An adiabatic compressor is used to pressurize air from $140$kPa to $1200$kPa. If the air entering the compressor is at $300K,$ and the isentropic efficiency of the air is $80\%,$ then calculate the required work by performing an:

$($a$)$ approximate analysis $($assume $300K$ values for specific heats$)$

$\frac{kJ}{kg}$

$($b$)$ exact analysis $($variable specific heats$)$

$\frac{kJ}{kg}$