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
- Install the most efficient OS available. In your case I'd vote for Linux x86_64, with tickless idle support ("y" to
cat /boot/config-$(uname -r) | grep CONFIG_NO_HZ
) and all other sorts of energy-saving goodies :-).
- Do not install any unnecessary system software (i.e., daemons/services). Start assuming that You Ain't Gonna Need It; you will always be able to install them later.
- Choose a sensible, high-contrast color scheme that will allow you to lower the level of display backlight (huge savings there, depending on display technology).
- Install PowerTop and check where the power actually goes (also check the "tunables" section).
- With lots of RAM, consider not having a swap file, and maybe a RAM disk for temporary data. This will ensure that hard disk activity is brought to a minimum, and with proper
hdparm
and BIOS settings, the hard disk will actually doze most of the time; there's 3-10 watt saved right there, depending on the hard disk (SSD and even Hybrid drives as the Seagate Momentus XT I have run quite cold and don't have a high power consumption, so cutting it even by 90% is still peanuts).
- Power off or set to power-idle mode all hardware supporting it: BlueTooth, WiFi, etc.
- Tune the CPU power management scheme and possibly, if the BIOS allows it, underclock the CPU. On some CPUs such as AMD, this is sometimes software controllable. Not only this saves power (which goes, if I remember it right, with the square of the clock - i.e., doubling the clock quadruples the power expenditure), but releases less heat, and therefore the fan will work less.
- Speaking of fans, there are fan control utilities too. Leaving the CPU working at 80 Celsius instead of 60 will lower its expected life, and the life of several other components such as the nearby capacitors - for the CPU, say from twenty years to ten - but that might be acceptable (your call!); meanwhile, telling the fans to not start until 80 Celsius will keep them off most of the time, saving further power.
- Unload any unused hardware modules (audio, etc.).
I'd advise reading this white paper, and check out the Green Linux Initiative.
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).