The surface temperature of the sun is `6000K`. If we consider it as a perfect black body, calculate the energy radiated away by the sun per second. Take radius of the sun `=6.92xx10^(5)km` and `sigma=5.67xx10^(-8)Jm^(-2)s^(-1)K^(-4)`

Answer

To calculate the energy radiated away by the sun per second, we can use the Stefan-Boltzmann law, which states that the power radiated by a black body is proportional to the fourth power of its temperature. The formula is given by:

\[ P = \sigma A T^4 \]

where:
- \( P \) is the power (energy per second) radiated,
- \( \sigma \) is the Stefan-Boltzmann constant (\( 5.67 \times 10^{-8} \, \text{J m}^{-2} \text{s}^{-1} \text{K}^{-4} \)),
- \( A \) is the surface area of the black body,
- \( T \) is the absolute temperature in Kelvin.

### Step 1: Calculate the surface area of the sun
The surface area \( A \) of a sphere is given by the formula:

\[ A = 4 \pi r^2 \]

Given:
- Radius of the sun \( r = 6.92 \times 10^5 \, \text{km} = 6.92 \times 10^5 \times 10^3 \, \text{m} = 6.92 \times 10^8 \, \text{m} \)

Now, substituting the value of \( r \):

\[ A = 4 \pi (6.92 \times 10^8)^2 \]

### Step 2: Calculate \( A \)
Calculating \( A \):

\[ A = 4 \times 3.14 \times (6.92 \times 10^8)^2 \]
\[ A = 4 \times 3.14 \times (4.796736 \times 10^{16}) \]
\[ A \approx 4 \times 3.14 \times 4.796736 \times 10^{16} \]
\[ A \approx 60.079 \times 10^{16} \]
\[ A \approx 6.0079 \times 10^{17} \, \text{m}^2 \]

### Step 3: Calculate \( T^4 \)
Now, we need to calculate \( T^4 \):

Given:
- \( T = 6000 \, \text{K} \)

Calculating \( T^4 \):

\[ T^4 = (6000)^4 = 1.296 \times 10^{15} \, \text{K}^4 \]

### Step 4: Calculate the power \( P \)
Now, substituting \( A \) and \( T^4 \) into the Stefan-Boltzmann law:

\[ P = \sigma A T^4 \]
\[ P = (5.67 \times 10^{-8}) \times (6.0079 \times 10^{17}) \times (1.296 \times 10^{15}) \]

### Step 5: Perform the multiplication
Calculating \( P \):

\[ P = 5.67 \times 10^{-8} \times 6.0079 \times 10^{17} \times 1.296 \times 10^{15} \]
\[ P \approx 5.67 \times 6.0079 \times 1.296 \times 10^{24} \]
\[ P \approx 44.2 \times 10^{24} \]
\[ P \approx 4.42 \times 10^{23} \, \text{J/s} \]

### Final Answer
The energy radiated away by the sun per second is approximately:

\[ P \approx 4.42 \times 10^{23} \, \text{J/s} \]