Total enthalpy change for freezing of 1 mol of water at $10^{\circ} \mathrm{C}$ to ice at $-10^{\circ} \mathrm{C}$ is ________

(Given: $\Delta_{\text {fus }} \mathrm{H}=x \mathrm{~kJ} / \mathrm{mol}$

$$\begin{aligned} & \mathrm{C}_{\mathrm{p}}\left[\mathrm{H}_2 \mathrm{O}(\mathrm{l})\right]=y \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \\ & \mathrm{C}_{\mathrm{p}}\left[\mathrm{H}_2 \mathrm{O}(\mathrm{~s})\right]=z \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \end{aligned}$$

Consider the given data :

(a) $\mathrm{HCl}(\mathrm{g})+10 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{HCl} .10 \mathrm{H}_2 \mathrm{O} \Delta \mathrm{H}=-69.01 \mathrm{~kJ} \mathrm{~mol}^{-1}$

(b) $\mathrm{HCl}(\mathrm{g})+40 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{HCl} .40 \mathrm{H}_2 \mathrm{O} \Delta \mathrm{H}=-72.79 \mathrm{~kJ} \mathrm{~mol}^{-1}$

Choose the correct statement :

One mole of an ideal gas expands isothermally and reversibly from $10 \mathrm{dm}^3$ to $20 \mathrm{dm}^3$ at 300 K . $\Delta \mathrm{U}, \mathrm{q}$ and work done in the process respectively are

Given: $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$

$\ln 10=2.3$

$\log 2=0.30$

$$\log 3=0.48$$

Let us consider a reversible reaction at temperature, T. In this reaction, both $\Delta \mathrm{H}$ and $\Delta \mathrm{S}$ were observed to have positive values. If the equilibrium temperature is Te , then the reaction becomes spontaneous at: