# Molecular Dynamics Simulation

## Pressure-Volume Relation

### Concepts

How does the pressure of a gas depend upon the volume of the gas?

For a fixed amount of gas at a constant temperature, Boyle's Law states that the quantity *P V* is a constant. (*P* is the pressure and *V* is the volume.) Does the Kinetic Molecular Theory correctly predict this behavior? If so, why does a decrease in system volume produce an increase in pressure?

Shown below are two molecular dynamics simulations. Both systems are at the same temperature and contain the same number and type of particles. System 1, however, is exactly twice the volume of System 2. Start the simulations and carefully observe the behavior of the particles.

### Things to remembers:

- Pressure is the ratio of the cumulative force on the walls of the system divided by the total surface area of the walls. The cumulative force on the walls is the sum of the forces exerted by all of the particles colliding with the walls.
- Because both systems are at the same temperature and the particles in each system are identical, the average speed of the particles is the same in both systems. The average force exerted by a particle colliding with a wall is the same in both systems.

### Questions

- Boyle's Law predicts that the pressure of System 2 should be twice the pressure of System 1. Compare the pressures for the two systems. Does Boyle's Law correctly predict the relative pressures?
- In terms of the behavior of the particles in the simulations, why is the pressure of System 2 larger than the pressure of System 1?
- Boyle's Law predicts that the pressure System 2 should be
*exactly*twice that of System 1. Is this the case? Boyle's Law applies to an*Ideal Gas*. Why do these gases display a slight degree of non-ideal behavior?

*MDS-PV.html version 3.0*

*© 2001, 2014, 2023 David N. Blauch*