$2-$a$.$

One mole of an ideal gas at $T=298K$ and at $P=1$ bar was compressed reversibly and adiabatically to $\frac{100}{b}ar.$ Calculate the final temperature, the final volume and the change in the internal energy. $Cv=(\frac{5}{2})R.$

Sketch the process path on PV diagram.

$2-$b

If the above one step process is replaced by a two steps process as follow:

i$-$ Isothermal compression to the final volume.

ii$-$ Heating at constant volume to the final temperature.

Calculate $Q,W,$ and $U$ in each step and in the two steps together.

Sketch the process path on PV diagram.