Acetic acid is treated with $Ca{\left(OH\right)}_2$ and the product so obtained is subjected to distillation. The final product is :

Acetic acid (as an example of a typical carboxylic acid) reacts with calcium hydroxide to form calcium acetate. This is a simple acid-base reaction which forms a salt and water:

$2C{H}_{3}COOH+{Ca(OH)}_2⟶(CH3COO{)}_{2}Ca+2H_{2}O$

Upon heating, calcium acetate undergoes decomposition to acetone and calcium carbonate. The acetone can be distilled off from the mixture, leaving behind solid calcium carbonate:

${(C{H}_{3}COO)}_{2}Ca\to \Delta CaC{O}_3+2{(C{H}_3)}_{2}C=O$

At even higher temperatures calcium carbonate itself can be decomposed to calcium oxide and carbon dioxide:

$CaCO3\stackrel{\Delta }{\to }CaO+CO$

Hence, the correct option is $C$