A simple derivation of a new equation of state (EOS) based on Eulerian finite strain and its applicability

We have derived a new equation of state (EOS) based on the Eulerian finite scheme utilising the 3/2th power of edge length by pressure. By truncating the order of finite strains in the expression of the Helmholtz free energy, we have derived new expressions for second- and third-order EOSs, as well as expressions for bulk modulus and its first pressure derivative. We have considered four materials, viz. CaO, Bi, NaCl and Fe_2 SiO_4 to test the applicability and validity of the derived EOS. The feature of this EOS shows more validity than other prominent EOSs and corresponds well with the available experimental results.