Which one of the following statements is correct?

Consider a $70 \%$ efficient hydrogen-oxygen fuel cell working under standard conditions at $1 \ bar$ and $298 \ K$. Its cell reaction is
$H_{2(g)} + \frac{1}{2} O_{2(g)} \rightarrow H_2O(\ell)$
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.
$O_{2(g)} + 4H^{+}(aq.) + 4e^- \rightarrow 2H_2O(\ell), E^{\circ} = 1.23 \ V$
$2H^{+}(aq.) + 2e^- \rightarrow H_{2(g)}, E^{\circ} = 0.00 \ V$
Use $F = 96500 \ C \ mol^{-1}, R = 8.314 \ J \ mol^{-1} \ K^{-1}$

Match the entries from Column $I$ and Column $II$ and choose the correct order.

$A$. Leclanche cell	$1$. Converts energy of combustion into electrical energy
$B$. Fuel cell	$2$. Rechargeable cell
$C$. Ni-Cd cell	$3$. At anode,$Zn \longrightarrow Zn^{2+} + 2e^{-}$

Consider an electrochemical cell: $A_{(s)} | A^{n+}(aq, 2 \ M) || B^{2n+}(aq, 1 \ M) | B_{(s)}$. The value of $\Delta H^{\ominus}$ for the cell reaction is twice that of $\Delta G^{\ominus}$ at $300 \ K$. If the emf of the cell is zero,the $\Delta S^{\ominus}$ (in $J \ K^{-1} \ mol^{-1}$) of the cell reaction per mole of $B$ formed at $300 \ K$ is. . . . . . . (Given: $\ln(2) = 0.7, R = 8.3 \ J \ K^{-1} \ mol^{-1}$.)

$(i)$ When a copper rod is dipped in $1 \ M$ silver nitrate solution,silver crystals are obtained. $(ii)$ Silver metal does not react with $1 \ M$ zinc nitrate solution. $(iii)$ When zinc metal is dissolved in $1 \ M$ copper sulfate solution,copper metal is displaced. Arrange the three metals in the decreasing order of their reducing power.

Consider the following two half-cell reactions:
$CO_2 + 6H^+ + 6e^- \rightarrow CH_3OH + H_2O$ $(E^{\ominus} = 0.02 \text{ V})$
$\frac{1}{2}O_2 + 2H^+ + 2e^- \rightarrow H_2O$ $(E^{\ominus} = 1.23 \text{ V})$
$A$ fuel cell was set up such that the cell operates under standard conditions. The fuel cell works with $80\%$ efficiency. If the work derived from the cell using $1 \text{ mol}$ of $CH_3OH$ is used to compress an ideal gas isothermally against a constant pressure of $1 \text{ kPa}$, then the change in the volume of the gas, $\Delta V =$ . . . . . . $\text{m}^3$. (nearest integer) Given: $F = 96500 \text{ C mol}^{-1}$