Consider a centrifugal compressor with backward leaning impeller with an angle of $20$ at exit and outer radius of $r_2=0\mathrm{.}07m.$ The impeller is rotating at $65,000rpm$ and the exit velocity in the radial direction is $C_{r2}=140\frac{m}{s}.$ Air enters the compressor with no swirl and at total pressure and temperature of $98$kPa and $300K,$ respectively. Consider $R=0\mathrm{.}287k\frac{J}{k}g.K,C_p=1\mathrm{.}002k\frac{J}{k}g.K$ and $=1\mathrm{.}4.$ Assume ideal operating condition.

a$)$ Find the specific work of the impeller.

b$)$ What is the total pressure ratio of the compressor if the efficiency is $80\%?$