"A sweat" is idiomatic and describes the physical condition of being sweaty.
Example: I worked up a sweat in my morning exercise class.
The use of an article before non-count nouns is idiomatic - sometimes we use it, and sometimes not. He wiped the sweat from his brow. (specific reference to the perspiration on his forehead)

can you give two more examples of " a sweat " as I don't really know how to use it.
are there any words have the case like a sweat.

the "idiomatic " in the first sentence mean (a) or(b)

(a)in accordance with the particular nature or structure of a language, dialect, etc
(b)containing an idiom or idioms
He broke into a sweat. (from fear, from hard exercise, from nervousness)
She woke up in a sweat. (she had a very bad dream, and it caused her to sweat)


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You can search on "a sweat" and get good examples of usage.
The countable sweat is an idiom, using the indefinite article. Perhaps someday it will become a word.

Regarding the adjective "idiomatic," any usage which correctly contains an idiom (definition (b)) would also fall under definition (a). That is, any correct usage is called "idiomatic."

"She stood up to the interrogation for two hours straight and never broke a sweat." (idiom)

"There was no air conditioning in the exam room, and [the] sweat kept dripping onto his test paper, making the ink run." (not an idiom)

"You'd better pump faster! I wanna see a real sweat!" (idiom)