Consider a 70 % efficient hydrogen-oxygen fuel cell working under...

Consider a $70$ efficient hydrogen-oxygen fuel cell working under standard conditions at $1$ bar and $298K$. Its cell reaction is

${H}_{2} ( g ) + \dfrac{1}{2}{O}_{2} ( g ) \to {H}_{2}O ( l )$

The work derived from the cell on the consumption of $1 . 0 \times {10}^{- 3}mol$ of ${H}_{2} ( g )$ is used to compress $1 . 00mol$ 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.

${O}_{2} ( g ) + 4{H}^{+} ( aq ) + 4{e}^{-} \to 2{H}_{2}O ( l ) , {E}^{0} = 1 . 23V$,

$2{H}^{+} ( aq ) + 2{e}^{-} \to {H}_{2} ( g ) , {E}^{0} = 0 . 00V$

Use $F = 96500C{mol}^{- 1}, R = 8 . 314J{mol}^{- 1}{K}^{- 1}$.