I am wondering how to translate the construction"so + adj." to French. Take the following sentences for example.
He works so hard. We are so far apart. The water is so cold.
Also, what kind of word is "so" in this case? Is it an adverb?
The most neutral translation is tellement.
Il travaille tellement dur ! (He works so hard!)
Nous sommes tellement éloignés ! (We are so far apart!)
L'eau est tellement froide ! (The water is so cold!)
J'en ai vu tellement ! or J'en ai vu tant ! (I've seen so many!)
J'en ai vu tellement peu ! (I've seen so few!)
When so qualifies an adjective (including peu), you can use si instead of tellement. Using si in this context is somewhat uncommon in spoken French these days, but still common in literary French. You can't use si without an adjective after it to express a large amount, but you can use tant. When it's followed by an adverb, si is more common than tellement except a few adverbs that don't end in -ment (bien, mal, but not vite which prefers si).
Il l'a accueillie si froidement ! (He greeted her so coldly!)
Un accident est si vite arrivé. (lit. “An accident can happen so quickly”; used to highlight the risk of an accident, i.e. the likelihood that an accident happens, not the speed at which an accident happens)
C'est tellement mal conçu ! (This is so badly designed!)
For “so … that …”, French uses a similar construction: “tellement … que …” or “si … que …”. Here si is common even in spoken French. Here too, you can't use si without an adjective; tant que is possible.
Il travaille tellement/si dur qu'on fait tout pour le garder. (He works so hard that we do everything we can to keep him.)
C'est tellement mal conçu que la plupart des gens renoncent. (This is so badly designed that most people give up.)
J'en ai vu tellement/tant que je suis blasé. (I've seen so many that I'm jaded.)
J'en ai vu tellement peu que je ne me souviens plus à quoi ils ressemblent. (I've seen so few that I don't remember what they look like.)
It can be translated with "si + adj." (or "tellement + adj." sometimes).
"Si" is a quantity / comparison / intensity adverb here.
In your examples: Il travaille si dur. Nous sommes si éloignés. L'eau est si froide
Alternatively vachement is a more slangy but popular term, as in c'est vachement chouette, it's so awesome. Or you might say super, as in c'est super cool.
Orally, we mostly use "très" ( very ) and "si" for exclamation ( but we really don't use a lot of exclamation unlike the english did with "so")
http://www.larousse.fr/dictionnaires/francais/tr%C3%A8s/79444
C'est très simple. Cela se produit très souvent. Il est très en colère. Il fait très froid. J'ai très faim.
Nous sommes très éloignés ( but here "si" is better for me according to how far you are, even orally )
And for "The water is so cold", we can say "L'eau est très froide" or "L'eau est gelé" ( gelé = frozen )