Some computers appear to have a shorter battery life when running on Linux than they do when running Windows or Mac OS. One reason for this is that computer vendors install special software for Windows/Mac OS that optimizes various hardware/software settings for a given model of computer. These tweaks are often highly specific, and may not be documented, so including them in Linux is difficult.
Unfortunately, there is not an easy way of applying these tweaks yourself without knowing exactly what they are. You may find that using some power-saving methods helps, though. If your computer has a variable-speed processor, you might find that changing its settings is also useful.
Another possible reason for the discrepancy is that the method of estimating battery life is different on Windows/Mac OS than on Linux. The actual battery life could be exactly the same, but the different methods give different estimates.
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