Aluminum conducts electricity well (and is lightweight) making itself ideal for uses in long distance electrical transmission. This is a property that it shares with other metals, and it conducts electricity for the same reasons that they do -- free electrons. The same free electrons that give reflectivity.
Another model of conductivity is called the electron well. This is based on the energy required to remove an electron from an atom. The idea is that in metals there are more electrons that have enough energy to move across the whole metal (ie. are in the "conduction band") than in insulators. Aluminum has a particularly large amount of electrons in the conduction band as it is such a good conductor (it has a very low resistivity: 2.65 x 10-8 Ohm metres).
With heat conductivity it works in a similar way. In non-metallic elements heat is transferred by vibrations of atoms causing the next atom to vibrate, and then the next, and so on. In this was the heat moves by conduction. In metals this process also occurs, but the delocalised electrons can also move around to pass on the heat energy. This greatly speeds the process up. Therefore as aluminum is a good electrical conductor it is also a good conductor of heat. This makes aluminum ideal in kitchen pans as it heats that food quickly, and evenly.
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