The power radiated by a perfect blackbody depends only on its

Options

A. material
B. nature of surface
C. colour
D. temperature

Answer

To solve the question regarding the power radiated by a perfect blackbody, we will analyze the relationship based on the Stefan-Boltzmann Law.

### Step-by-Step Solution:

1. **Understanding Blackbody Radiation**:
A perfect blackbody is an idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. It is also a perfect emitter of radiation.

2. **Stefan-Boltzmann Law**:
The power radiated by a blackbody is described by the Stefan-Boltzmann Law, which states that the power \( P \) radiated per unit area of a blackbody is directly proportional to the fourth power of its absolute temperature \( T \). The law is mathematically expressed as:
\[ P = \sigma A T^4 \]
where:
- \( P \) is the total power radiated,
- \( \sigma \) is the Stefan-Boltzmann constant,
- \( A \) is the surface area of the blackbody,
- \( T \) is the absolute temperature in Kelvin.

3. **Analyzing the Options**:
- **Option 1: Material** - The material does not affect the power radiated by a perfect blackbody since it is defined as a perfect emitter.
- **Option 2: Nature of Surface** - Similar to material, the nature of the surface does not play a role in the radiation of a perfect blackbody.
- **Option 3: Color** - Color is related to the wavelength of emitted radiation but does not determine the total power radiated.
- **Option 4: Temperature** - According to the Stefan-Boltzmann Law, the power radiated depends solely on the absolute temperature \( T \).

4. **Conclusion**:
Based on the analysis, the power radiated by a perfect blackbody depends only on its temperature. Therefore, the correct answer is:
\[ \text{Option 4: Temperature} \]