One mole of $\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l)$ was completely burnt in oxygen to form $\mathrm{CO}_2(g)$ and $\mathrm{H}_2 \mathrm{O}(l)$. The standard enthalpy of formation $\left(\Delta_f H^{\ominus}\right)$ of $\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l), \mathrm{CO}_2(g)$ and $\mathrm{H}_2 \mathrm{O}(l)$ is $x, y$, $z \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. What is $\Delta_r H^{\ominus}\left(\right.$ in $\left.\mathrm{kJ} \mathrm{mol}^{-1}\right)$ for this reaction?

Identify the correct statements from the following.

I. Work is a path function.

II. Enthalpy is an extensive property.

III. Lattice enthalpy of ionic compounds can be obtained from Born-Haber cycle.

Which of the following processes entropy change $(\Delta S)$ is negative?

I. Sublimation of dry ice

II. Freezing of water

III. Crystallisation of the dissolved substance

IV. Burning of rocket fuel

Consider the following :

Statement I : During isothermal expansion of an ideal gas its enthalpy decreases.

Statement II : When 2.0 L of an ideal gas expands isothermally into vaccum, $\Delta U=0$.

The correct answer is :