Air $(1\mathrm{.}0$ bar, $298\mathrm{.}15$ K$)$ is being compressed into $5\mathrm{.}5$ bar, $320\mathrm{.}15$ K by two reversible, mechanical processes:

$($a$)$ Constant pressure compression followed by heating at constant volume;

$($b$)$ heating at fixed volume followed by cooling at constant pressure.

Calculate heat, work, $$U$,$ and $$H of each process.

Assume that air is an ideal gas with Cp $=28\mathrm{.}10$ J mol$-1$K$-1$ and molar volume of $0\mathrm{.}02479$ m$3$ mol$-1(298\mathrm{.}15$ K$,1\mathrm{.}0$ bar$).$