- じゅう (or, rarely: ぢゅう) is used for expressions covering a length of time (resp. area) from start to finish, in its entirety. I.e. "through", "all of":
一年中【いちねんじゅう】all】 all year
一日中【いちにちじゅう】all】 all day
世界中【せかいじゅう】all】 all over the world
- ちゅう is for pointing a particular time (resp. specific location) out of an interval (resp. general area). I.e. "out of", "during":
午前中【ごぜんちゅう】[at】 [at some point] during morning
会議中【かいぎちゅう】in】 in a meeting [e.g. "he is in a meeting at the moment"]
Note that in some cases, both can be used and the only way to tell would be from context (e.g. an expression followed by に is more likely to be ちゅう) or in speech:
来月中【らいげつじゅう】all】 all of next month
来月中【らいげつちゅう】[some】 [some time] next month