[i] I spent all the day cooking. (CGEL, p.374)
[ii] She worked hard all day. (Webster Learner’s)
[iii] I think about her all the time. (Webster Learner’s)
When I first came across [i], I assumed that the definite article is there for denoting the totally of the day. That is, a particular totality, as well as a particular part, surely could be identifiable and thus would have the article.
However this may not be quite simple as I thought, for [ii] has not the article. So I added another guess that objects need the article, but adverbs not. But this is not good either. As you see, in [iii] all the time has the article and it’s an adverbial phrase. What are the reasons they have or not have the article?