Heat flows radially outward through a spherical shell of outside radius R₁ and inner radius R₂.The temperature of inner surface of shell is q₁ and that of outer is q₂.The radial distance from center of shell where the temperature is just half way between q₁ and q₂ is:

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$\frac{2 R_{1} R_{2}}{R_{1} + R_{2}}$

$\frac{R_{1} R_{2}}{R_{1} + R_{2}}$

$R_{1} + \frac{R_{2}}{2}$

$\frac{R_{1} + R_{2}}{2}$

answer is C.

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Detailed Solution

$\frac{Q}{t} = K 4 π \frac{R_{1} R_{2}}{R_{2} - R_{1}} (T_{1} - T_{2}) \to (1) \frac{Q}{t} = K . 4 π \frac{R_{1} . R}{R - R_{1}} (T_{1} - \frac{T_{1} + T_{2}}{2}) \to (2) (1) = (2) \frac{R_{1} R_{2}}{R_{2} - R_{1}} (T_{1} - T_{2}) = \frac{R_{1} . R}{R - R_{1}} (T_{1} - \frac{T_{1} + T_{2}}{2}) \frac{R_{2}}{R_{2} - R_{1}} (T_{1} - T_{2}) = \frac{R}{R - R_{1}} (\frac{T_{1} - T_{2}}{2}) 2 R_{2} (R - R_{1}) = R (R_{2} - R_{1}) R = \frac{2 R_{1} R_{2}}{R_{1} + R_{2}}$