Translation guide
The second book or part in a series, often used for multi-volume works like novels, manga, or textbooks.
Used for the second volume of a two-volume set, or the last volume in a set. Often paired with 上巻 (first volume).
The second volume of this novel will be released next month.
Literally 'volume 2'. A straightforward, neutral way to indicate the second volume in a series of any length.
In the second volume, the protagonist sets out on a journey.
Used for the second volume in a three-volume set (上中下). If the work has exactly three volumes, this is the middle one.
I finished reading the second volume of the trilogy.
Means 'continuation volume' or 'sequel volume'. Can be used for the second volume when emphasizing it as a follow-up.
The publication of the second volume is eagerly awaited.
Specifically the latter half of a work split into two physical books.
下巻 implies a two-volume set (上巻 and 下巻). 第2巻 is used when there are more than two volumes, or when numbering is explicit. If the series has three volumes, the second is 中巻, not 下巻.
Do not translate 'second volume' as 二番目の巻 or 第二巻物. These sound unnatural. Use the standard terms above.
This book is the second volume of a two-volume set.