Q$1(10$ marks$)-$ M$$rks are equally distributed in sub$-$questions

An adiabatic c$$mpressor takes air $($assuimed as ideal gas$)$ flowing at a rate of $0\mathrm{.}3k\frac{g}{5}$ from $100$kPa and

$22C$ to $800$kPa. Assuming constant values of $cp+1\mathrm{.}020k\frac{J}{k}gK,cv=0\mathrm{.}733k\frac{J}{k}gKk=1\mathrm{.}391,$ and

negle$$ing the changes in kinetic and potential energles, determine

$(3)$ The exit temperature if the process is reversible, T$2$s $($K$).$

$($b$)$ the exit temperature if the compressor has an isentropic efficiency of $80\%,T2(K)$

$($c$)$ the power input required to drive the compressor with the isentropic efficiency of $80\%,W_{-}$in $($kW$).$

$($d$)cp,cv$ and $k$ change with temperature. What is the assumed temperature $(K)$ at which $cp=1\mathrm{.}020k\frac{g}{k}g$

$K,cv=0\mathrm{.}733\frac{k}{k}gK,k=1\mathrm{.}391?$

Write correct numerical answers to $3$ significant figures.