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(B) The solar constant $S$ is given by the relation $S = \left(\frac{R}{r}\right)^2 \sigma T^4$,where $R$ is the radius of the sun,$r$ is the distance

Vedclass · Accepted Answer

$-4$

Vedclass · Answer

(B) The solar constant $S$ is given by the relation $S = \left(\frac{R}{r}ight)^2 \sigma T^4$,where $R$ is the radius of the sun,$r$ is the distance from the sun to the earth,$\sigma$ is the Stefan-Boltzmann constant,and $T$ is the temperature of the sun.Since $R$,$r$,and $\sigma$ are constants,we have $S \propto T^4$.Taking the logarithmic derivative,we get $\frac{\Delta S}{S} = 4 \frac{\Delta T}{T}$.Given that the temperature decreases by $1 \%$,we have $\frac{\Delta T}{T} = -1 \%$.Substituting this value,we get $\frac{\Delta S}{S} = 4 	imes (-1 \%) = -4 \%$.Therefore,the solar constant will change by $-4 \%$.

If the temperature of the sun is decreased by $1 \%$,then the value of the solar constant will change by ........... $\%$

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