For the process $H_2O_{(l)} \rightarrow H_2O_{(g)}$ at $100^{\circ}C$ and $1 \ atm$ pressure,which of the following is true?

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) $\Delta S_{X \to Y \to Z} = \Delta S_{X \to Y}$

The enthalpy change on freezing of $1 \ mol$ of water at $5 \ ^\circ C$ to ice at $-5 \ ^\circ C$ is ..... $kJ \ mol^{-1}$.
(Given $\Delta _{fus}H = 6 \ kJ \ mol^{-1}$ at $0 \ ^\circ C$,
$C_p(H_2O, l) = 75.3 \ J \ mol^{-1} \ K^{-1}$,
$C_p(H_2O, s) = 36.8 \ J \ mol^{-1} \ K^{-1}$)

For isothermal expansion of an ideal gas, the correct combination of the thermodynamic parameters will be

The value of $\Delta H$ for cooling $2 \ mol$ of an ideal monoatomic gas from $225^{\circ} C$ to $125^{\circ} C$ at constant pressure will be [given $C_{p} = \frac{5}{2} R$]. (in $R$)

When $128 \, g$ of oxygen gas is heated from $0 \, ^oC$ to $100 \, ^oC$,the average values of $C_v$ and $C_p$ are $5 \, cal \, mol^{-1} \, K^{-1}$ and $7 \, cal \, mol^{-1} \, K^{-1}$ respectively. Find the values of $\Delta U$ and $\Delta H$.