$1$emit$2($Marks $=30)[$Answer in the space provided, show important calculation steps$]$

A small gas turbine engine that drives an air compressor is supplied from a large pipeline with combustion gas at $420$kPa and $1000K.$ The turbine exhaust pressure $105$kPa. The gas flow rate is $3\mathrm{.}0k\frac{g}{s}.$ Turbine isentropic efficiency is ${}_t=0\mathrm{.}85.$ At the compressor inlet, the pressure and temperature of the air are $100$kPa and $300K,$ respectively. The air flow rate is $10k\frac{g}{s}.$ Compressor isentropic efficiency is ${}_c=0\mathrm{.}80.$

For air $($compressor$)$: ${}_a=1\mathrm{.}4,C_{Q,a}=1\mathrm{.}005k\frac{J}{kg*K}$; For combustion gas: ${}_9=1\mathrm{.}333,C_{p,0}=1\mathrm{.}148k\frac{J}{kg*K}.$