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I might be misunderstanding, but this question could be taken many ways.
First off, Twitter is an application, and so the Tweeter (or whatever you'd like to call it) controls the wattage he or she takes up, depending on the current emotional state he/she is in, as well as how often he/she "Tweets". For example, a man of 35 years old will burn about 122 calories/hour while typing on Twitter. Doing some quick calculations, we find that the average Tweeter will use about 0.128 watts.
Did I answer your question correctly, or were you looking for the wattage of a bird?
Some birds tweet louder than others..
You need a DB sound level meter in order to differentiate and calc the energy..
Uh... how about... voltage squared divided by impedance? Like, kind of the same thing as Ohm's law, (V=I*R, P=V*I=V^2/R=I^2*R ) but, like, with impedance instead of resistance.
Do you have estimates for those numbers? RMS voltage seen across the tweeter? Impedance of the tweeter, in ohms, at the frequency of the signal driving it?
ROFLHow desperate must one be to "ask" such a meaningless question? ;)