Question $3($Homework$)$

Through a series of mechanically reversible processes, an ideal gas initially at $303K$ and $\frac{1}{b}ar,$ undergoes the following cyclic processes in a closed system:

$(1-2)$ It is first compressed adiabatically to $5$ bar.

$(2-3)$ Secondly, it is cooled at a constant pressure of $5$ bar to $303K.$

$(3-1)$ Finally, it is expanded isothermally to its original state.

Sketch the cycle on a PV diagram and calculate $Q,W,U,$ and $H$ for each process of the cycle. Does this cycle obey the first law of thermodynamics? Take constant specific heats to be $C_P=(\frac{7}{2})R$ and $C_V=(\frac{5}{2})R.$