Berthelot equation

The Berthelot equation, `P = (R *T)/(V_m-b)-a/(T *V_m^2)`, computes the pressure of a gas and is a closely related formula to the  more common gas laws like Boyle's Law (click HERE) and the Ideal Gas Law (click HERE). 

INPUTS

The Berthelot equation relates temperature, pressure and volume of ideal gases.

• `V_m` - the molar volume, the volume occupied by one mole of a substance at a given temperature and pressure. It is equal to the molar mass divided by the mass density.
• T - temperature
• a - empirical coefficient that is a function of the critical temperature and pressure, sometimes called Van de Waals constants
• b - empirical coefficient that is a function of the critical temperature and pressure, sometimes called Van de Waals constants

DERIVATION

The coefficients a & b are referred to as the Van der Waals constants and are in units of `m^6* "Pa" / "mol"^2` for a and `m^3/"mol"` for b

NOTES

The Berthelot equation, named for Daniel Berthelot,  is one of the Real Gas equations of state developed to relate the properties of gases.  This Berthelot equation makes only an approximation of gas properties and is more of a historic artifact in the lineage of the equations used more commonly to model the properties of real gases. The modified Berthelot equation is expected to be more accurate.

Coefficients a and b are functions of critical pressure and critical temperature of the gas and therefore are directly dependent on the specific type of gas.

There are a number of well-known equations which do similar predictions of the interrelated variations in temperature, pressure and volume of real gases and these have often have been made more accurate by incorporating empirical data into coefficients of the same basic gas equations that were discovered in earlier history.  It is also important to note that these gas equations are almost always more accurate for specific ranges of temperature and pressure.