USB backups under linux, changing dev names

When dealing with USB backups, I would traditionally just mount and rsync to the device, with a simple script like this :

mount /dev/sdc1 /mnt

rsync /home /mnt

umount /dev

This approach fails though when the device is unplugged while backups are working (the device name will change from /dev/sdc1 to /dev/sdd1), or if a new usb drive is plugged in instead.

A more reliable way to back up is to find the first usb drive plugged in and back up to that.