Problem $5-2.$ Consider a two$-$stage gas turbine engine which operates as an air$-$standard Brayton cycle as shown below. Air enters the compressor at $\backslash (100\backslash$mathrm$\{$kPa$\},290\backslash$mathrm$\{$~K$\}\backslash )$ and a volumetric flow rate of $\backslash (5\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$ The compressor pressure ratio is $10.$ The temperature at the inlet of the first turbine stage is $1300$ K $.$ The expansion takes place isentropically in two stages with reheat to $1300$ K between the stages at a constant pressure of $350$ kPa $.$ A regenerator having an effectiveness of $\backslash (85\backslash \%\backslash )$ is also used in the cycle.

$1.$ Show the cycle on a temperature$-$entropy diagram, then calculate:

$2.$ The net power output from the engine,

$3.$ The thermal efficiency of the cycle.

Note: Assume air as an ideal gas with variable specific heats.