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The rate of fall of temperature of two identical solid spheres of different materials are equal at a certain temperature.

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Their specific heat capacities are proportional to their densities

Their specific heat capacities are equal

Their heat capacities are equal

Their specific heat capacities are inversely proportional to their densities

answer is B, D.

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Detailed Solution

Rate of fall of temperature $\frac{d θ}{d t} = \frac{e A σ}{m s} (T^{4} - T_{5}^{4})$ $\frac{d θ}{d t} α \frac{1}{m s}$

$\frac{d θ}{d t} =$ constant ms = constant Heat capacities are equal $m_{1} s_{1} = m_{2} s_{2} \Rightarrow ρ_{1} V S_{1} = ρ_{2} V S_{2}$

$\Rightarrow ρ_{1} S_{1} = ρ_{2} S_{2}$ $ρ S$ = constant $S α \frac{1}{ρ}$

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