The radiant energy from the sun incident norm | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) According to the Stefan-Boltzmann law,the radiant energy emitted by a black body is proportional to the fourth power of its absolute temperature,i

Vedclass · Accepted Answer

$320$

Vedclass · Answer

(C) According to the Stefan-Boltzmann law,the radiant energy emitted by a black body is proportional to the fourth power of its absolute temperature,i.e.,$E \propto T^4$.Let $E_1$ be the initial radiant energy incident on the earth and $T_1$ be the initial temperature of the sun.Given $E_1 = 20 \, kcal/(m^2 \cdot min)$.Let $E_2$ be the new radiant energy when the temperature of the sun becomes $T_2 = 2T_1$.Using the ratio formula:$\frac{E_2}{E_1} = \left( \frac{T_2}{T_1} ight)^4$Substituting the values:$\frac{E_2}{20} = \left( \frac{2T_1}{T_1} ight)^4$$\frac{E_2}{20} = (2)^4 = 16$Therefore,$E_2 = 16 	imes 20 = 320 \, kcal/(m^2 \cdot min)$.

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

Similar Questions

Two spheres of radii $4 \, m$ and $1 \, m$ have temperatures $2000 \, K$ and $4000 \, K$ respectively. Find the ratio of their emitted energy.

$A$ black rectangular surface of area $A$ emits energy $E$ per unit time at $27^{\circ}C$. If length and breadth are reduced to $(1/4)^{th}$ of their initial values and the temperature is raised to $327^{\circ}C$, then the energy emitted per unit time becomes:

The total radiant energy per unit area,normal to the direction of incidence,received at a distance $R$ from the centre of a star of radius $r$,whose outer surface radiates as a black body at a temperature $T \ K$ is given by

The temperature of a perfect black body is $727^{\circ}C$ and its surface area is $0.1\, m^{2}$. If the Stefan-Boltzmann constant is $\sigma = 5.67 \times 10^{-8} \, W/m^{2} \cdot K^{4}$,then the heat radiated in $1\, min$ is ........ $cal$.

If the radiation emitted by a perfect radiator has maximum intensity at a wavelength of $2900 Å$, the intensity of radiation emitted by it is (Stefan-Boltzmann's constant $= 5.67 \times 10^{-8} W m^{-2} K^{-4}$ and Wien's constant $= 2.9 \times 10^{-3} m K$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module