I assume you are dropping it in a notebook of some sort?
Is there a reason you want to do this? Did your CPU die out and you can't find an exact replacement of the T8300?
The socket is compatible but the P8400 runs at a higher bus speed and a lower multiplier. You probably can't change the bus speed on your laptop in the BIOS and even if you could it may not run at the higher speed. You can't increase the multiplier so this means the P8400 would run at only 1.7GHz in your machine which is much slower than it's default speed of 2.26GHz and slower than the T8300 default speed of 2.4GHz.
Depending on the BIOS of your machine and how it handles the change it may not run at all. Notebooks are notorious for limiting end user control over the BIOS.
Maybe if you post the make and model of your notebook someone may know a way to workaround this issue but if possible, try to replace your chip with the exact type. The T8300 is faster and the only advantage the P8400 could offer you is a lower power requirement.