There are notebooks with regular Pentium 4 CPUs, with Pentium 4-mobile CPUs, and with Pentium-Mobile (P-M) CPUs. The P-Ms are usually bundled with a particular low voltage motherboard and wireless to give a "Centrino" system.
To determine your CPU in Windows XP, if you right click on My computer and go to properties then it'll show the type of CPU and amount of RAM. You might also have a sticker on the left part of notebook under your palm that tells what kind of CPU
They don't make a 2.8GHz P-M, and I don't recall them making a 2.8GHz P4-M either. So I'd guess it's a desktop chip. Can you underclock it? IBM has a power management setup that will let you adjust the speed of parts (CPU, hdd, GPU, cd-rom) when on battery vs. AC to extend battery life. If you can do that on your notebook then just throttle the CPU down and see if you even notice the difference. I never have on anything other than doing brief molecular simulations on planes. I'm not sure if notebooks with desktop CPUs can even do the speedstep or whatever it's called anyway...