A classical mechanics problem by puneet mangla
A spherical source of surface temperature is emitting heat radiations at a constant rate of . The conductivity of air is 1/30. Find the minimum distance in meter from the center of sphere from which a person can feel comfortable. The radius of the sphere is 2 m.
Details and Assumptions :
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A person is comfortable only in surrounding temperature i.e .
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Assume steady state.
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Assuming the expansion of air to be negligible.
The answer is 6.
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1 solution
we consider this shell as made up of infinite hollow shells of radius x and width dx. so resistance of this shell is dR=dx/k(4pix^(2))
integ(dR)=1/4k{int(1/x^2)}
putting limits integrate and put values provided and get net R.
use V=iR
and get the unknown distance.