One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^{\circ} {C}$ to $37^{\circ} {C}$. If the ideal gas is composed of polyatomic molecule that has $4$ vibrational modes which of the following is true?

Thermodynamic processes are indicated in the following diagram. 

Match the following

 $\begin{array}{|l|l|} \hline Column\,\,-\,\,1 & Column\,\,-\,\,2 \\ \hline P\,:\,Process\,\,-\,\,I & \,\,A\,\,:\,\,Adiabatic \\ \hline Q\,:\,Process\,\,-\,\,II & \,\,B\,\,:\,\,Isobaric \\ \hline R\,:\,Process\,\,-\,\,III & \,\,C\,\,:\,\,Isochoric \\ \hline S\,:\,Process\,\,-\,\,IV & \,\,D\,\,:\,\,Isothermal \\ \hline \end{array}$

A cyclic process $ABCD$ is shown in the figure $P-V$ diagram. Which of the following curves represent the same process

A reversible cyclic process for an ideal gas is shown below. Here, $P , V$, and $T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q, w, H$ and $U$ are heat, work, enthalpy and internal energy, respectively.

The correct option ($s$) is (are)

$(A)$ $q_{A C}=\Delta U_{B C}$ and $W_{A B}=P_2\left(V_2-V_1\right)$ $(B)$ $W _{ BC }= P _2\left( V _2- V _1\right)$ and $q _{ BC }= H _{ AC }$ $(C)$ $\Delta H _{ CA }<\Delta U _{ CA }$ and $q _{ AC }=\Delta U _{ BC }$ $(D)$ $q_{B C}=\Delta H_{A C}$ and $\Delta H_{C A}>\Delta U_{C A}$

A system goes from $A$ to $B$ via two processes $I$ and $II$ as shown in figure. If $\Delta {U_1}$ and $\Delta {U_2}$ are the changes in internal energies in the processes $I$ and $II$ respectively, then