In which of the following processes is the maximum increase in entropy observed?

What is entropy? Explain its role in spontaneity.

Observe the following reactions:
$I$. $CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$
$II$. $Cl_{2(g)} \rightarrow 2 Cl_{(g)}$
$III$. $H_2O_{(l)} \rightarrow H_2O_{(s)}$
Identify the reactions in which entropy increases.

Amongst the chemical reactions given below, the reactions with increasing entropy are
$(i)$ $H_2O_{(l)} \rightarrow H_2O_{(g)}$
$(ii)$ $C_{(s)} + CO_{2(g)} \rightarrow 2CO_{(g)}$
$(iii)$ $2H_{2(g)} + O_{2(g)} \rightarrow 2H_2O_{(l)}$
$(iv)$ $N_{2(g)} + O_{2(g)} \rightarrow \text{Mixture of } N_2 \text{ and } O_2$

$1$ mole of a diatomic gas is heated through an isochoric process from $300\,K$ to $500\,K$. The change in entropy is: (in $,J/K$)

The change of entropy $(dS)$ is defined as