XPost: rec.audio.pro, comp.dsp   
   From: dpierce@cartchunk.org   
      
   Don Pearce wrote:   
   > On Sun, 21 Nov 2010 07:26:52 -0500, Mike Rivers    
   >>Consider the effective value of RMS. It's the amount of heat   
   >>can be produced by the electrical energy. If you have only   
   >>one sample, no matter how high it is, do you really think it   
   >>will warm up your coffee?   
   >   
   > It will if you have a similarly tiny sample of coffee. I think you are   
   > confusing power and energy here.   
      
   Since energy is power integrated over an interval of time,   
   we have all the information we need. The power is whatever   
   the scaled sample value is. The interval is 1 sample period.   
   Thus the energy is knowable.   
      
   Reducing this to its silly extreme, assume a 16 oz (475 g)   
   cup of black coffee, no sugar. Assume coffee's specific heat   
   is that of water, 1 cal/g C. And assume the coffee is at room   
   temperature (20C), and we want to make it drinkably hot   
   (50C). We need to add 475g * (50C-20C) * 1 cal/g C of energy   
   to it, or about 15000 calories or (at 4.18 calories/Joule),   
   bout 3600 Joules). And we have to do it in, say, one sample   
   period (44.1 kS/s, or 23 uS).   
      
   Since:   
      
       Energy = Power * Time   
      
   then   
      
       Power = Energy/Time   
      
   and since a joule = 1 Watt second   
      
       Power = 3600 Ws / 23uS   
      
   or one hundred and fifty eight million, give or take.   
      
   For anyone that gives a hoot, that is.   
      
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