Abstract: A new equation of state v-vc=(R/p)(h-hc) with the assumption R=R(p) (where v, p, h are specific volume, pressure and specific enthalpy respectively, R is substance parameter, the subscript c refers to the state not depending temperature), has been used in the study of the shock compression of porous materials, since it was developed by Qiang Wu et al. However, this EOS was on the basis of the assumption that the specific heat at constant pressure cp remains constant, so its physics base about the EOS has not been proved and the concert form was not got. In this paper, a proof to the N-EOS was finished with solid physics and statistical mechanics, and the normal formula of substance parameters was obtained in microphysics. We also proved that the physics base of the N-EOS with R=R(p) is in correspondence with the law of states of the Debye theory and its validity is not limited by the assumption which the cp remains constant. In addition, the calculation results of R with experimental data under normal pressure shows that R=R(p) is not very accurate approximation. A tentative discussion about the problem of =(v) approximation of the Gruneisen EOS was done.