I recently purchased a new laptop with an Intel i5 and 6 Gigs memory for general usage. I'll have the time to install it this weekend and I'm wondering whether installing an x86 instead of an x86_64 Linux distro will improve my battery performance and make it last longer ?
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Not directly. I.e., the same algorithm, running in 32bit or 64bit mode, should not, per se, require appreciably different amounts of power from the CPU. Yes, the number of commuting logic gates will be different, but I think not by very much, and is actually equally likely that the processor is optimized for 64bit operation.
But a x86 Linux and a x86_64 Linux are not "the same algorithm". Memory addressing is different, and several operations are simpler using 64bit than they are with 32bit.
So a x86_64 process will probably be slightly (or not so slightly) more efficient, will require less time, and the CPU will stay idle longer; with variable-speed CPUs this will translate into less power drawn, and longer battery endurance, even if the CPU were to actually draw more power per unit of time.
Better memory management will also translate into less disk usage, and this (be it through less read/write load, or even better, longer periods in disk idle mode) will give even better savings.
All that said, I think you should examine your goal: a longer battery life. Choosing between 32 or 64 bit is one way of pursuing that goal, but not the only one, nor the most important.
How to increase battery life
Finally, there are "emergency power packs" that are essentially DC batteries with ~20V output and a set of connector jacks. They usually store from 5Ah to 10Ah, which means more than twice the bang of a notebook battery. With one of these and your battery, you can have a 24h autonomy, easy.
And for the really eco-minded, I remember seeing a regulated solar panel power supply that can be tacked to the laptop's cover. I think it was around 5W, which means that it can supply 250 mA of current. Say you have a 4000 mAh battery and get four hours out of it; in those same four hours, if fully exposed to the Sun, the panel yields 4*250 = 1000 mAh, or one quarter charge, extending total time from four to five hours (to get more juice, you'd need a bigger panel).