Question

The radiation from the sun, incident normally at the surface of the earth is $20{\text{kcal/m}}^2\text{min}$. What would have the radiant energy, incident normally on the earth, if the sun had a temperature twice of the present one?

• A. $80{\text{kcal/m}}^2\text{min}$
• B. $320{\text{kcal/m}}^2\text{min}$
• C. $160{\text{kcal/m}}^2\text{min}$
• D. $40{\text{kcal/m}}^2\text{min}$

Answer 1

The correct option is B $320{\text{kcal/m}}^2\text{min}$

We know that, for a source, emitting power per area $E$ at temperature $T$
$E=\sigma T^4$
As temperature is doubled,
$\Rightarrow E_1=\sigma (2T{)}^4$
$\frac{E}{E_1}=\frac{\sigma T^4}{16\sigma T^4}=\frac{1}{16}$
Now radiation falling on the earth will be proportional to radiation being emitted so.
$\frac{E}{E_1}=\frac{20}{X}$
Here, $X$ is the radiation falling in the earth in the latter case.
$\frac{20}{X}=\frac{1}{16}$
$\Rightarrow X=20\times 16=320{\text{kcal/m}}^2\text{min}$