Q$2.($a$)$ Air at $1\mathrm{.}5$x$105$ Pa$,27\backslash$deg C$,$ initially occupying a volume of $0\mathrm{.}030$ m$3$ in closed cylinder$-$piston assembly is heated reversibly and at constant volume to a pressure of $3\mathrm{.}0$x$105$ Pa$.$ It is cooled to $27$oC and volume of $0\mathrm{.}015$m$3$ at constant pressure. Finally, it is expanded isothermally to its original state. Calculate W$,$ Q$,\backslash$Delta U and $\backslash$Delta S for each of the three processes and the entire cycle.

$[$Take CV $=3/2$R$,$ R $=8\mathrm{.}314$ Jmol$-1$K$-1]$