The W-polynomial is applied in two ways to questions involving the Kauffman
bracket of some families of links. First we find a geometric property of a link
diagram, which is less than or equal to the twist number, that bounds the
Mahler measure of the Kauffman bracket. Second we find a general form for the
Kauffman bracket of a link found by surgering in a single rational tangle along
n unlinked components, all in a particular annulus. We then give a condition
under which the Mahler measure of the Kauffman bracket of such families
diverges. We give examples of the condition in action.