[ad_1]
An equation of state (EOS) describes the interconnection between state variables for a particular state, such as a solid, liquid, gas, or plasma. Parameters can be modified to approximate real-world behavior, but liquids are more difficult due to molecular interactions. The “lattice-gas” theory is used to model associated liquids, but the mathematics can become complex.
In thermodynamics, an equation of state (EOS) is the mathematical expression that describes the interconnection between state variables – generally observable and macroscopically measurable properties – for a particular state. This state can be solid, liquid, gaseous or plasma. The observables or properties used in an equation of state can be varied by theorist, but generally describe the state completely. For example, the equation of state for “n” moles of an ideal gas can be fully described using the equation PV=nRT, where P=pressure, V=volume, R=ideal gas constant, and T=temperature. Note that an EOS is intended to describe no more than one state, whether that state is solid, liquid, or gas.
In order for an equation of state to more closely approximate real-world behavior, parameters such as the three listed above are modified by additional empirical—experimental—and even computational terms. Among these terms are atomic volume, which subtracts from the total volume, and intermolecular force, which affects the distance between particles. Even these adjustments may not be enough. To reconcile the equation with the measured data that is intended to be explained, virial mathematical terms and iterative computational methods may be required. Such terms obscure intellectual interpretation, but enhance practical application.
An acceptable equation of state can be difficult to derive for liquid systems, because they experience a much greater degree of molecular interaction resulting from the molecules being much closer together than gases. Liquids are classified based on the extent of these interactions as unbound or bound. Most of London’s dispersion forces are quite weak, and if they are the only intermolecular forces present, the liquid – perhaps an oil or other hydrocarbon – is unattached. If, however, the bonding of the molecules is stronger, such as for molecules bonded to hydrogen, the liquid is associating. The stronger the forces, the more complex the mathematical modeling and the corresponding equation of state.
For the development of an acceptable equation, the associated liquids can be considered more similar to solids than unassociated liquids. Some scientists use a model that incorporates a two-dimensional lattice, suggesting that associated liquids possess at least some solid characteristics. A two-dimensional rather than three-dimensional lattice indicates that the solid behavior component is limited. Since some of the particles are not considered to be part of the lattice, the name given to this model for fluids, both gaseous and liquid, is the “lattice-gas” theory. The mathematics of lattice-gas liquid equations of state can become counterintuitive and complex, as is well illustrated by polymer-in-solvent systems.
[ad_2]