An ideal gas $(Cv=2k\frac{J}{k}gK,Mr=8\mathrm{.}315k\frac{g}{k}$mol undergoes the following processes

A$.1-2$ : Adiabatic compression.

B$.2-3$ Constant pressure heating

C$.3-4$: Adiabatic expansion.

D$.4-1$ : Constant pressure cooling. $P1=\frac{1}{b}ar,T1=300K,P2=\frac{10}{b}ar,q23=1250k\frac{J}{k}g.$

Calculate $($a$)$ T$2,$ T$3$ and T$4,($b$)$ All technical works exchanged, $($c$)$ All heats exchanged, $($d$)$ the thermal efficiency of the thermodynamic cycle.

Considering that the direction of the cycle is changed $($from clockwise to anticlockwise$),$ calculate $($e$)$ All technical works exchanged, $($f$)$ All heats exchanged, $($g$)$ the Coefficient of Performance $($both modes$)$

For both cycles $($clockwise to anti$-$clockwise operation$),$ confirm that the cycles do not violate $2^{nd}$ law of Thermodynamics.

For both cycles $($clockwise to anti$-$clockwise operation$),$ create the P$.$V$,$ P$.$T and V$-$T diagrams.