Here is the fourth-power RADIATION constant that relates WARMTH to GLOW. the warmer things are the more brightly they shine with thermal radiation.
In talent mile you take the temperature---eg 3 grade, which is baking oven temp---square twice and divide by six (in this case 81 x 1/6 = 13.5) and that is the power radiated per sq. pace. The TM power unit is about 360 watts or half a horsepower and called 'pony'
for short. It is the delivery of unit energy per unit time---ocmile per minute (ocmile being about 5 food Calories.)
Outside now the temp is 283 kelvin (10 celsius) and even though they are cold the flagstones of the garden terrace are glowing with invisible heat radiance. How brightly? Their temp is 2 grade. Square twice to get 16, and divide by 6 to get 2.7 power units per square pace. It may surprise you, if you convert that to watts, how many watts of infrared even cold things radiate.
*****footnotes on the algebra*****
The exact constant is (pi^2/60)k^4/hbar^3 c^2. In talent-mile the constants k,hbar,c have exact poweroften values so that the radiation law constant is exactly (pi^2/60) power units per sq.pace per quartic grade. The (pi^2/60) is approx 1/6 so we can square temp twice and divide by six and get the answer in (halfhorsepower, 360 watt) power units per sq. pace.
CORRESPONDING ALGEBRA IN METRIC IS MESSIER
To find the metric value of the radiation constant from the (pi^2/60)k^4/hbar^3 c^2 formula
is a bit messy. One must square c, that is square 299792458 meter/second. And one must cube hbar, that is cube 1.05457...x10^-34 joule second. And one must raise k, that is 1.38065...x10^-23 joule/kelvin, to the fourth power, and after a lot of calculation one gets 5.6704...x10^-8 watts per sq.meter per quartic kelvin. The system makes something inherently beautiful rather off-putting. But for us at this moment it is the square of pi divided by 60---pi^2/60.
This message has been edited by poundinchrules on Feb 7, 2003 8:12 PM
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