Q$5($a$).[10+10+12=32$ points$]$ A mass of $1$ kg of air contained in a cylinder at $1\mathrm{.}5$ MPa, $1000$ K expands in a reversible isothermal process to a volume $10$ times larger. Assume constant specific heat Cv$0=0\mathrm{.}717$ kJ$/$kg$-$K$,$ R $=0\mathrm{.}287$ kJ$/$kg$-$K$.($a$)$ Determine the work for this process. $($b$)$ What is the amount of heat added during the process? Explain your answer. $($c$)$ Calculate the change in total entropy in kJ$/$K of the air.