SimuLab 10: Ideal Gas Law

                        

Your objective is to: Test the ideal gas law by obtaining V, T and P measurements and evaluating the consistency of the  PV/NT ratio at various conditions. You will be able to: Test the validity of the ideal gas law at low densities and high temperatures. Define the Boltzmann constant. Test that the ideal gas law is valid for various molecular masses. Find the limits of the ideal gas law in terms of gas density and temperature.

1. Open SMD, select IdealGasLaw in the IdealGas folder. To better visualize the particles, select Edit: Background Gray.

You are visualizing a gas mixture that consists of 100 green and 100 blue particles as shown in figure 2.6. You will perform three experiments (set ups A, B and C).

2. Set Iterations Between Displays to 1000. Select Show Averages.

Higher number of Iterations Between Displays speeds up the program.

3. Press Start and wait for approximately 20 time units. Press Pause. Record temperature T, pressure P, volume V, number of particles N (set-up A in your table). Calculate number density  N/V and  PV/NT.

The system has reached the equilibrium and you are collecting data for further analysis.

Table I




	T	P	V	N	N/V	PV/NT
A
B
C

Set-up A: 100 green particles, 100 blue, mass = 1

Set-up B: 100 green particles, mass = 1

Set-up C: 100 blue particles, mass = 10

4. Select File - Reset Experiment. Select Edit - Particles and choose Remove all B particles (blue particles) and click on the display window to take this action. Select Reset Averages in the Average Values panel. Repeat Step 3, using set-up B in your table.

Resetting Averages eliminates the data from previous experiments. You are now collecting data for this experiment.

5. Select File - Reset experiment. Select Edit - Particles and choose Remove all G which removes all green particles. Set the B particle mass to 10. Select Reset Averages in the Averages Values panel. Repeat Step 3 using set-up C in your table.

                        

Q2.60: Compare the values of  PV/NT found in set-ups A, B, and C. Calculate the average value which represents the Boltzmann constant in computer units. Theoretically, the Boltzman constant is 1.0 in our computer simulation. In set-up A the gas density is 0.02 and is too high to give the theoretical value. In set-up B and C, the gas density is 0.01 and approaches ideal behavior.

  Now we will determine the range of densities for which the ideal gas law equation is valid.

6. Select File - Reset experiment. Select Edit - Particles and choose Change all particles to G (making all particles green).

You are preparing experimental set-up D.

7. Select Show Additional Parameters. Using scroll bar and / or arrow key, set Number Density to 0.1. Press Start. Wait approximately 10 time units so that equilibrium is reached. At this point, Reset Averages in the Average Values panel and wait another 20 time units. Press Pause. Record parameters in your table and compute  N/V and  PV/NT.

You are watching the approach to equilibrium and collecting data for set-up D when equilibrium has been reached.

Table II




	T	P	V	N	N/V	PV/NT
D
E
F

Set-up D: 200 green,  N/V=0.1

Set-up E: 200 green,  N/V=0.2

Set-up F: 200 green,  N/V=0.5

                        

Q2.61: How does your ratio  PV/NT compare to the theoretical value of 1.0?

8. Repeat Step 7 for Number Density 0.2 and 0.5.

You are collecting data for set-ups E and F.

                        

Q2.62: Comment on the consistency of the  PV/NT ratio as number density of the gas increases.

Now we will determine the range of temperatures for which the ideal gas law equation is valid.

9. To configure setup G : set Number Density to 0.02.

You are creating a very low density gas. You can choose the option distribute particles  instantaneously'' to save time.

10. Set Temperature to 2. Press Start. Wait approximately 10 time units so that equilibrium is reached. At this point, Reset Averages in the Average Values panel and wait another 20 time units. Record parameters in your table and compute  PV/NT in the data table.

You are collecting data for set-up G. Resetting Averages eliminates data from when the system was not yet at equilibrium.

Table III




	T	P	V	N	N/V	PV/NT
G
H
I

Set-up G: 200 green, T=2

Set-up H: 200 green, T=1

Set-up I: 200 green, T=0.5

11. Repeat Step 10 for temperatures 1 and 0.5.

You are collecting data for set-up H and I.

                        

Q2.63: How consistent is the  PV/NT ratio when the temperature is varied in set-ups G, H, and I? Comment on conditions necessary for ideal gas behavior.