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

Consider the reactions given below. On the basis of these reactions find out which of the algebraic relationship given in options (a) to (d) is correct?

1. $\mathrm{C}(\mathrm{g})+4 \mathrm{H}(\mathrm{g}) \rightarrow \mathrm{CH}_4(\mathrm{~g}) ; \Delta_r H=x \mathrm{~kJ} \mathrm{~mol}^{-1}$

2. C (graphite) $+2 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{CH}_4(\mathrm{~g}) ; \Delta_r H=y \mathrm{~kJ} \mathrm{~mol}^{-1}$

The enthalpies of elements in their standard states are taken as zero. The enthalpy of formation of a compound