Two thin metallic spherical shells of radii r 1 and r 2 r 1

Question

Two thin metallic spherical shells of radii $r_{1}$ and $r_{2} (r_{1} < r_{2})$ are placed with their centres coinciding. A material of thermal conductivity $K$ is filled in the space between the shells. The inner shell is maintained at temperature $θ_{1}$ and the outer shell at temperature $θ_{2} (θ_{1} < θ_{2}) .$ The rate at which heat flows radially through the material is :

Question diagram: Two thin metallic spherical shells of radii r 1 and r 2 r 1

Options:

Answer:

D

Solution:

Equivalent resistance $(R) = \frac{r_{2} - r_{1}}{K 4 π r_{2} r_{1}}$
Thus, Heat flow $= \frac{4 π K (r_{1} r_{2}) (θ_{2} - θ_{1})}{(r_{2} - r_{1})}$

TestHub · Accepted Answer

Equivalent resistance ( R ) = r 2 - r 1 K 4 π r 2 r 1 Thus, Heat flow = 4 π K r 1 r 2 θ 2 - θ 1 r 2 - r 1

Physics - Heat & Thermo Question with Solution | TestHub

Options:

Doubts & Discussion