In a $3$-stage air compressor, the inlet pressure is $p_1$, discharge pressure is $p_4$.and the intermediate pressures are $p_2$ and $p_3 ( p_2 < p_3)$. The total pressure ratio of the compressor is $10$ and the pressure ratios of the stages are equal. If $p_1 = 100$ $kPa$, the value of the pressure $p_3$ (in $kPa$) is __________