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

${\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\ell \right)$

The work derived from the cell on the consumption of 1.0 × 10^–3mol of H₂(g) is used to compress 1.00 mol of a monoatomic ideal gas in a thermally insulted 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. 

${\mathrm{O}}_2\left(\mathrm{g}\right)+4{\mathrm{H}}^{+}(\mathrm{aq}.)+4{\mathrm{e}}^{-}\to 2{\mathrm{H}}_2\mathrm{O}\left(\ell \right),{\mathrm{E}}^{\mathrm{o}}=1.23\mathrm{V}$

$2{\mathrm{H}}^{+}(\mathrm{aq}.)+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2\left(\mathrm{g}\right),{\mathrm{E}}^{\mathrm{o}}=0.00\mathrm{V}$

Use F = 96500 C mol^–1 , R = 8.314 J mol^–1K^–1