Equation of State
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
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