The Trouble With Watts

Some time ago I wrote a paper entitled “What is a Watt.”  Although this paper seems lost in history (I can not find a copy of it), I can remember the point that I was trying to make when I wrote it.  In essence, it made the case that a watt is only an instantaneous measure of the rate of energy development or consumption (power), not a measurement of overall energy.  Part of the problem is the fact that “Watt” is a somewhat unique unit of measure.  A watt equals a rate of energy consumption or generation of 1 joule of energy per second.  If you substitute joules per second for watts, it is easy to see that watts does not equal energy (joules) but, rather, a rate of generation or consumption of energy (joules).  You need to integrate the rate of energy consumption or generation over the amount of time the energy is applied to achieve a measure of accumulated energy.  I say that a watt is unique because in most cases the rate of achieving a total quantity is defined as the amount of that quantity per unit of time  eg. miles per hour.  An example? – There is no unit that I know of that is the equivalent of miles per hour.  The closest is the knot which is one nautical mile per hour.  Using a reverse analogy, it might be simpler if we adopted the term Andretti as the equivalent of one mile per hour. Our speedometers would be marked in Andrettis, not miles per hour. In simple terms, Andretti’s would be to miles as watts are to joules.

Watts can be related to miles per hour as the rate of travel but not the total distance covered.  Miles per hour, for example, is not an appropriate response to the question, “How far is it from Detroit to Cleveland.”  Similarly, watts, by itself, is not an appropriate answer to, “How much ultrasonic energy is there in this ultrasonic tank.”  The dimension of time is missing.  Think of it this way – – If you were on your way from Detroit to Cleveland you could drive at a constant speed of 65 miles per hour or, you could drive at a speed of 80 miles per hour from Detroit to Toledo (60 miles) and then at a speed of 45 miles per hour from Toledo to Cleveland (118 miles) on the snow-covered Ohio Turnpike.  You could boast that you had traveled at 80 miles per hour in the course of your trip but, in truth, you had really only travelled at a speed of 52.8 miles per hour overall for an accumulated distance of 178 miles in 3.37 hours.  If you had travelled at a continuous 80 miles per hour for the entire trip, you would have been at your destination in 2.23 hours.  In summary, miles per hour does not describe the distance travelled any more than watts describes the amount of energy in an ultrasonic cleaning tank.

Sometimes speed is important while at others, it is distance that counts.  Although both move by moving their legs, a sprinter wants speed while a hiker wants distance.  In the ultrasonic world, any power in a liquid above that required to produce cavitation at a given frequency will provide cleaning.  A higher rate of delivering power (watts) to the liquid will result in larger numbers of more energetic cavitation bubble collapses and could result in faster and, perhaps better, cleaning but not always as we will see in upcoming blogs. 

–  FJF  –