Think of which article ("the" or "a") you would use were the word "second" omitted in each case. The articles in these examples do not refer to the word "second", but rather to the nouns they are modifying. The speakers are essentially referring to "the floor" and "a bite".
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hanuman_2000Could anybody explain it?second has nothing to do with it. You're talking about the floor and a bite. In the first case the floor is named the second floor. In the second case, the bite is not named the second bite. We name the floors of a building; we don't name each bite of food that we take. Which floor we are