Acid catalysed dehydration of t-butanol is faster than that of n-butanol because

Explanation

Acid-catalysed dehydration of alcohols occurs through the intermediate formation of carbocations.
`underset("t-Butanol")(CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-OH) underset(-H_(2)O)overset(+H^(+))to underset("t-Butyl carbocation (more stable)")(CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C^(+)),underset("n-Butanol")(CH_(3)CH_(2)CH_(2)CH_(2)-OH) underset(-H_(2)O)overset(+H^(+))to underset("n-Butyl carbocation (less stable)")(CH_(3)CH_(2)CH_(2)overset(+)(C)H_(2))`
Since t-butyl carbocation is more stable than n-butyl carbocation, therefore, acid-catalysed dehydration of t-butanol occurs fater than n-butanol.