A carbon compound ' $P$ ' on heating with excess conc. $\mathrm{H}_2\mathrm{SO}_4$ forms another carbon compound ' $Q$ ' which on addition of hydrogen in the presence of nickel catalyst forms a saturated carbon compound 'R'. One molecule of ' $R$ ' on combustion forms two molecules of carbon dioxide and three molecules of water. Identify $P, Q$ and $R$ and write chemical equations for the reactions involved.