A black body is at `727^(@)C`. It emits energy at a rate which is proportional to

Options

A. `(727)^(2)`
B. `(1000)^(4)`
C. `(1000)^(2)`
D. `(727)^(4)`

Answer

To solve the problem, we need to determine how the energy emitted by a black body is related to its temperature. We will use Stefan-Boltzmann Law, which states that the energy emitted per unit area of a black body is proportional to the fourth power of its absolute temperature.

### Step-by-Step Solution:

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

2. **Convert the given temperature from Celsius to Kelvin**:
The temperature given is \( 727^\circ C \). To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
Therefore:
\[ T = 727 + 273 = 1000 \, K \]

3. **Apply the Stefan-Boltzmann Law**:
Now, we can substitute the temperature into the Stefan-Boltzmann Law:
\[ P \propto (1000)^4 \]

4. **Conclusion**:
Thus, the energy emitted by the black body is proportional to \( 1000^4 \).

### Final Answer:
The energy emitted by the black body at \( 727^\circ C \) is proportional to \( T^4 \) where \( T = 1000 \, K \).