Air is compressed in an internally reversible process from p$1=0\mathrm{.}3969$ bar and T$1=240$K to a final pressure of p$2=20$ bar and behaves as an ideal gas.

Determine all properties of the initial and final states $($T$,$p$,$v$,$h$,$ and u$),$ calculate the change in entropy and the work of the process per unit mass, and sketch the process in the T$-$s and p$-$v diagrams assuming the ideal gas behavior in the following case.$$Adiabatic compression in an ideal compressor $($one inlet and one outlet$)$

Bonus $($extra points$)$ question: Verify that ideal gas model is applicable in the most challenging state among the considered ones.