A steady flow compressor handles $133m^3*m^{-1}$ of nitrogen $)$ measured at intake, where $P_1=97$kPa and $T_1=27C.$ Air discharges to the atmosphere at $311$kPa at the end of compression. The changes in kinetic and potential energies are negligible. For each of the following cases, determine the final temperature and work if the process is:

a$)P{V}^r=$ constant $($adiabatic$)$

b$)$ PV $=$ constant $($isothermal$)$

$($In this problem, air inside the cylinder compressed from $97$kPa to $311$kPa. Compression process, starting from the lower pressure to the state just prior to release, can be considered as the process takes place in a closed system.$)$