In this research, polyethylene of different molecular weights (PE198, PE507, PE619, PE110) were studied using the Simha-Somcynsky (SS) theory with the Cannes-Hillard (CH) theory together extracting the physical properties of these polymers as the energy gradient in detecting and innvation new polymers in these polymeric materials play an important role in detecting new polymers and the surface tensile of the polymer is closely eliminate is related with the gradient energy coefficientwith as afunction molecular wieghts and temperaturers. We heve been extracted the state equation for the polymers material system and they had been obtained the minimum and maximum erroin volume by using the Newton Raphson method to obtain the valume of external freeedom under pressure (1-150) MPa and up to 513K to temperature the minimum and maximum error in volume ratio for PE1100 was (0.014518) and (1.4148) for PE198.resepictively