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JEE Main 202131 AugustEvening Shift
Exam
JEE Main
Year
2021
Date
31 August
Shift
Evening Shift
Subject
Physics
Chapter
Thermal Properties of Matter

JEE Main 2021 · 31 August · Evening Shift · Physics · Thermal Properties of Matter

Two thin metallic spherical shells of radii r _ 1 and r _ 2 ( r _ 1...

Two thin metallic spherical shells of radii r1{r}_{1} and r2{r}_{2}\left({r}_{1} < {r}_{2}\right)areplacedwiththeircentrescoinciding.Amaterialofthermalconductivityare placed with their centres coinciding. A material of thermal conductivityKisfilledinthespacebetweentheshells.Theinnershellismaintainedattemperatureis filled in the space between the shells. The inner shell is maintained at temperature{\theta}_{1}andtheoutershellattemperatureand the outer shell at temperature{\theta}_{2}\left({\theta}_{1} < {\theta}_{2}\right) . The rate at which heat flows radially through the material is :Two thin metallic spherical shells of radii r _ 1 and r _ 2 ( r _ 1 < r _ 2 ) are placed with their centres coinciding.

Options

  1. AK(θ2−θ1)r2−r1\dfrac{K\left({\theta}_{2} - {\theta}_{1}\right)}{{r}_{2} - {r}_{1}}
  2. BK(θ2−θ1)(r2−r1)4πr1r2\dfrac{K\left({\theta}_{2} - {\theta}_{1}\right)\left({r}_{2} - {r}_{1}\right)}{4\pi{r}_{1}{r}_{2}}
  3. C\piKr1r2(θ2−θ1)r2−r1\dfrac{\piK{r}_{1}{r}_{2}\left({\theta}_{2} - {\theta}_{1}\right)}{{r}_{2} - {r}_{1}}
  4. D4\piKr1r2(θ2−θ1)r2−r1\dfrac{4\piK{r}_{1}{r}_{2}\left({\theta}_{2} - {\theta}_{1}\right)}{{r}_{2} - {r}_{1}}

Correct answer

D. 4\piKr1r2(θ2−θ1)r2−r1\dfrac{4\piK{r}_{1}{r}_{2}\left({\theta}_{2} - {\theta}_{1}\right)}{{r}_{2} - {r}_{1}}

Step-by-step solution

Two thin metallic spherical shells of radii r _ 1 and r _ 2 ( r _ 1 < r _ 2 ) are placed with their centres coinciding.
Equivalent resistance (R)=r2−r1K4πr2r1( R ) = \dfrac{{r}_{2} - {r}_{1}}{K4\pi{r}_{2}{r}_{1}}
Thus, Heat flow =4\piK(r1r2)(θ2−θ1)(r2−r1)= \dfrac{4\piK\left({r}_{1}{r}_{2}\right)\left({\theta}_{2} - {\theta}_{1}\right)}{\left({r}_{2} - {r}_{1}\right)}
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