Is "out" a preposition or an adverb in these sentences?

Is "out" a preposition or an adverb in these sentences?

1. "We need to get the hell out of this place."




2. "We need to get out and leave this place."

It depends on the grammar that you are following or are being taught. Some traditional grammars categorize the word "out"--depending on how it is used--as either a preposition, or as an adverb, or as a part of a complex preposition, etc.

Modern grammars usually categorize the word "out" differently. In some of these grammars, some traditional adverbs (such as "out") have been re-categorized as being purely as prepositions, which happens to simplify the grammar overall -- for instance, according to the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL), the word "out" is categorized as a preposition. CGEL, on pages 616-7:

Notice that their examples are similar to your two examples.

Also, on page 616:

The traditional definition of preposition excludes the underlined words, precisely because they are not followed by NPs. For the most part, these and other words of the same kind are therefore analyzed as adverbs in traditional grammar.

In some cases, however, the similarity between the whole bracketed expression and a PP is recognized, and catered for by analysing the first two words as a single unit. This unit does have an NP as complement, and hence is traditionally analyzed as a preposition -- what is often called a 'complex preposition'.

This topic is also covered in the 2005 textbook by Huddleston and Pullum, A Student's Introduction To English Grammar, pages 127-33.