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

The work derived from the cell on the consumption of $$1.0 \times 10^{−3}$$ mol of $$H_{2}$$(g) is used to compress
1.00 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.
$$O_{2}(g) + 4H^{+} (aq) + 4e^{-} \rightarrow 2 H_{2}O (l), E^{0} = 1.23 V$$,

$$2H^{+} (aq) + 2e^{-} \rightarrow H_{2} (g), E^{0} = 0.00 V$$.

Use $$𝐹 = 96500 C mol^{−1},𝑅 = 8.314 J mol^{−1} K^{−1}$$.