A small hole is made in a hollow enclosure whose walls are maintained at a temperature of 1000 K. The amount of energy being emitted per square metre per second is :

Options

A. 567 J
B. 5670 J
C. 56700 J
D. 567000 J

Explanation

To solve the problem of finding the amount of energy emitted per square meter per second from a small hole in a hollow enclosure at a temperature of 1000 K, we can use Stefan-Boltzmann Law. Here’s a step-by-step solution:

### Step 1: Understand the Concept
The energy emitted per unit area per second (intensity) from a black body is given by the Stefan-Boltzmann Law:
\[ I = \sigma T^4 \]
where:
- \( I \) is the intensity (energy emitted per square meter per second),
- \( \sigma \) is the Stefan-Boltzmann constant (\( 5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4 \)),
- \( T \) is the absolute temperature in Kelvin.

### Step 2: Identify Given Values
From the problem, we have:
- Temperature, \( T = 1000 \, \text{K} \).

### Step 3: Substitute the Values into the Formula
Now, we can substitute the values into the Stefan-Boltzmann Law:
\[ I = \sigma T^4 \]
\[ I = 5.67 \times 10^{-8} \times (1000)^4 \]

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

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

### Step 6: Perform the Multiplication
Now perform the multiplication:
\[ I = 5.67 \times 10^{4} \, \text{W/m}^2 \]

### Step 7: Convert to Joules
Since \( 1 \, \text{W} = 1 \, \text{J/s} \), we can express this as:
\[ I = 56700 \, \text{J/m}^2\text{s} \]

### Step 8: State the Final Answer
Thus, the amount of energy emitted per square meter per second is:
\[ \boxed{56700 \, \text{J/m}^2\text{s}} \]