces exerted by the air outside the box?

D. Predict what will happen to the net force if you increase the pressure inside of the box.

E. Test your prediction while keeping the volume constant. (Hint: think about how you can increase the pressure inside the box.) If you increase the pressure, does the top of the box move? Explain your findings. Try increasing the pressure as high as you can.

Lab: Gas Properties Phys 242

IV. Changing the temperature with the volume free to change Reset the simulation. With 100 heavy particles in the box and a width of 10 nm, select the “Pressure ↕V” option in the right panel. This will allow the box to expand. Now imagine that you will heat the system. A. Predict whether the following quantities would increase, decrease, or remain the same. In each case,

explain your reasoning. • the temperature of the gas in the system

• the pressure of the gas in the system

• the volume of the gas in the system

In the process above, which of the quantities P, V, n, and T are held constant and which are allowed to change? Sketch the process above on a PV diagram.

Lab: Gas Properties Phys 242

B. Check your predictions by heating the bottom of the box (drag the bottom toggle toward “heat”). 1. Heat the box and record the resulting T, P, and V.

2. Repeat your measurement for three additional temperatures. In the table below, record the temperature, pressure and volume of the air in the system.

C. Examine the PV diagram you drew for this experiment and check that your prediction is consistent with the data you recorded. Resolve any inconsistencies.

D. Consider the following statement made by a student. "According to the ideal gas law, the pressure is proportional to the temperature. That means that whenever I increase the temperature of the gas, the pressure must go up." Explain what is incorrect about this student’s statement.

Temperature (K) Gauge pressure (atm) Volume [nm3]

Lab: Gas Properties Phys 242

E. Plot all four measurements of the volume of the gas in the system versus the temperature using your data from part B above.

The four points should lie nearly along a straight line. Draw a line that is a good approximation to that line.

Use your graph to estimate the temperature at which the volume of the air in the system would be zero. We will give an interpretation of this temperature after the experiment in the next part.

The process you carried out in this experiment is commonly referred to as an isobaric process.

Lab: Gas Properties Phys 242

V. Changing the temperature with the volume fixed Reset the simulation and add 100 heavy particles to the box. Now select the “Volume” option in the left panel. Imagine that we will again heat the box. A. Predict whether the following quantities would increase, decrease, or remain the same. In each case,

explain your reasoning.

• the temperature of the gas in the system

• the volume of the gas in the system

• the pressure of the gas in the system

In this process, which of the quantities P, V, n, and T are held constant and which are allowed to change? Sketch the process above on a PV Diagram. The plotted point denotes the initial pressure and volume of the gas.

Lab: Gas Properties Phys 242

B. Check your predictions by heating the box. (Make sure that the volume option is selected in the right panel.) 1. Heat the box and record the resulting T, P, and V.

2. Repeat your measurement for three additional temperatures. In the table below, record the temperature, pressure and volume of the air in the system.

a. Does the pressure change?

b. Plot your measurements of the (absolute) pressure of the gas in the system versus the

temperature.

Temperature [K] Volume [nm3] Pressure [atm]

Lab: Gas Properties Phys 242

3. The points should lie nearly along a straight line. Draw a line that is a good approximation to that line. Use your graph to estimate the temperature at which the pressure of the air in the system would be zero. The value given in your textbook is –273.15°C. This temperature is referred to as absolute zero, or 0 Kelvin. How do your results compare?

The process you carried out in this experiment is commonly referred to as an isovolumetric process.