A black body is at temperature of `500 K`. It emits energy at rate which is proportional to

Options

A. `(500)^(4)`
B. `(500)^(3)`
C. `(500)^(2)`
D. `500`

Answer

To solve the problem, we need to understand how a black body emits energy according to Stefan-Boltzmann law.

### Step-by-Step Solution:

1. **Understanding the Stefan-Boltzmann Law**:
The Stefan-Boltzmann law states that the power (energy emitted per unit time) emitted by a black body is proportional to the fourth power of its absolute temperature (T). Mathematically, this can be expressed as:
\[ E \propto T^4 \]
where \(E\) is the energy emitted per unit time and \(T\) is the absolute temperature in Kelvin.

2. **Given Temperature**:
We are given that the temperature \(T = 500 \, K\).

3. **Applying the Stefan-Boltzmann Law**:
According to the law, we can express the energy emitted as:
\[ E \propto (500)^4 \]

4. **Calculating \(500^4\)**:
To find the proportionality, we calculate \(500^4\):
\[ 500^4 = 500 \times 500 \times 500 \times 500 \]
This can be simplified step by step:
- First, calculate \(500^2 = 250000\).
- Then, \(500^4 = 250000 \times 250000 = 62500000000\).

5. **Conclusion**:
Therefore, the energy emitted by the black body at a temperature of \(500 K\) is proportional to \(500^4\), which is \(62500000000\).

### Final Answer:
The energy emitted by the black body at \(500 K\) is proportional to \(500^4\).

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