(a)
$CaCO_{3}\overset{\ \ \ \ \ \mathrm{\Delta}\ \ \ \ \ }{\rightarrow}\ CaO + CO_{2}$
$(X)$
$CaO + H_{2}O\ \longrightarrow Ca(OH)_{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (Y)$
$Ca(OH)_{2} + 2CO_{2} \longrightarrow Ca\left( HCO_{3} \right)_{2}$
(Z)
$Ca\left( HCO_{3} \right)_{2}\overset{\ \ \ \ \ \mathrm{\Delta}\ \ \ \ \ }{\rightarrow}\ CaCO_{3}\ \rightarrow CO_{2} + H_{2}O\$
(X)