exhaust vs eat up

exhaust is a noun but eat up is not a noun.

Word	Noun	Adjective	Verb	Adverb
exhaust	Yes	No	Yes	No
eat up	No	No	Yes	No

As verbs, exhaust and eat up are synonyms defined as:

Other synonyms of exhaust include consume, deplete, eat, expend, run through, use, use up, wipe out.

As verbs, eat up is a hypernym of exhaust; that is, eat up is a word with a broader meaning than exhaust:

Other hypernyms of exhaust include consume, deplete, eat, exhaust, expend, run through, use, use up, wipe out.

exhaust (noun)	eat up (noun)
system consisting of the parts of an engine through which burned gases or steam are discharged
gases ejected from an engine as waste products

exhaust (verb)	eat up (verb)
wear out completely	finish eating all the food on one's plate or on the table
eliminate (a substance)	use up (resources or materials)
use up the whole supply of	enclose or envelop completely, as if by swallowing
use up (resources or materials)
deplete