$($b$)$ A centrifugal compressor runs with a tip rotor speed of $400\frac{m}{s}$ and the slip factor is $0\mathrm{.}96.$ The compressor takes in air at $\frac{1}{b}ar,300k$ at ambient conditions. If the mass four rate of air is $20k\frac{g}{s}$ and the compressor works with an isentropic efficiency of $85\%,$ calculate: $(07)[$CO$4]$

$($i$)$ Compressor power

$($ii$)$ Total pressure and temperature at exit of impeller

Assume $C_p=1\mathrm{.}05k\frac{J}{k}gK$ and $v=1\mathrm{.}4$