$(213$ An air$-$standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes:

$1-2)$ Isentropic compression from $100$ kPa and $22C$ to $600$ kPa

$2-3.v=$ constant heat addition to $1500$ K

$3-4$ Isentropic expansion to $100$ kPa

$4-1)P=$ constant heat rejection to initial state

$($a$)$ Show the cycle on $P-$V and $T-$s diagrams.

$($b$)$ Calculate the net work output per unit mass.

$($c$)-$Determine the thermal efficiency.