How do we determine complex state equations for substances?

[mech-eng]

Hello. I am reading about state equations from a physics textbook, Physics by Frederick J. Keller, W. Edward Gettys, Malcolm j. Skove (Volume I). I don't understand some parts but since I have the Turkish translation of the book I must translate it as good and clear as possible.

"State equations of some substances may be very complex functions of state variables. In that case, relations between variables are determined empirically\experimentally."

The above statement does not make much sense to me because aren't there just a few state equations, most common being PV=mRT?

The statement makes me think that as if state equations vary from substance to substance and they are very very complex that they are determined by experimentally.

The situation of determining them experimentally does not make sense to me, too.

Regards,

 

[Chestermiller]

Hello. I am reading about state equations from a physics textbook, Physics by Frederick J. Keller, W. Edward Gettys, Malcolm j. Skove (Volume I). I don't understand some parts but since I have the Turkish translation of the book I must translate it as good and clear as possible.

"State equations of some substances may be very complex functions of state variables. In that case, relations between variables are determined empirically\experimentally."

The above statement does not make much sense to me because aren't there just a few state equations, most common being PV=mRT?

This equation applies only to an ideal gas, which is how a real gas behaves at relatively low pressures. The more general behavior of a real gas is $$f(P, \frac{V}{m},T)=0$$How would you describe this behavior for a specific gas without doing experiments.