If a black body at 400 K surrounded by atmos | vedclass

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Question

(C) According to Stefan-Boltzmann law,the rate of cooling $R$ of a body is given by $R \propto (T^4 - T_0^4)$,where $T$ is the temperature of the body

Vedclass · Accepted Answer

$36 R_0$

Vedclass · Answer

(C) According to Stefan-Boltzmann law,the rate of cooling $R$ of a body is given by $R \propto (T^4 - T_0^4)$,where $T$ is the temperature of the body and $T_0$ is the temperature of the surroundings.For the first case: $R_0 = k(400^4 - 300^4) = k(256 	imes 10^8 - 81 	imes 10^8) = k(175 	imes 10^8)$.For the second case: $R' = k(900^4 - 300^4) = k(6561 	imes 10^8 - 81 	imes 10^8) = k(6480 	imes 10^8)$.Taking the ratio: $\frac{R'}{R_0} = \frac{6480}{175} \approx 37.02$.Comparing this with the given options,the closest value is $36 R_0$.

If a black body at $400 \ K$ surrounded by atmosphere at $300 \ K$ has a rate of cooling '$R_0$',the same body at $900 \ K$,surrounded by the same atmosphere,will have a rate of cooling nearly:

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