Problem $8$: $(15$ pts$)$ Ideal gas air in a piston$/$cylinder device $(0\mathrm{.}1kg,300K,100$kPa$),$ is compressed to a final pressure of $300$ kPa $.$

$($a$)$ If the process is isothermal, find the work and heat transfer. Show the process in a $P-v$ diagram.

$($b$)$ The process is changed so that it is polytropic with $n=1\mathrm{.}3.$ What is the new work and the new heat transfer?