Pressure Simulation

Description:

Pressure is the force per area acting on a surface. This simulation shows a container of particles on the left and the instantaneous pressure in the container due to the particles colliding with the walls as a function of time in the graph on the right.

The table underneath calculates the pressure three ways: a) from the ideal gas law; P = NkT/V where Boltzmann's constant, k, is set to 1 b) from the momentum change of the particles hitting the walls; P = dp/dt and c) the average pressure; ‹P> over 100 time steps.

Question 1:

In an ideal gas the particles do not interact with each other but in this simulation they do interact (as you can see from the simulation). The following three buttons start the simulation with 40 particles but in each case the particles have different sizes. Run each case for at least 50 time units. In which case is the real average pressure, <P>, closest to the theoretical ideal gas law pressure, P = NkT/V?

Small; N = 40

Medium; N = 40

Large; N = 40

Question 2:

Explain why only one of the three cases is close to the ideal gas law.

Question 3:

Examine the average pressure, <P> for each of the three cases for a smaller number of particles. Why does the size of the particle make less of a difference in this case than in the case for 40 particles?

Small; N = 4

Medium; N = 4

Large; N = 4

Question 4:

You may have noticed that in the case of 4 particles the graph is very spiky but is somewhat smoother for the case of 40 particles. Look at the following case for 100 particles, below. Why is the pressure graph smoother with more particles?

Small; N = 100

Question 5:

In a real gas you might have quite a few more particles than 40 or 100 (after all, a mole is 6.02x10²³ molecules!). Draw a sketch of what the pressure versus time graph would look like if you could run the simulation with a mole of particles.