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(A) According to Stefan-Boltzmann law,the rate of cooling $H$ is proportional to the difference of the fourth powers of the temperatures of the body a

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$(3/16)H$

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(A) According to Stefan-Boltzmann law,the rate of cooling $H$ is proportional to the difference of the fourth powers of the temperatures of the body and the surroundings: $H \propto (T^4 - T_0^4)$.Given $T_1 = 600\,K$,$T_0 = 200\,K$,and the initial cooling rate is $H$.So,$H = k(600^4 - 200^4)$.When the temperature reduces to $T_2 = 400\,K$,the new cooling rate $H'$ is $H' = k(400^4 - 200^4)$.Taking the ratio:$\frac{H'}{H} = \frac{400^4 - 200^4}{600^4 - 200^4} = \frac{(400^2 - 200^2)(400^2 + 200^2)}{(600^2 - 200^2)(600^2 + 200^2)}$$= \frac{(160000 - 40000)(160000 + 40000)}{(360000 - 40000)(360000 + 40000)} = \frac{120000 	imes 200000}{320000 	imes 400000} = \frac{12 	imes 20}{32 	imes 40} = \frac{240}{1280} = \frac{3}{16}$.Therefore,$H' = \frac{3}{16}H$.

$A$ sphere at temperature $600\,K$ is placed in an environment of temperature $200\,K$. Its cooling rate is $H$. If its temperature is reduced to $400\,K$,then the cooling rate in the same environment will become:

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