* **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 year
> 
> 一日中【いちにちじゅう】all day
> 
> 世界中【せかいじゅう】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 some point] during morning
>
> 会議中【かいぎちゅう】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 of next month
>
> 来月中【らいげつちゅう】[some time] next month