$\Delta_f U^{\mathrm{s}}$ of formation of $\mathrm{CH}_4(\mathrm{~g})$ at certain temperature is $-393 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The value of $\Delta_f H^{\mathrm{s}}$ is

In an adiabatic process, no transfer of heat takes place between system and surroundings. Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following.

The pressure-volume work for an ideal gas can be calculated by using the expression $W=-\int_\limits{V_i}^{V_f} p_{e x} d V$. The work can also be calculated from the $p V$-plot by using the area under the curve within the specified limits. When an ideal gas is compressed (a) reversibly or (b) irreversibly from volume $V_i$ to $V_f$. Choose the correct option.

The entropy change can be calculated by using the expression $\Delta S=\frac{q_{\text {rev }}}{T} \cdot$ When water freezes in a glass beaker, choose the correct statement amongst the following.

On the basis of theromochemical equations (1), (2) and (3), find out which of the algebraic relationships given in options (a) to (d) is correct

1. C (graphite) $+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) ; \Delta_r H=x \mathrm{~kJ} \mathrm{~mol}^{-1}$

2. C (graphite) $+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{g}) ; \Delta_r H=y \mathrm{~kJ} \mathrm{~mol}^{-1}$

3. $\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) ; \Delta_r H=z \mathrm{~kJ} \mathrm{~mol}^{-1}$