Two thin metallic spherical shells of radii r1 and r2 (r1 < r2) 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 q1 and the outer shell at temperature q2(q1

Option 1 -

$\frac{π r_{1} r_{2} (θ_{2} - θ_{1})}{r_{2} - r_{1}}$

Option 2 -

$\frac{K (θ_{2} - θ_{1}) (r_{2} - r_{1})}{4 π r_{1} r_{2}}$

Option 3 -

$\frac{K (θ_{2} - θ_{1})}{r_{2} - r_{1}}$

Option 4 -

$\frac{4 π K r_{1} r_{2} (θ_{2} - θ_{1})}{r_{2} - r_{1}}$

2 Views | Posted 2 months ago

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 4

Detailed Solution:

Thermal resistance of spherical shell = $\frac{r_{2} - r_{1}}{4 π K r_{1} r_{2}}$

Rate of heat flow = $\frac{Δ T}{R} = \frac{(θ_{2} - θ_{1})}{(\frac{r_{2} - r_{1}}{4 π K r_{1} r_{2}})} = \frac{4 π K r_{1} r_{2} (θ_{2} - θ_{1})}{(r_{2} - r_{1})}$

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Two thin metallic spherical shells of radii r1 and r2 (r1 < r2) 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 q1 and the outer shell at temperature q2(q1

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