Same CPU - redo OS?

Sorry for my noob question.

I think this should be possible with no issues, but I figured I'd ask just in case. I am replacing my CPU with another one that is the exact same model. Will there be any issues if I just toss it in and leave my OS the way it was with the old CPU?

Thanks.

should be no issue at all, the os will recognize the cores load accordingly. Most times it will require a reboot the first time you start the computer with the new processor

Just as long as the mainboard is the same. Doesn't matter if you upgrade your cpu for a faster one for instance.