fdisk /dev/sdb
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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.