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A spherical shell of inner radius R₁ , temperature T₁ , outer radius R₂ and temperature T₂ conducts heat current radially. Let r be the distance of any point from the centre of the shell. For ${R_1} < r < {R_2}$ , temperature T in the shell as a function of r can be expressed as T =

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$frac{{left[ {{T_1}{R_2}left( {r - {R_1}} right) + {T_2}{R_1}({R_2} - r)} right]}}{{{R_2} - {R_1}}}$

$frac{{left[ {{T_2}{R_2}left( {r - {R_1}} right) + {T_1}{R_1}({R_2} - r)} right]}}{{rleft( {{R_2} - {R_1}} right)}}$

$frac{{left[ {{T_2}left( {r - {R_1}} right) + {T_1}({R_2} - r)} right]}}{{{R_2} - {R_1}}}$

$left( {frac{{{T_1} + {T_2}}}{2}} right)frac{{{R_1}{R_2}}}{{{r^2}}}$

answer is B.

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Detailed Solution

$H = \frac{(T_{1} - {T_{2}}_{}) 4 π K R_{1} R_{2}}{R_{2} - R_{1}} = \frac{(T_{1} - θ) (4 π K) R_{1} r}{r - R}$

Solving “ θ ” can be obtained.

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