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(B) According to Stefan-Boltzmann Law,the rate of heat loss is given by $dQ/dt = \sigma A (T^4 - T_0^4)$.For a small temperature difference,the rate o

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$1:1$

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(B) According to Stefan-Boltzmann Law,the rate of heat loss is given by $dQ/dt = \sigma A (T^4 - T_0^4)$.For a small temperature difference,the rate of cooling $d	heta/dt$ is proportional to the rate of heat loss divided by the heat capacity $(ms)$:$d	heta/dt = \frac{\sigma A (T^4 - T_0^4)}{ms}$.Since $m = ho V = ho (\frac{4}{3}\pi r^3)$ and $A = 4\pi r^2$,we have:$d	heta/dt \propto \frac{r^2}{ho r^3 s} \propto \frac{1}{ho r}$.Given the ratios $r_1:r_2 = 1:2$ and $ho_1:ho_2 = 2:1$,the ratio of the rate of cooling is:$\frac{(d	heta/dt)_1}{(d	heta/dt)_2} = \frac{ho_2 r_2}{ho_1 r_1} = \frac{1}{2} 	imes \frac{2}{1} = 1:1$.

Two spheres have a radius ratio of $1:2$ and a density ratio of $2:1$. They have the same specific heat. If they are heated to the same temperature and placed in the same environment,what is the ratio of their rate of cooling?

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