$6\mathrm{.}115$ An air compressor operates at steady state with air entering at $p_1=0\mathrm{.}1$MPa,$T_1=16C.$ The air undergoes a polytropic process, and exits at $p_2=0\mathrm{.}5$MPa,$T_2=146C.$

$($a$)$ Evaluate the work and heat transfer, each in $k\frac{J}{k}g$ of air

flowing. $($b$)$ Sketch the process on $p-v$ and $T-s$ diagrams and associate areas on the diagrams with work and heat transfer, respectively. Assume the ideal gas model for air and neglect changes in kinetic and potential energy.