Current Attempt in Progress

Air at $26$kPa,$230K,$ and $220\frac{m}{s}$ enters a turbojet engine in flight. The air mass flow rate is $25k\frac{g}{s}.$ The compressor pressure ratio is $13,$ the turbine inlet temperature is $1400$ K $,$ and air exits the nozzle at $26$ kPa $.$ The diffuser and nozzle processes are isentropic$,$ the compressor and turbine have isentropic efficiencies of $85\%$ and $90\%,$ respectively, and there is no pressure drop for flow through the combustor. Kinetic energy is negligible everywhere except at the diffuser inlet and the nozzle exit. The states are numbered as in the figure below.

On the basis of air$-$standard analysis, determine:

$($a$)$ the pressures, in KPa $,$ and temperatures, in K $,$ at each principal state.

$($b$)$ the rate of heat addition to the air passing through the combustor, in $k\frac{J}{s}.$

$($c$)$ the velocity at the nozzle exit, in $\frac{m}{s}.$