# Hard Disk PVT Measurement Using the Virial

This applet allows you to measure the pressure-volume-temperature (PVT) relationship for a system of hard disks. It functions exactly as the "SimpleHDPressure" applet, except it uses a different technique to
measure the pressure. In the other applet, the pressure is measured as the momentum flux accompanying
the collisions of the disks with the walls containing them. In this applet, periodic boundary conditions
are used, and there are no walls. The pressure is instead computed using the virial formula as applied
to hard spheres (note: this is not the same thing as the virial equation of state). The virial formula determines
the pressure by summing over all collisions occurring in a given time interval.

Another difference from the other applet is in the presentation of the data. Here the pressure
is presented as the group (pressure * area / N*k), which is listed in the data table as PV/N.
Note that the units of this quantity are independent of the dimensionality of the system (e.g.,
3D vs. 2D). The group is reported here in units of Kelvin (temperature units).
The descriptive text for the other applet is repeated below (after this applet), for your convenience.

#### Text from other applet

Observe the atom motions in one panel; notice that the particles interact with one another according to a pure hard repuslive potential. In the
other panel observe averages for the pressure at different settings for the temperature and density. If you change the settings for the simulation (number of molecules and/or temperature), you can reset the simulation averages by pressing the corresponding button in the Averages panel.

The simulated system is surrounded by hard walls. Momentum transfer between the disks and the walls is used to measure the system pressure.

The simulation is conducted for a two-dimensional system. To permit the pressure and density to be reported in three-dimensional units (bar and mol/liter), the system is assumed to have a "depth" of 3.5 Angstroms. Note that this artificial term (which has no effect on the dynamics of the system) cancels upon taking the ratio PA/NkT. The disks are 2.8 Angstroms in diameter, and the simulation box is square with 35 Angstroms on each side.

Adjustment of the particle number halts the simulation. Press the "Continue" button to restart.