An ideal gas undergoes a reversible cyclic process as shown in the figure. The work done in this process is: (in $,V_1P_1$)

Match the following items in List-$I$ with their corresponding expressions in List-$II$.

List-$I$	List-$II$
$A$. At constant volume the change in internal energy of a system	$I$. $W = -2.303 nRT \log \frac{V_f}{V_i}$
$B$. Isothermal irreversible change	$II$. $W_{adiabatic} = \Delta U$
$C$. Isothermal reversible change	$III$. $q_V = \Delta U$
$D$. Adiabatic change	$IV$. $W = -p_{ex} (V_f - V_i)$
	$V$. $\Delta U = \Delta H - \Delta nRT$

For an ideal gas, consider only $P-V$ work in going from an initial state $X$ to the final state $Z$. The final state $Z$ can be reached by either of the two paths shown in the figure. Which of the following choice$(s)$ is (are) correct? [take $\Delta S$ as change in entropy and $w$ as work done].
$(A)$ $\Delta S_{X \to Z} = \Delta S_{X \to Y} + \Delta S_{Y \to Z}$
$(B)$ $w_{X \to Z} = w_{X \to Y} + w_{Y \to Z}$
$(C)$ $w_{X \to Y \to Z} = w_{X \to Y} + w_{Y \to Z}$
$(D)$ $\Delta S_{X \to Y \to Z} = \Delta S_{X \to Y}$

What is the enthalpy of vaporization of ethanol in $kJ/mol$? Given: boiling point $(b.p.)$ = $79.5 \, ^\circ C$ and entropy change $(\Delta S_{vap})$ = $109.8 \, J K^{-1} mol^{-1}$.

$A$ sample of gas is compressed from an initial volume of $2V_0$ to $V_0$ using three different processes.
First: Using reversible isothermal.
Second: Using reversible adiabatic.
Third: Using irreversible adiabatic under a constant external pressure.
Then

An isolated box,equally partitioned,contains two ideal gases $A$ and $B$ as shown in the figure. When the partition is removed,the gases mix. The changes in enthalpy $(\Delta H)$ and entropy $(\Delta S)$ in the process,respectively,are