(10)In the conduction equation Q = ( kA ? T ) t/L , the combination of factors k
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Question
(10)In the conduction equation Q = (kA?T)t/L, the combination of factors kA/L is called the conductance. The human body has the ability to vary the conductance of the tissue beneath the skin by means of vasoconstriction and vasodilation, in which the flow of blood to the veins and capillaries underlying the skin is decreased and increased, respectively. The conductance can be adjusted over a range such that the tissue beneath the skin is equivalent to a thickness of 0.065mm of Styrofoam or 3.7 mm of air. By what factor can the body adjust the conductance?
(12)The amount of radiant power produced by the sun is approximately 3.9 ? 1026 W. Assuming the sun to be a perfect blackbody sphere with a radius of 6.96 ?108 m, find its surface temperature (in kelvins)
Explanation / Answer
12
You have total output in Watts (3.9 x 10^26 W)
You have enough information to find the surface area of the Sun
Area = 4*pi*R^2 (careful, you have to use metres, not kilometres) = 4*pi*(6.96 x 10^8 m)^2
Surface flux = Output / Surface area
the answer will be in Watts per square metre (W/m^2)
The temperature depends directly on the surface flux. The conversion factor is called the Stefan-Boltzmann constant:
5.6704 x 10^-8 W/(m^2 K^4)
the inverse is 1.7635 x 10^7 m^2 K^4 / W
Temperature = 4thRoot [ flux / constant ]
T = 4thRoot [ flux * inverse of constant ]
T = 4thRoot [flux in W/m^2 * 1.7635 x 10^7 m^2 K^4 / W ]
The m^2 and the W will cancel out, leaving you with K^4 as the only unit; after a 4th root (do the square root twice in a row), this will leave you with K as the unit (K = Kelvin, the units of absolute temperature)
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