A turbojet engine operating at steady state is shown below. Mass flow rate of air is $25k\frac{g}{s}.$ Air steadily enters a well$-$insulated diffuser at an absolute pressure of $20$kPa and an absolute temperature of $200K$ with a velocity of $300\frac{m}{s}($State $1)$ and exits at an absolute pressure of $45$kPa with negligible velocity $($State $2).$ Air then flows through an adiabatic compressor and exits at an absolute pressure of $675$kPa and an absolute temperature of $560K($State $3).$ Air is then heated in a combustor to $1600K$ with negligible pressure drop $($State $4).$ Air expands to an absolute pressure of $230$kPa $($State $5)$ through an adiabatic turbine. All the work produced by the turbine is used to drive the compressor. Air leaving the turbine flows through a wellinsulated nozzle and exits at an absolute pressure of $20$kPa and an absolute temperature of $750K($State $6).$

$P_1=20$kPa

$T_1=200K$

$V_1=300\frac{m}{s}$

$P_2=45$kPa

$P_4=675$kPa

$($a$)$ Determine the absolute temperature of air at the diffuser exit, in $K.$

$($b$)$ Find the rate of heat transfer for the combustor, in $kW.$

$($c$)$ Determine the absolute temperature of air at the turbine exit, in K$.$

$($d$)$ Calculate the velocity of air at the nozzle exit, in $\frac{m}{s}.$