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

Process $1-2$: Polytropic expansion from $500K$ and $P_1=0\mathrm{.}3$MPa to $P_2=0\mathrm{.}2$MPa with $n=k.$

Process $2-3$: Cooling to $T_3=72C$ at constant pressure.

Process $3-4$: Return to the initial state $($point $1)$ by heating at constant volume.

Accordingly,

a$.$ Find the work and heat transfer in kJ$/$kgfor each process.

b$.$ Draw the P$-$V diagram for the cycle.

c$.$ Calculate the thermal efficiency.