To study on the behavior of the early stage of the spark kernel at constant pressure condition, the expressions of the thermal properties such as compressibility factor, thermal conductivity, and electrical conductivity of the high temperature air were newly suggested. The newly suggested simple expressions of the thermal properties of the high temperature air showed good results. Under the assumption of constant pressure, one dimensional numerical analysis was executed by varying surrounding conditions and discharging current of electrical spark. Numerical results show tat high surrounding pressure suppresses the growth of the spark kernel but supplies much electrical energy into the air, on the other hand high surrounding temperature increases the growth of the spark kernel but supplies less electrical energy. Also the result shows that , in case of direct current discharge, deposited electrical energy is able to be expressed in linear function of time approximately.