CPU socket for Mid 2007 MA878LL is Socket P or in Intel specs PPGA478, LF80537, xxxGHz; 4M; 800MHz; SLAF4 or SLAF6Z for the Intel Core 2 Duo Extreme X7800 2.66GHz. The question is whether the CPU is soldered to the logic board, which in this case it may be possible as the socket description indicates that it is a pin-out type of CPU that is held in place by locking levers. No information has been discovered for a 'guide' to change out this particular iMac 7,1 model CPU. Educated guess is that it is possible, again no info for doing so precisely. PassMark web site lists CPUs and their ratings. Upgrading from 2.4GHz to 2.60GHz is better by their data than going to the 2.8GHz CPU performance wise. Check it out here: http://www.cpubenchmark.net/cpu_list.php search all of their pages and click on your model for specs etc. Replacement CPUs on Ebay are expensive for this older performance technology, but this iMac is a very good model. The Mid 2007 accepts Mavericks OS, however the question is whether it can keep...
This guide is not exactly precise for the iMac 24" MA878LL 7,1. There are some differences on the connections of the thermal sensors to the Hard Drive. I find it is not necessary to also disconnect the Thermal sensor from the board location only on the drive so as to move it to the new drive. Reassembly did not go well as far as the microphone cable connection. Whatever did not re-connect as expected did NOT result in a functioning internal microphone. The external input functions with a separate microphone, but the internal is dead. It could be software/driver malfunction or the fact that the tiny miniscule connections at the bezel are so delicate that it will no longer function, even after taking the bezel off 2 more times to insure the connection is correct and using electrical tape to keep the delicate connectors together. Wishing you better 'luck' than I had with this process.