In a piston$-$cylinder system, air $($k $=1\mathrm{.}4)$ initially at $0\mathrm{.}3$ MPa and $500$ K undergoes the following processes respectively.

Process $1-2$: Polytropic expansion from $500$ K and P$1=0\mathrm{.}3$ MPa to P$2=0\mathrm{.}2$ MPa with n $=$ k$.$

Process $2-3$: Cooling to T$3=72\backslash$deg C at constant pressure.

Process $3-4$: Return to the initial state $($point $1)$ by heating at constant volume.Draw the P$-$V diagram for the cycle.