For an ideal gas, the heat of reaction at constant pressure and heat of reaction at constant volume are related by equation _________

For the reaction $\mathrm{CH}_{4(\mathrm{~g})}+\mathrm{H}_{2(\mathrm{~g})} \longrightarrow \mathrm{C}_2 \mathrm{H}_{6(\mathrm{~g})}$ $\mathrm{K}_{\mathrm{p}}=3.356 \times 10^{17}$, calculate $\Delta \mathrm{G}^{\circ}$ for the reaction at 298 K .

A gas expands isothermally against a constant external pressure of 1 bar from 10 dm$^3$ to 20 dm$^3$ by absorbing 800 J of heat from surrounding. Calculate value of $\Delta$U.

Which of the following equations indicates increase in entropy?