Question

What is the total energy radiated in Jmin-1, by the sun to the universe? Distance of the sun from the earth is 1.49$ \times $ 1011m.
A) 2.3444$ \times $ 1028 Jmin-1
B) 2.33$ \times $ 1024 Jmin-1
C) 2.34$ \times $ 1020 Jmin-1
D) None of these

Answer 1

Hint:
Energy radiated by the sun in the atmosphere is P =2cal cm-2min-1.
Total surface area of earth is $4\pi {r^2}$
Using the above relations we will solve the problem along with some unit conversion standards.

Complete step by step solution:
First discuss the sun’s source of light energy and then proceed to the calculation part.
Sun’s energy is created by nuclear fusion that takes place within the sun itself. The process of fusion occurs when protons of hydrogen atoms violently collide in the sun’s core and fuse to create a helium atom. The process is known as the proton proton chain reaction, which emits an enormous amount of energy.

Now comes the calculation part:
Energy which the sun shares with the atmosphere is - P =2cal cm-2min 1.
Or we can write as P = 8.4 J cm-2min (because 1 cal =4.2 Joules)
r is given as 1.49$ \times $ 1011m or 1.49$ \times $ 1013 cm ( 1m =100cm)
Therefore, Total energy of sun which is radiated to the universe is
E =P$ \times $ $4\pi {r^2}$.
$
   \Rightarrow E = 8.4 \times 4\pi {(1.49 \times {10^{13}})^2} \\
   \Rightarrow E = 105.356 \times {(1.49 \times {10^{13}})^2} \\
   \Rightarrow E = 234.34 \times {10^{26}} \\
   \Rightarrow E = 2.344 \times {10^{28}}J{\min ^{ - 1}} \\
 $

Thus option 1 is correct.

Note:
Solar energy is harvested by capturing light for direct photovoltaic conversion into electricity, or as thermal energy(heat) water heating, space heating and other uses. Solar energy is essential for all the plant life existing in the universe, because they synthesise their food using sunlight. . We human beings get vitamin D from sunlight by directly standing in the sun at morning time.