Question

State Berthelot's equation for real gases?

Answer 1

Berthelot's Equation of State (EOS) is a modified version of the van der Waals EOS, which is a modified version of the ideal gas law. It's not often used.

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IDEAL GAS LAW

The ideal gas law is:

`PV = nRT`

or the more compact version, with `barV = V/n`:

`color(green)(P = (RT)/barV)`

VAN DER WAALS EOS

From accounting for the varying degrees of intermolecular forces upon real gases and the relative excluded volume, we get the van der Waals EOS:

`color(green)(P = (RT)/(barV - b) - a/(barV^2))`

However, the van der Waals fails to accurately represent real gases near the critical point. What it's good for is modeling the attractive and repulsive forces of real gases relative to ideal gases.

BERTHELOT'S EOS

Berthelot's EOS is a slight modification getting:

`color(blue)(P = (RT)/(barV - b) - a/(TbarV^2))`

Apparently it's not often used, though it's supposed to be good for calculating `barV`.

The modified Berthelot EOS is more interesting though.

`\mathbf(P = (RT)/(barV)[1 + (9P"/"P_c)/(128T"/"T_c)(1 - 6/(T"/"T_c)^2)])`

And it doesn't use `a` and `b`.

`T_c` is the critical temperature, and `P_c` is the critical pressure. They are essentially those values at the critical point, when gas/liquid exist at the same time as a supercritical fluid.