The product P in the reaction $CH_3-C \equiv CH \xrightarrow{Hg^{2+}, H_2SO_4} P$ is:

The reaction of alkynes with water in the presence of mercuric sulphate ($HgSO_4$) and dilute sulphuric acid ($H_2SO_4$) at 333 K is known as hydration of alkynes.

1. Mechanism: Water adds to the triple bond according to Markovnikov's rule. The negative part of the addendum ($OH^-$) attaches to the carbon with fewer hydrogen atoms ($C-2$ in propyne).
2. Intermediate: An unstable enol intermediate ($CH_3-C(OH)=CH_2$) is formed.
3. Tautomerization: The enol rapidly tautomerizes to the more stable keto form, which is Propanone (Acetone, $CH_3-CO-CH_3$).

$CH_3-C \equiv CH + H_2O \xrightarrow{Hg^{2+}/H^+} [CH_3-C(OH)=CH_2] \rightleftharpoons CH_3-CO-CH_3$

Note: Only ethyne yields an aldehyde (ethanal) under these conditions; all other alkynes yield ketones.