Consider a \(70 \%\) efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and \(298 \mathrm{~K…

Consider a \(70 \%\) efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and \(298 \mathrm{~K}\). Its cell reaction is \(\mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

The work derived from the cell on the consumption of \(1.0 \times 10^{-3} \mathrm{~mol}^{2}\) of \(\mathrm{H}_{2}(\mathrm{~g})\) is used to compress \(1.00 \mathrm{~mol}\) of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in K) of the ideal gas? The standard reduction potentials for the two half-cells are given below:

\(\mathrm{O}_{2}(\mathrm{~g})+4 \mathrm{H}^{+}(\mathrm{aq})+4 \mathrm{e}^{-} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}), \mathrm{E}^{\circ}=1.23 \mathrm{~V}\),

\(2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{H}_{2}(\mathrm{~g}), \mathrm{E}^{\circ}=0.00 \mathrm{~V}\).

Use \(\mathrm{F}=96500 \mathrm{~C} \mathrm{mol}^{-1}, \mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\). (Nearest integer)

[JEE Advanced 2020, Paper-1]