### SimuLab 4: Quantitative Investigation of Boyle's Law

 Your objective is to: Test that the product PV remains constant for several positions of the piston at constant temperature. You will be able to: State Boyle's Law. Construct a P versus V graph from collected data. Construct a P versus  1/V graph. Contrast the two curves. Explain the significance of the slope on the P versus  1/V graph. Predict what will happen to the PV product if the temperature is changed. Construct a P versus number density graph. Reformulate Boyle's Law in terms of gas density.

 1. Open SMD, select Boyle1000 in the IdealGas folder.
 You will see 200 particles compressed in a container whose volume is fixed at 1000. The Temperature is set at 1.25 and the Heat Bath is on (i. e. the temperature is maintained at a relatively constant value).

 2. Press Start.
 The molecules start to move and bump into the walls of the container. The graph panel represents the internal pressure created by 200 gas particles at a given moment.

 Q2.23: How do you explain the relatively large fluctuations in the pressure of the system?

 3. Select Show Averages.
 Observe the time and the other values carefully.

 Q2.24: Wait for about five time units. Do you notice any change in the fluctuations of the pressure values in the Average Values panel?

 4. Change Iterations Between Displays to 500. Let the program run for approximately 20 time units. Press Pause.

 In order to obtain accurate value for pressure we need to average data over a longer period of time. Iteration setting of 500 speeds up the simulation.

 5. Record temperature, number density, volume, and pressure data from the Average Values panel into the table. Calculate the PV value.
 You will need these data for further analysis.

Table I

 Volume 1000 2000 4000 8000 10,000 Temperature Number Density Pressure PV Deviation from average % deviation

Calculate (PV)ave value = åi=15 Pi Vi :________

Deviation from average = | (P V)i - (P V) avg|

% deviation = (|(PV)ave-PiVi|)/((PV)ave)   x   100

Calculate average % deviation = åi=15(|(PV)ave-PiVi|)/((PV)ave)  x   100 value:________

 6. Select File : Open Preset Experiment and open Boyle2000. Press Start. After approximately 20 time units press Pause. Record the values and calculate the PV value as described in Step 5.
 In order to test Boyle's law, we will measure the pressure of the same amount of gas at the same temperature and different volumes.

 7. Repeat Steps 6 for Boyle4000, Boyle8000, and Boyle10000.

Q2.25: Compare the values of PV for various volumes. Find the average value of these products and calculate the deviation of each PV value from the average. Calculate the percent deviation of each ( PV) i value from the average (PV) ave by using this formula:

 %deviation = æè | (PV)i-(PV)ave| (PV)ave ×100 öø

Find the largest percent deviation.

To what extent are your results consistent with Boyle's Law? Hint: Refer to your percent deviation and range of values of pressure.

 Q2.26: Construct a Pressure vs. Volume graph. This plot represents the dependence of pressure on volume at constant temperature. According to Boyle's law, when the temperature is constant, the graph should be a hyperbola. If your graph varies significantly from a hyperbola, do you have any idea why this may have been so?

 Q2.27: Construct a Pressure vs.  1/Volume graph. Draw the line of best fit through the data points. Determine the slope of this line and compare it to the average PV product in the above chart. What is the relationship between the slope and the average PV product? What is the difference between the graph of P vs.  1/V and the graphs of P vs. V graph?

 Q2.28: Construct a Pressure vs. Number Density graph. Number Density is defined as Number of particles over volume: n =  N/V. The distribution of data points should fall as a straight line. What is the relationship between pressure and number density? Compare this graph to the Pressure vs.  1/Volume graph. We should now be able to state an alternative form of Boyle's law: at constant temperature, the gas pressure is directly proportional to the gas number density.

 Q2.29: Find the slope of the Pressure vs. Number Density graph and comment on the relationship between the slope and temperature of the system.

 Q2.30: Graph the PV product vs. Pressure. What slope do you expect? What do you find? Explain the deviation from your prediction (Hint: consider that ideal gas behavior is followed at low pressures and high temperatures).