P $=$ RT$/$V $+$ Rf$($t$)/$V $+$ Rg$($t$)/$V$^2$ where f$($T$)$ and g$($T$)$ are functions of temperature only.

Which correlation must exist between the two functions f$($t$)$ and g$($t$)$ so that the equations of

state above represent stables states, that is $$true$$ thermodynamic properties?