#### Equations of State: Interactive Simulations

These simulations were prepared using Mathematica. Download the free CDF player, and then download the simulation CDF file (link given below or click on figure to download). Try to predict the behavior when a parameter changes before using a slider to change that parameter. Screencasts below explain how to use these simulations.

The van der Waals equation of state for water is used to generate isotherms on a pressure-log volume (P-V) diagram and isobars on a temperature-log volume (T-V) diagram. Sliders change the isotherm temperature on the P-V diagram and the isobar pressure on the T-V diagram. Liquid and vapor are in equilibrium within the phase envelope, which was generated from data for water. The horizontal, dashed orange line (at P^{sat} and T^{sat}) represents a mixture of liquid and gas. On the P-V diagram, the green area above the orange line is equal to the area below the orange line when volume is plotted on a linear scale.

**Try to answer these questions before determining the answer with the simulation**. We suggest that you write down the reasons for your answers.

- For the critical isotherm obtained from the van der Waals equation of state, what can you say about the slope of the isotherm at the critical point?
- Do isotherms generated by a cubic equation of state have three solutions for temperatures below the critical temperature?

The compressibility factor chart plots the compressibility factor, Z, equal to PV/RT, where V is the molar volume, versus the reduced pressure P_{r} for several values of the reduced temperature T_{r}. The reduced pressure and temperature are defined by P_{r} = P/P_{c} and T_{r} = T/T_{c}, respectively, where P_{c} is the critical pressure and T_{c} is the critical temperature. Use buttons to select one of five molecules, and move the black dot to display the compressibility factor curve (blue) for any value of T_{r} between 1.0 and 1.8. The Z and P_{r} values for the location of the back dot are displayed on the chart. For an ideal gas, Z = 1 (green line).

**Try to answer these questions before determining the answer with the simulation**. We suggest that you write down the reasons for your answers.

- If the compressibility factor for carbon dioxide is 0.52 at a reduced pressure of 1.59 and a reduced temperature of 1.10, what reduced temperature would you expect for nitrogen to have a compressibility factor of 0.52?
- Why is the compressibility factor mostly less than one?