Question

There are two concentric metallic shells of negligible thickness of radii 5 cm and 20 cm.The region between the two shells is filled with a medium of thermal conductivity k. The temperature of inner and outer sphere is maintained at 5C and 10C respectively. If the heat current flowing from inner to outer sphere is 100 W, find the value of k.

Answer 1

Two spheres A and B

Cut a sphere of radius r width dr

Heat will flow across width

$H=\frac{dQ}{dt}=\frac{KAd\theta }{dr}$

K= thermal conductivity

A = Area

$d\theta$= change in temperature

dr= distance

${\int }_K^{100}\frac{dr}{4\pi r^2}={\int }_5^{10}d\theta$

$\frac{100}{K4\pi }[\frac{100}{5}-\frac{100}{20}]=5$

$\frac{100\times 100}{K\times 4\pi }\left[\frac{3}{20}\right]=5$

$K=\frac{300}{4\pi }w/m-K$