2003 NISSAN MICRA III K12 - 2003 NISSAN MICRA III K12 Identifying rubber pipe - MrD2018

I recently removed the car battery and I noticed a rubber pipe behind it with one end not connected to anything. The following links show the end of the pipe in the engine compartment with a red arrow pointing to it -

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The other end of the pipe is connected to a lower part of the engine below the battery shown in the following link also with a red arrow -

photo3

I am unsure how long it has been like this as I have removed the battery before but maybe I just didn't notice it was disconnected. The warning light for the engine being too hot has been showing lately and I am unsure if this pipe is related to it or if I just need the coolant topped up.

I have checked all around the area of the pipe and can see nowhere that it should be connected to. Does anyone know what the purpose of the pipe would be and where the loose end should be connected? Sorry but my knowledge of car engines is limited.

2003 NISSAN MICRA III K12 - 2003 NISSAN MICRA III K12 Identifying rubber pipe - elekie&a/c doctor
Looks like the gearbox vent pipe. The top end is open and not connected to anything. May be an idea to secure it to something else to stop it falling down.
2003 NISSAN MICRA III K12 - 2003 NISSAN MICRA III K12 Identifying rubber pipe - MrD2018

Thanks for answering, I agree, this seems to be most likely what it is.