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(D) According to the Stefan-Boltzmann law,the total power radiated by a spherical body of radius $R$ and temperature $T$ is given by $P = \sigma (4\pi

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(D) According to the Stefan-Boltzmann law,the total power radiated by a spherical body of radius $R$ and temperature $T$ is given by $P = \sigma (4\pi R^2) T^4$.Since the radiant energy $Q$ received on Earth is proportional to the power radiated by the sun,we have $Q \propto R^2 T^4$.Let the initial energy be $Q_1 = k R^2 T^4$ and the final energy be $Q_2 = k (2R)^2 (2T)^4$.Taking the ratio,we get $\frac{Q_2}{Q_1} = \left( \frac{2R}{R} ight)^2 	imes \left( \frac{2T}{T} ight)^4$.$\frac{Q_2}{Q_1} = (2)^2 	imes (2)^4 = 4 	imes 16 = 64$.Therefore,the ratio of the radiant energy received on the earth is $64$.

If the temperature of the sun were to be increased from $T$ to $2T$ and its radius from $R$ to $2R$,then the ratio of the radiant energy received on the earth to what it was previously will be

Similar Questions

$A$ spherical black body of radius $r$ radiates power $P$ and its rate of cooling is $R$. Which of the following relations are correct?
$(i) \ P \propto r$
$(ii) \ P \propto r^2$
$(iii) \ R \propto r^2$
$(iv) \ R \propto \frac{1}{r}$

Two spherical black bodies have radii $r_1$ and $r_2$. Their surface temperatures are $T_1$ and $T_2$. If they radiate the same power,then $\frac{r_2}{r_1}$ is:

If the temperature of a black body increases from $7^{\circ}C$ to $287^{\circ}C$,then what is the ratio of the rate of energy emission?

Which of the following helps us in the determination of the temperature of the sun?

If the temperature of a black body increases from $7^oC$ to $287^oC$,then the rate of energy radiation increases by a factor of:

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