The Peng-Robinson Equation of State calculator computes the pressure of a real gas (and in some cases does a good job for liquids also).
INSTRUCTIONS: Choose your preferred units and enter the following:
Peng-Robinson: The calculator returns the pressure in pascals (Pa). However this can be automatically converted to other pressure units (e.g. millibars) via the pull-down menu.
The Peng-Robinson equation describes the state of the gas under given conditions, relating pressure, temperature and volume of the constituent matter. The Peng-Robinson equation of state has the basic form:
`p = (R*T)/(V_m - b) - (a*alpha)/ (V_m^2 + 2 * b * V_m - b^2) `
Variables a, b, and `alpha` are further described by:
`a = (0.457235 * R^2 * T_c^2)/p_c` , where R is the universal gas constant (8.3144626181532 J/(K·mol)) and Tc and pc are defined in the Inputs above.
`b = (0.077796 * R * T_c) / p_c`
`alpha = (1 + kappa * (1 - T_r^(1/2) ) )^2`, where `T_r = T/T_c`
Further `kappa` in the definition of `alpha` is defined as:
`kappa = 0.37464 + 1.54226* omega - 0.26992* omega^2`, where `omega` is the acentric factor which is a function of the saturated vapor pressure and the critical pressure
It is easy to see in the first term of the Peng-Robinson equation that this state equation had its origins in the Ideal gas law: pV = nRT, since `V/n` gives you molar volume. To apply the Ideal gas law to real gases, correction terms have been included that are composed of empirically derived offsets.
The Peng-Robinson equation was specifically deigned to meet the following criteria1:
This equation is popular for us with natural gas systems found in petroleum industries. Equations of state are useful in describing the physical properties of fluids, solids, and even the interior of stars.