$$\Delta_{\text {vap }} \mathrm{H}^{\ominus}$$ for water is $$+40.79 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ at 1 bar and $$100^{\circ} \mathrm{C}$$. Change in internal energy for this vapourisation under same condition is ________ $$\mathrm{kJ} \mathrm{~mol}^{-1}$$. (Integer answer) (Given $$\mathrm{R}=8.3 \mathrm{~JK}^{-1} \mathrm{~mol}^{-1}$$)

Consider the figure provided.

$$1 \mathrm{~mol}$$ of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at $$18^{\circ} \mathrm{C}$$. If the piston is moved to position $$\mathrm{B}$$, keeping the temperature unchanged, then '$$\mathrm{x}$$' $$\mathrm{L}$$ atm work is done in this reversible process.

$$\mathrm{x}=$$ ________ $$\mathrm{L}$$ atm. (nearest integer)

[Given : Absolute temperature $$={ }^{\circ} \mathrm{C}+273.15, \mathrm{R}=0.08206 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}{ }^{-1} \mathrm{~K}^{-1}$$]

For the reaction at $$298 \mathrm{~K}, 2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{C}, \Delta \mathrm{H}=400 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ and $$\Delta S=0.2 \mathrm{~kJ} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$$. The reaction will become spontaneous above __________ $$\mathrm{K}$$.

An ideal gas, $$\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$$, is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is $$298 \mathrm{~K}$$ and $$5 \mathrm{~atm}$$, respectively then the final temperature is _________ $$\mathrm{K}$$ (nearest integer).

[$$\overline{\mathrm{c}}_{\mathrm{v}}$$ is the molar heat capacity at constant volume]