Step 1: Identify the nature of alcohol.
$(CH_3)_3C{-}OH$ is tert-butanol, which is a tertiary alcohol.
Step 2: Effect of heated copper at 573 K.
Tertiary alcohols do not undergo dehydrogenation with copper. Instead, they undergo dehydration to form alkenes.
Step 3: Dehydration reaction.
Tert-butanol loses a molecule of water to form an alkene:
\[
(CH_3)_3C{-}OH \rightarrow (CH_3)_2C{=}CH_2 + H_2O
\]
Step 4: Identify product A.
The alkene formed is 2-methylpropene.
Step 5: Conclusion.
The product obtained in the reaction is 2-methylpropene.