Given below are two statements :

Statement I : For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure.

Statement II : In a constant volume process, no work is produced and all the heat withdrawn goes into the chaotic motion and is reflected by a temperature increase of the ideal gas.

In the light of the above statements, choose the correct answer from the options given below

At $\mathrm{T}(\mathrm{K})$, the equilibrium constant of

$\mathrm{A}_2(g)+\mathrm{B}_2(g) \rightleftharpoons \mathrm{C}(g)$ is $2.7 \times 10^{-5}$.

What is the equilibrium constant for

$\frac{1}{3} \mathrm{~A}_2(\mathrm{~g})+\frac{1}{3} \mathrm{~B}_2(\mathrm{~g}) \rightleftharpoons \frac{1}{3} \mathrm{C}(\mathrm{g})$ at the same temperature?

In order to oxidise a mixture of 1 mole each of $\mathrm{FeC}_2 \mathrm{O}_4, \mathrm{Fe}_2\left(\mathrm{C}_2 \mathrm{O}_4\right)_3, \mathrm{FeSO}_4$ and $\mathrm{Fe}_2\left(\mathrm{SO}_4\right)_3$ in acidic medium, the number of moles of $\mathrm{KMnO}_4$ required is

Consider the first order reaction $\mathrm{R} \rightarrow \mathrm{P}$.

The fraction of molecules decomposed in the given first order reaction can be expressed as