A body of area `1cm^2` is heated to a temperature 1000K. The amount of energy radiated by the body in 1 s is (Stefan’s constant `sigma = 5.67 xx 10^(-8)Wm^(-2)K^(-4)`)

Options

A. 5.67 joule
B. 0.567 joule
C. 56.7 joule
D. 567 joule

Explanation

To solve the problem, we will use the Stefan-Boltzmann law, which states that the power radiated by a black body per unit area is proportional to the fourth power of its absolute temperature. The formula for power (P) is given by:

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

Where:
- \( P \) is the power in watts (W),
- \( \sigma \) is the Stefan-Boltzmann constant (\( 5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4 \)),
- \( A \) is the area in square meters (m²),
- \( T \) is the absolute temperature in kelvins (K).

### Step 1: Convert the area from cm² to m²
The area given is \( 1 \, \text{cm}^2 \). We need to convert this to square meters:

\[ 1 \, \text{cm}^2 = 1 \times 10^{-4} \, \text{m}^2 \]

### Step 2: Use the Stefan-Boltzmann law to calculate the power
Now we can substitute the values into the formula:

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

Substituting the values:

\[ P = (5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4) \cdot (1 \times 10^{-4} \, \text{m}^2) \cdot (1000 \, \text{K})^4 \]

### Step 3: Calculate \( (1000 \, \text{K})^4 \)
Calculating \( (1000)^4 \):

\[ (1000)^4 = 10^{12} \]

### Step 4: Substitute back into the power equation
Now substituting \( (1000)^4 \) back into the power equation:

\[ P = (5.67 \times 10^{-8}) \cdot (1 \times 10^{-4}) \cdot (10^{12}) \]

### Step 5: Simplify the expression
Now we simplify the expression:

\[ P = 5.67 \times 10^{-8} \times 10^{-4} \times 10^{12} \]
\[ P = 5.67 \times 10^{0} \, \text{W} = 5.67 \, \text{W} \]

### Step 6: Calculate the energy radiated in 1 second
Since power is the rate of energy transfer, the energy radiated in 1 second (E) is equal to the power:

\[ E = P \cdot t = 5.67 \, \text{W} \cdot 1 \, \text{s} = 5.67 \, \text{J} \]

### Final Answer
The amount of energy radiated by the body in 1 second is:

\[ \boxed{5.67 \, \text{J}} \]