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Problem 42 Easy Difficulty

A sphere with radius 1 m has temperature $ 15^oC. $ It lies inside a concentric sphere with radius 2 m and temperature $ 25^oC. $ The temperature $ T(r) $ at a distance $ r $ from the common center of the spheres satisfies the differential equation
$ \frac {d^2T}{dr^2} + \frac {2}{r}\frac {dT}{dr} = 0 $
If we let $ S = dT/dr, $ then $ S $ satisfies a first-order differential equation. Solve it to find an expression for the temperature $ T(r) $ between the spheres.

Answer

$T(r)=\frac{-20}{r}+35$

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Video Transcript

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