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212 The Extra Degree

  

If you have some water on the stove and you start adding heat, you take it from room cold water right out of the tap to 211 degrees and pretty much nothing happens. But if you go just a little farther, to 212 degrees, there is a state change, the water boils, real action takes place, nothing is the same. That little change makes all the difference. There is the minor problem that when you take water from 211 degrees to 212 degrees, in fact nothing changes under standard, idealized conditions (i.e. the thermodynamic equivalent of the frictionless surface used in mechanics). This then leads us into the major problem of taking water from 212 degrees in liquid form, to 212 degrees in vapor form. Since the latent heat of vaporization is roughly 540 calories per gram, depending on conditions, it turns out that the state change effect, which is "just a little farther", is in fact a lot of work. So to keep it all in metric, if the water out of your tap is 20 degrees, it takes 80 calories per gram to heat it to the boiling point. But, to actually get it to boil takes almost seven times the energy that it took to get it there. So you think you’re almost there but, you now have to be prepared to plow 6.75 times as much energy into it to achieve the state change.

Put another way, excellence is asymptotic . An asymptote is a curve that approaches a line, but will never touch it. In other words, the trip from beginner to not bad goes pretty fast, the trip from not bad to very good takes quite a while and the trip from very good to perfect can’t be attained. The difference is that it only took  80 calories to be good. But the investment of another 540 calories made him great. From incompetence to competence takes 80 calories. From competence to excellence takes 540 calories.

Maybe it’s not that the amount of effort required for the state change is massively different, but that more of the same will typically not get you there at all. It may take different skills to make a huge leap like the one from liquid to gas than the skills it took to get you from cold to hot.

If that is right, more won’t help. What is required is different.

 

 

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