$6\mathrm{.}173$ An air compressor operates at steady state with air entering at $p_1=15lb\frac{f}{i}{n}^2{?}^2,T_1=60F.$ The air undergoes

a polytropic process, and exits at $p_2=75lb\frac{f}{i}{n}^2,T_2=294F.$

$($a$)$ Evaluate the work and heat transfer, each in Btu per lb 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.