fdisk /dev/sdb
...
...
Assuming target fs is ext4
and device is /dev/sdb1
mkfs.ext4 /dev/sdb1
mkdir /var2
mount /dev/sdb1 /var2
rsync -a /var/ /var2
Run blkid
and copy the UUID
of /dev/sdb1
UUID="<UUID from previous step>" /var ext4 defaults 0 2
You can cleanup the old /var
to free up space by mounting /
to another location using a LiveCD.