Need advice on cooltube

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Hoi
Gona start a new grow in a week or so, its gona be in a homebox s and i think ill have to use a cooltube, question: do i have to get air outside the box to run through the tube or would it do any good if i hooked up my carbonfilter to it, carbonfilter -> cooltube -> fan -> out ?

 

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after googlin this for a while it seems it will be ok.
Some say filter go first and some say filter last to avoid gettin carbon in the tube, guess ill have to try it out myself.