The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ and kept at temperatures $T_1$…

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
  1. $\frac{r_2-r_1}{r_1 r_2}$
  2. $\ln \left(\frac{r_2}{r_1}\right)$
  3. $\frac{r_1 r_2}{r_2-r_1}$
  4. $\ln \left(r_2-r_1\right)$

Solution

$\left(\frac{\mathrm{dQ}}{\mathrm{dt}}\right)=\left(\mathrm{T}_1-\mathrm{T}_2\right) \frac{4 \pi \mathrm{r}_1 \mathrm{r}_2 \mathrm{~K}}{\left(\mathrm{r}_2-\mathrm{r}_1\right)}$

Asked in: JEE Main 2005

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