BARD/GPT - comparison 5.
Question - what are choices for cubic equation-of-state? ChatGPT missed PREOS completely and that is a big miss. I gave it a thumbs down and program came back with PREOS included.
BARD - I liked draft 3 the best since it included some context on accuracy vs complexity tradeoff.
The most common cubic equations of state are:
Van der Waals equation
Redlich–Kwong equation
Peng–Robinson equation
Soave–Redlich–Kwong equation
Peng–Robinson–Stryjek–Vera equation (PRSV)
The Van der Waals equation is the oldest and simplest cubic equation of state. It is based on the idea that a real gas can be modeled as a collection of ideal gas molecules that interact with each other through attractive and repulsive forces. The Van der Waals equation has two adjustable parameters, the Van der Waals radius and the Van der Waals attraction constant.
The Redlich–Kwong equation is a more accurate cubic equation of state than the Van der Waals equation. It has three adjustable parameters, the critical temperature, the critical pressure, and the acentric factor.
The Peng–Robinson equation is a more accurate cubic equation of state than the Redlich–Kwong equation. It has four adjustable parameters, the critical temperature, the critical pressure, the acentric factor, and the binary interaction parameter.
The Soave–Redlich–Kwong equation is a modification of the Redlich–Kwong equation that improves its accuracy at high pressures. It has three adjustable parameters, the critical temperature, the critical pressure, and the acentric factor.
The Peng–Robinson–Stryjek–Vera equation is a modification of the Peng–Robinson equation that improves its accuracy at low pressures. It has five adjustable parameters, the critical temperature, the critical pressure, the acentric factor, the binary interaction parameter, and the attractive coefficient.
The choice of which cubic equation of state to use depends on the accuracy and complexity required for the application. The Van der Waals equation is the simplest and least accurate, but it is also the easiest to use. The Redlich–Kwong equation is more accurate than the Van der Waals equation, but it is also more complex. The Peng–Robinson equation is the most accurate of the cubic equations of state, but it is also the most complex.
CharGPT -
The cubic equation of state refers to a class of equations used to model the behavior of gases. Three well-known choices for cubic equations of state are:
Van der Waals Equation of State: The Van der Waals equation is one of the earliest cubic equations of state and was proposed by Johannes Diderik van der Waals. It is given by:
(P + a/V^2)(V - b) = RT
where P is the pressure, V is the molar volume, T is the temperature, R is the gas constant, and a and b are constants that depend on the particular gas.
Redlich-Kwong Equation of State: The Redlich-Kwong equation is another cubic equation of state that was developed by J. N. Redlich and J. S. Kwong. It is given by:
P = (RT)/(V - b) - (a/(T^0.5 * V * (V + b)))
where P is the pressure, V is the molar volume, T is the temperature, R is the gas constant, and a and b are constants specific to the gas.
Soave-Redlich-Kwong Equation of State: The Soave-Redlich-Kwong equation is a modification of the Redlich-Kwong equation that was proposed by G. Soave. It is a more accurate representation for gases that exhibit high pressure and low temperature non-ideal behavior. It is given by:
P = (RT)/(V - b) - (a * a / (T^0.5 * V * (V + b)))
where P is the pressure, V is the molar volume, T is the temperature, R is the gas constant, a and b are constants specific to the gas, and a is a parameter that accounts for the attraction between gas molecules.
These are just a few examples of cubic equations of state, and there are other variations and modifications available as well. The choice of equation depends on the specific application and the accuracy required for the given system.
