Say I do the exact same amount of computations. Obviously the 2.9 GHz will get them done 7% or so faster but will it also use more battery in the process?
Same battery life 100%. The CPUs both run at extremely varying frequencies from 800mhz to 2.9ghz and up to their boost clock depending on the load. For battery-light tasks both CPUs are likely at very similar frequencies. Same applies for Pro 450/455/460. Identical battery life.