$(2)$ A piston$-$cylinder device initially contains $0\mathrm{.}2$ kg of helium at $3$ MPa and $400C($point #$1).$ The helium is first expanded isothermally to $600$ kPa $($point #$2),$ then compressed polytropically with a polytropic exponent of $1\mathrm{.}3$ to the initial pressure $($point #$3),$ and finally compressed at the constant pressure to the initial state. Determine $($a$)$ the temperature at point #$3$ and the volume at each point, and $($b$)$ the heat transfer for each process and the net heat transfer of the cycle. $(25\%)$