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In order for a balloon to float in air, its weight must be the same as the weight of an amount of air having the same volume as the balloon.
Is 'same' here an pronoun or an adjective? And is the 'as' immediately after it a preposition, meaning 'like'?
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"the" is a clue. Only nouns take it.
In the context you provided, 'same' functions as a (pro)noun.
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