Confusion about usage of いっぱい

Question

The usage of いっぱい never ceases to confound me. I many cases it makes perfect sense but then I see a sentence like this:

お風呂のお湯がいっぱいです。
The bath is full of hot water

This seems to me to be saying that the water is full, rather than that the bath is full.

Is my literal meaning correct (the bath water is full)? I'm wondering if it's a colloquialism like saying 'the kettle has boiled' where we clearly mean that the water in the kettle has boiled rather than that the metal of the kettle has become molten.

If the above is not the case then I'm left wondering how to actually interpret いっぱい in this sentence.

I would have said

お風呂はお湯でいっぱいです。

Is there any difference between this and the original in nuance?

Answer 1

I'm wondering if it's a colloquialism like saying 'the kettle has boiled' where we clearly mean that the water in the kettle has boiled rather than that the metal of the kettle has become molten.

Exactly this. I've also heard of いっぱい used as (enough) the positive kind. You could also translate it as:

お風呂のお湯がいっぱいです。

There's enough/a lot (hot)water in the bath

If you scroll the いっぱい definitions a bit, you'll find things like, full, a lot, much, entire. Better to remember these kind of sentances as is.

お風呂はお湯でいっぱいです。

Is there any difference between this and the original in nuance?

I think your example is correct but, the original is more natural where as in the second example you are just pointing out that the bath is filled with hot water for some different reason, I guess?