The figure shows a system of two concentric spheres of radii r_1 and r_2 and kept at temperatures T_1 and T_2 respectively. The radial rate of flow of - Physics MCQ AIEEE 2026 | ExamTest.live

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The figure shows a system of two concentric spheres of radii r_{1} and r_{2} and kept at temperatures T_{1} and T_{2} respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to:

Solution & Step-by-step Explanation

The rate of heat flow \frac{d Q}{d t} for a spherical shell is given by: \frac{d Q}{d t} = \frac{4 πk ( T _{1} - T _{2} )}{\frac{1}{r _{1}} - \frac{1}{r _{2}}} \frac{d Q}{d t} = \frac{4 πk ( T _{1} - T _{2} )}{\frac{r _{2} - r _{1}}{r _{1} r _{2}}} = \frac{4 πk r _{1} r _{2} ( T _{1} - T _{2} )}{r _{2} - r _{1}} Thus, \frac{d Q}{d t} \propto \frac{r _{1} r _{2}}{r _{2} - r _{1}} .

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The figure shows a system of two concentric spheres of radii r_{1} and r_{2} and kept at temperatures T_{1} and T_{2} respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to:

\frac{r _{2} - r _{1}}{r _{1} r _{2}}

ln \frac{r _{2}}{r _{1}}

\frac{r _{1} r _{2}}{r _{2} - r _{1}}

(r_{2} - r_{1})^{2}

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