The figure shows the $P-V$ plot of an ideal gas taken through a cycle $ABCDA.$ The part $ABC$ is a semicircle and $CDA$ is half of an ellipse. Then,

One mole of an ideal gas in initial state $A$ undergoes a cyclic process $ABCA$,as shown in the figure. Its pressure at $A$ is $P_0$. Choose the correct option$(s)$ from the following:
$(A)$ Internal energies at $A$ and $B$ are the same
$(B)$ Work done by the gas in process $AB$ is $P_0 V_0 \ln 4$
$(C)$ Pressure at $C$ is $\frac{P_0}{4}$
$(D)$ Temperature at $C$ is $\frac{T_0}{4}$

The density $\rho$ versus volume $V$ graph is shown in the figure. Find the corresponding pressure $P$ versus temperature $T$ graph.

If a gas is taken from $A$ to $C$ through $B$, the heat absorbed by the gas is $8 \, J$. Calculate the heat absorbed by the gas when it is taken from $A$ to $C$ directly.

In the reported figure,the heat energy absorbed by a system in going through a cyclic process is $......\,\pi \text{ J}$.

$A$ cyclic process $ABCD$ is shown below in the given $P-V$ diagram. Which of the following diagrams represents the same process in a $P-T$ diagram?