I was going to suggest, but I see everyone answered already. Backup in a partition won't offer you much advantage, unless you want to limit the size of the backup. Also, it will create a lot of disk work, since the disk you are reading to the one you are backing up to are the same. Thought you have 2 partitios, it is still one drive. With this task you will have a slow backup, and it will also considerably raise your temperature. Then you might kill your drive
I personally don't recomend partitioning since you actually split the HD, and in real life, if you partition 40 GB in half, it doesn't mean you still have 40 GB. Because you have to leave empty space for the computer to run smoothly, so before you know it you have 2 partitions that have less than 10% and you can defragment. I Strongly recomend another drive instead of partition the one you have. IF you are up to, buy a bigger, newer, faster drive, transfer all data (probably the drive includes the tool, if not you can download from the manufaturer's web site) and leave the 40GB for the backup
There is only one reason that I recomend partitioning. If you are going to have absolutely only one drive, like for example in bussiness. Why? C drive is usually the one that gets corrupted and you can't see thru Windows (because the beggining of the drive is more likely to go bad). This happened in my office at least 5 times (We have 100 PCs) So, it is easy enought for me to plug the HD in another computer, pull the files from the D drive (where all users save their files) and then with time I can run recovery software to pull other files from the C if needed, but in the mean time, the user got all important files related to work