#### Interactive Self-Study Module: Equations of State (EOS)

##### Overview:

This module use screencasts and interactive simulation(s) to explain how to use equations of state for a single component. Your retention of material in this module will increase if you write down reasons for your answers to ConcepTests, questions in screencasts, and questions to answer before using interactive simulation(s), and you try to solve the example problems before watching the screencast solutions. We suggest using the learning resources in the following order:

- Attempt to answer the multiple-choice ConcepTests before watching the screencasts or working with the simulations.
- Watch the screencasts that describe the equations of state and calculation of saturation pressures and answer the questions within the screencasts.
- Review important equations for this topic.
- Use the interactive simulation(s) to further understand compressibility factor diagrams and phase diagrams obtained from an equation of state.
- Try to solve the example problems before watching the solutions in the screencasts.
- Answer the ConcepTests.
- Look at the list of key points, but only after you try to list the key points yourself.

##### Motivation:

- Many gases at higher pressures and/or lower temperatures are not ideal, but pressure-volume-temperature data are not available. An equation of state is then used to model P-V-T behavior using critical pressures and temperatures and acentric factors.
- This module is intended for use in a thermodynamics course.

##### Before studying this module, you should:

- Know how to apply the ideal gas law.
- Understand single-component phase diagrams and vapor-liquid equilibrium.

##### After studying this module, you should be able to:

- Calculate properties (U, S, H, A, G, V, f) of real fluids using the Peng-Robinson (PR) equation of state (EOS) spreadsheet, which also uses heat capacity data.
- Explain why the PR cubic EOS has three roots and what the physical meaning of each root is.
- Interpret the EOS spreadsheet results to determine which state (root) is most stable.
- Describe what corresponding states means.
- Sketch and interpret processes on P-V-T diagrams and their projections.
- Calculate reduced temperature, reduced pressure, and compressibility factor.
- Explain which terms are repulsive and which are attractive in a cubic EOS.