# Equations of State (EoS)

### Equations of State

• From molecular considerations, identify which intermolecular interactions are significant (including estimating relative strengths of dipole moments, polarizability, etc.)
• Apply simple rules for calculating P, v, or T
• Calculate P, v, or T from non-ideal equations of state (cubic equations, the virial equation, compressibility charts, and ThermoSolver)
• Apply the Rackett equation, the thermal expansion coefficient, and the isothermal compressibility to find v for liquids and solids
• State the molecular components that contribute to internal energy
• Relate macroscopic thermodynamic properties/behaviors with their molecular origins, including point charges, dipoles, induced dipoles, dispersion interactions, repulsive forces, and chemical effects
• Define van der Waals forces and relate it to the dipole moment and polarizability of a molecule
• Define a potential function
• Write equations for ideal gas, hard sphere, Sutherland, and Lennard-Jones potentials and relate them to intermolecular interactions
• Explain the origin of an use "complex" equations of state
• State the molecular assumptions of the ideal gas law
• Explain how the terms in the van der Waals equation relax these assumptions
• Describe how cubic equations of state account for attractive and repulsive interactions
• State and use the principle of corresponding states to develop expressions for the critical property data of a species
• Describe the purpose of the acentric factor and its role in the construction of compressibility charts
• Adapt our approach to mixtures
• Write the van der Waals mixing rules and explain their functionality in terms of molecular interactions
• Write the mixing rules for the virial coefficients and for pseudo-critical properties using Kay's rule
• Using mixing rules to solve for P, v, and T of mixtures
• Write the exact differential of one property in terms of two other properties
• Use departure functions to calculate property data for real fluids (and use them to solve engineering problems)
• Calculate departure functions from Lee-Kesler charts
• Use equations of state to calculate departure functions