The energy reveived from the sun by the earth and surrounding atmosphere is 2 cal`cm^(-2)` `min^(-1)` on a surface normal to the rays of sun.
Q. What is the total energy radiated, in J `min^(-1)`, by the sun to the universe? Distance of the sun from the earth is `1.49xx10^(11)`m.

Options

A. `2.3444xx10^(28)J"min"^(-1)`
B. `2.33xx10^(24)J"min"^(-1)`
C. `2.34xx10^(20)J"min"^(-1)`
D. none of these

Explanation

To solve the problem, we need to calculate the total energy radiated by the sun to the universe based on the energy received by the Earth and the distance from the sun to the Earth.

### Step-by-Step Solution:

1. **Identify the energy received by the Earth:**
The energy received from the sun by the Earth is given as \( E = 2 \, \text{cal} \, \text{cm}^{-2} \, \text{min}^{-1} \).

2. **Convert calories to joules:**
We know that \( 1 \, \text{cal} = 4.2 \, \text{J} \). Therefore,
\[ E = 2 \, \text{cal} \times 4.2 \, \text{J/cal} = 8.4 \, \text{J} \, \text{cm}^{-2} \, \text{min}^{-1} \]

3. **Calculate the surface area over which this energy is distributed:**
The total energy radiated by the sun can be calculated using the formula for the surface area of a sphere, which is \( A = 4\pi D^2 \), where \( D \) is the distance from the sun to the Earth. Given \( D = 1.49 \times 10^{11} \, \text{m} \), we first convert this distance to centimeters:
\[ D = 1.49 \times 10^{11} \, \text{m} \times 100 \, \text{cm/m} = 1.49 \times 10^{13} \, \text{cm} \]

4. **Calculate the surface area:**
Now, substituting \( D \) into the surface area formula:
\[ A = 4\pi (1.49 \times 10^{13} \, \text{cm})^2 \]
\[ A = 4\pi (2.2201 \times 10^{26} \, \text{cm}^2) \approx 2.785 \times 10^{27} \, \text{cm}^2 \]

5. **Calculate the total energy radiated by the sun:**
The total energy radiated by the sun to the universe can be calculated by multiplying the energy received per unit area by the total surface area:
\[ \text{Total Energy} = E \times A = 8.4 \, \text{J} \, \text{cm}^{-2} \, \text{min}^{-1} \times 2.785 \times 10^{27} \, \text{cm}^2 \]
\[ \text{Total Energy} \approx 2.34 \times 10^{28} \, \text{J/min} \]

### Final Answer:
The total energy radiated by the sun to the universe is approximately \( 2.34 \times 10^{28} \, \text{J/min} \).