You can read my post above... T7800 is a 2.6Ghz chip.
T8300 is indeed a 2.4Ghz chip.
You did not specify what CPU you currently have, so I went with data from contemporary advertisements and reviews and basic google searches. Just going off the model isn't really enough, but if you have an 8000 series processor now, then you can consider the fastest from the line up.
If we look at the Penryn line of CPUs, that actually takes you all they way to the Core 2 Duo 9000 series. So potentially a 3.06Ghz T9900 at still 35W. Just no guarantee that it will work with the board revision, bios revision, etc that is inside that chassis.
Broken record rant:
T9900 look like they go for abut $50. As a comparision you can get an entire second gen i5 laptop with a Radeon GPU for $120, with OS... Not a recommendation, just a thought:
https://www.newegg.com/Product/Product.aspx?Item=9SIAAJ277V5513
If you start looking at passmark scores on CPU performance, most 2nd gen i5 and 3rd gen i3 outperform the T9900. Looking at nearly 10 year old processors. If I had a little cash to spend, I would not spend it on such an old platform.