Emissive power of any surface (e), Absorptive power (a), Reflecting power (r) and transmission power (t) are related as –

Options

A. `a+e+t=1`
B. `a+r+t=1`
C. `r+e+t=1`
D. `r+e+a=1`

Answer

To solve the problem regarding the relationship between emissive power (e), absorptive power (a), reflecting power (r), and transmission power (t) of any surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- **Emissive Power (e)**: The ability of a surface to emit thermal radiation.
- **Absorptive Power (a)**: The fraction of incident radiation that is absorbed by the surface.
- **Reflecting Power (r)**: The fraction of incident radiation that is reflected by the surface.
- **Transmission Power (t)**: The fraction of incident radiation that passes through the surface.

2. **Establishing the Relationship**:
- For any surface, the total incident radiation must either be absorbed, reflected, or transmitted. Therefore, we can express this relationship mathematically:
\[ r + t + a = 1 \]
- This equation states that the sum of the reflecting power, transmission power, and absorptive power must equal 1, as they account for all the incident radiation.

3. **Special Case for Black Bodies**:
- For an ideal black body, which is a perfect absorber and does not reflect or transmit any radiation, we have:
\[ r = 0, \quad t = 0, \quad a = 1 \]
- In this case, the emissive power (e) is equal to the absorptive power (a), leading to:
\[ e = a = 1 \]

4. **Generalizing to Any Surface**:
- For any surface, we can still use the relationship established earlier:
\[ r + t + a = 1 \]
- If we replace absorptive power (a) with emissive power (e) for a black body, we can also express:
\[ r + t + e = 1 \]
- However, this is specifically true for black bodies, where \(e = a\).

5. **Conclusion**:
- The general relationship that holds for any surface is:
\[ r + t + a = 1 \]
- Therefore, the correct answer to the question is that the emissive power, absorptive power, reflecting power, and transmission power are related by:
\[ r + t + a = 1 \]