The amount of thermal radiations emitted from one square centimetre area of a black body in one second when at a temperature of 1000 K is:

Options

A. 5.67 J
B. 56.7 J
C. 567 J
D. 5670 J

Explanation

To solve the problem of finding the amount of thermal radiation emitted from a black body at a temperature of 1000 K, we will use the Stefan-Boltzmann law. Here’s a step-by-step solution:

### Step 1: Understand the Formula
The amount of thermal radiation emitted by a black body is given by the formula:
\[ P = E \cdot A \cdot \sigma \cdot T^4 \]
Where:
- \( P \) = Power (thermal radiation emitted in watts)
- \( E \) = Emissivity of the body (for a black body, \( E = 1 \))
- \( A \) = Area (in square meters)
- \( \sigma \) = Stefan-Boltzmann constant (\( 5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4 \))
- \( T \) = Temperature in Kelvin

### Step 2: Convert Area to Square Meters
The area given in the problem is 1 square centimeter. We need to convert this to square meters:
\[ 1 \, \text{cm}^2 = 1 \times 10^{-4} \, \text{m}^2 \]

### Step 3: Substitute Values into the Formula
Now, we can substitute the values into the formula:
- \( E = 1 \)
- \( A = 1 \times 10^{-4} \, \text{m}^2 \)
- \( \sigma = 5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4 \)
- \( T = 1000 \, \text{K} \)

Substituting these values into the formula:
\[ P = 1 \cdot (1 \times 10^{-4}) \cdot (5.67 \times 10^{-8}) \cdot (1000)^4 \]

### Step 4: Calculate \( T^4 \)
Calculate \( (1000)^4 \):
\[ (1000)^4 = 10^{12} \]

### Step 5: Substitute \( T^4 \) Back into the Equation
Now substitute \( T^4 \) back into the equation:
\[ P = 1 \cdot (1 \times 10^{-4}) \cdot (5.67 \times 10^{-8}) \cdot (10^{12}) \]

### Step 6: Simplify the Equation
Now simplify the equation:
\[ P = (1 \times 10^{-4}) \cdot (5.67 \times 10^{-8}) \cdot (10^{12}) \]
\[ P = 5.67 \times 10^{12 - 4 - 8} \]
\[ P = 5.67 \times 10^{0} \]
\[ P = 5.67 \, \text{W} \]

### Final Answer
The amount of thermal radiation emitted from one square centimeter area of a black body in one second at a temperature of 1000 K is:
\[ \boxed{5.67 \, \text{W}} \]