Seagate offers the "DriveDetect.exe" Windows program to check the exact model/rev/firmware of your drive. Under Linux, you can simply get all information with the "hdparm" utility (should come pre-installed on most Linux distros, if not, it's in your Distro's repositories).
Issue the following command as root:
(For example, "hdparm -I /dev/sda" if /dev/sda is your Seagate drive.)
hdparm -I /dev/your_hard_drive
You can do this while the drive is actually used. You don't need to unmount anything and it's perfectly safe. It's a read-only operation.