#### 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.

##### Simulation: Single-Component Pressure-Volume and Temperature-Volume Diagrams

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 Psat and Tsat) 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.

1. 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?
2. Do isotherms generated by a cubic equation of state have three solutions for temperatures below the critical temperature?