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The Food Lab: Perfect Boiled Eggs
Kenji,
The contradition I pointed out still stands no matter what constants are involved since any constant divided by zero is still infinity.
The rate of heating per area is proportional to the temperature difference and inversely proportional to the distance (this actually means that in the instant right after the cool egg is put in the boiling water, the rate of heat transfer to the outer surface of the egg is infinite; note that this is not a paradox since an infinite rate times an infinitely small time interval is still a finite amount of heat). The temperature itself is not inversely proportional to the distance (or the square of the distance); solving the rate equation, the temperature approaches that of the boiling water exponentially fast with time so that if you wait long enough the whole egg will be the same temperature as the bath. The distance to the heat bath appears only in the exponent, so that the closer to the bath, the faster the temperature changes.
The Food Lab: Perfect Boiled Eggs
As a scientist, I'm glad that someone is starting a series focusing on this aspect of cooking. However, I would like to point out an inconsistency:
"when a mass is exposed to heat for a given period of time, a temperature gradient will form within that mass, with the area closest to the heat source being hottest, and the area furthest from the heat source being coolest. With very few exceptions, the temperature of a given spot in the food is proportional to the inverse square of its distance from the surface exposed to the heat source."
If this were true, since the distance from the heat source at the surface of the egg is zero, this would imply that the surface of the egg has infinite temperature. I think you mean to say that the RATE of heat conduction depends on the distance from the heat source (as well as the temperature difference). Also, the rate of heat conduction is proportional to the inverse of the distance from the source, NOT the inverse squared (Newton's law of cooling).
The Nasty Bits: Crisp Fried Pig's Ears
I, for one, hope that offal is indeed becoming a trend. Apparently, identifying and condemning any new trend is also becoming a trend; it used to be that such positive trends were called "progress."
Having tasted offal prepared the right way according to recipes from many cultures, I must say that the textures and concentrated flavor of the nasty bits adds a whole new dimension to the enjoyment of meat.
In this land of gastronomic plenty, limiting oneself to a few muscle groups is just plain shortsighted (and, as noted above, wasteful). I'm not saying chicken breasts and pork chops are bad, but they're not offal either.
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Kenji,
The heat transfer rate/area = (coefficient of thermal conductivity)*(T_bath-T_egg)/distance
The equation is the same regardless of the medium. The dependence on the medium comes from the thermal conductivity coefficient.
Also, I agree with you that we are the only two involved in this conversation right now :)