There are two thin spheres A and B of the same material and same thickness. They emit like black bodies. Radius of A is double that of B. A and B have same temperature T. When A and B are kept in a ro

Question

There are two thin spheres A and B of the same material and same thickness. They emit like black bodies. Radius of A is double that of B. A and B have same temperature T. When A and B are kept in a room of temperature T 0 ​ ( < T ) , the ratio of their rates of cooling (rate of fall of temperature) is : [assume negligible heat exchange between A and B]

TestHub · Accepted Answer

Thin shells have the same thickness and material.
$m = ρ (4 π r^{2} Δ x)$
$m c \frac{d T}{d t} = - σ (4 π r^{2}) (T^{4} - T_{0}^{4})$
$\frac{d T}{d t} = - \frac{σ ( T ^{4} - T _{0}^{4} )}{ρ c Δ x}$
The radius cancels; the rates of cooling are equal. Answer B.

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