The present paper derives rigorously an equation of state by use of virial theorem at 0°K. No assumption is made concerning the potential energy of system and only the total kinetic energy of system is to be calculated, which signifies a new development in EoS. The new method in the calculation of EoS could be applied to all materials. Considering the difference of the electrons' distribution between TFD model and quantum mechanical statistics, we have introduced quantum corrections to the calculation of th...