Why does the entropy of a substance increase with an increase in temperature?

Give the mathematical equation for entropy change.

$9.0 \, g$ of $H_2O$ is vaporized at $100 \, ^\circ C$ and $1 \, atm$ pressure. If the latent heat of vaporization of water is $x \, J / g$,then $\Delta S$ is given by :-

For the oxidation of iron:
$4 Fe_{(s)} + 3 O_{2(g)} \rightarrow 2 Fe_2O_{3(s)}$
The entropy change is $-549.4 \ J \ K^{-1} \ mol^{-1}$ at $298 \ K$. Despite the negative entropy change of this reaction,why is the reaction spontaneous?
($\Delta_r H^\Theta$ for this reaction is $-1648 \times 10^3 \ J \ mol^{-1}$)

Which of the following reactions exhibits a decrease in entropy?

In a reversible adiabatic process $\Delta S$ is :-