$(35\%)0\mathrm{.}35kg$ of the ideal gas argon is contained within a piston$-$cylinder device. The argon goes through a two$-$step process. The first step from State $1$ to State $2$ is an isentropic compression process from a temperature of $40C$ and specific volume of $0\mathrm{.}7\frac{m^3}{k}g$ to a pressure $P_2=1200$kPa. In step $2,$ the argon goes through a constant pressure process to a final temperature $T_3=725C.$ The molecular weight of argon is $40$ and its ratio of specific heats is k $=1\mathrm{.}67.$

a$)(8pts)$ Find the temperature of State $2(K).$

b$)(7$ pts$)$ Find the heat transfer and work $($kJ$)$ going from State $1-2.$

c$)(11$ pts$)$ Find the heat transfer and work $($kJ$)$ going from State $2-3.$

d$)(6$ pts$)$ Find the change in specific entropy from State $2-3(k\frac{J}{k}gK)$

e$)(3pts)$ Qualitatively sketch the process on a T$-$s diagram $($no numbers needed$).$