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Thermal properties of Matter

Thermal conductivity

Two thin metallic spherical shells of radii r_{1} and r_{2}(r_

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Two thin metallic spherical shells of radii $r_{1}$ and $r_{2} (r_{1} < r_{2})$ are placed 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 :

\frac{K ( θ _{2} - θ _{1} ) ( r _{2} - r _{1} )}{4 π r _{1} r _{2}}

\frac{π r _{1} r _{2} ( θ _{2} - θ _{1} )}{r _{2} - r _{1}}

\frac{K ( θ _{2} - θ _{1} )}{r _{2} - r _{1}}

\frac{4 π Kr _{1} r _{2} ( θ _{2} - θ _{1} )}{r _{2} - r _{1}}

Views: 6,134 students

Updated on: Feb 9, 2023

Exam:

JEE Mains 2021 Aug 31 Shift 2

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Benjamin Discussed

Two thin metallic spherical shells of radii

r_{1}

and

r_{2} (r_{1} < r_{2})

are placed 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 :

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

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} )}

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Question Text	Two thin metallic spherical shells of radii $r_{1}$ and $r_{2} (r_{1} < r_{2})$ are placed 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 :
Updated On	Feb 9, 2023
Topic	Thermal properties of Matter
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 5
Upvotes	618
Avg. Video Duration	7 min

Text solutionVerified

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