  In this paper, we investigate the four-dimensional Einstein-Gauss-Bonnet
black hole. The thermodynamic variables and equations of state of black holes
are obtained in terms of a new parameterization. We discuss a formulation of
the van der Waals equation by studying the effects of the temperature on P-V
isotherms. We show the influence of the Cauchy horizon on the thermodynamic
parameters. We prove by different methods, that the black hole entropy obey
area law (plus logarithmic term that depends on the Gauss-Bonnet coupling
{\alpha}). We propose a physical meaning for the logarithmic correction to the
area law. This work can be extended to the extremal EGB black hole, in that
case, we study the relationship between compressibility factor, specific heat
and the coupling {\alpha}.
