To understand why a tertiary butyl carbocation is more stable than a secondary butyl carbocation, we need to consider the factors that stabilize carbocations.$\\$A carbocation is a positively charged carbon atom with three bonds and an empty p orbital. The stability of a carbocation is influenced by:$\\$• Hyperconjugation$\\$• Inductive effect$\\$• Resonance (if applicable)$\\$In this case, the most relevant factor is hyperconjugation.$\\$Hyperconjugation is the delocalization of electrons from adjacent C-H bonds (sigma bonds) into the empty p orbital of the carbocation. This delocalization helps to stabilize the positive charge.