JEE Main · 2005 · 08 May 2005 · Offline · Heat & Thermodynamics

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

(A) $\frac{r _{2} - r _{1}}{r _{1} r _{2}}$
(B) $ln (\frac{r _{2}}{r _{1}})$
(C) $\frac{r _{1} r _{2}}{r _{2} - r _{1}}$ ✓ Correct
(D) $ln (r_{2} - r_{1})$

Answer: (C)

Solution

In steady radial conduction the same heat current flows through every spherical shell between the surfaces. Applying Fourier's law across a shell of radius

r

and integrating from

r_{1}

r_{2}

gives

\frac{d Q}{d t} = \frac{4 π K r _{1} r _{2} ( T _{1} - T _{2} )}{r _{2} - r _{1}}

, so the rate of heat flow is proportional to

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

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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JEE Main · 2005 · 08 May 2005 · Offline · Heat & Thermodynamics

Solution

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