Explanation

(a) Average kinetic theory of one molecule is
$E = \frac{3}{2}kT$
where $k$ is Boltzmann constant and $T$ the absolute temperature.
Given, $T_{1} = - 68℃ = 273 - 68 = 205\ K,\ $
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ E_{1} = E,\ \ E_{2} = 2E$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{E_{1}}{E_{2}} = \frac{T_{1}}{T_{2}}\ \ $
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T_{2} = \frac{T_{1}E_{2}}{E_{1}}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T_{2} = \frac{205 \times 2E}{E} = 410\ K$