Two identical objects A and B (emissivity `e_(A)` and `e_(B),e_(A)ne e_(B)`) are planced in an enclosure, Temperature of body A, B and enclosure are same and constant.

Options

A. A) Heat emitted by body A is not equal to heat emitted by body B
B. B) Heat absorbed by body A is not equal to heat absorbed by body B
C. C) If `e_(A)gte_(B)`, body A absorbs more heat than body B
D. D) If `e_(A)lte_(B)`, body A emits less heat than body B

Answer

To solve the problem regarding the two identical objects A and B with different emissivities placed in an enclosure at the same constant temperature, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding Emissivity**:
- Emissivity (e) is a measure of how effectively a surface emits thermal radiation. It ranges from 0 to 1, where 1 means the body is a perfect black body.

2. **Identical Objects in an Enclosure**:
- Since both objects A and B are identical and placed in the same enclosure, they will reach thermal equilibrium with the enclosure. This means they will have the same temperature as the enclosure.

3. **Heat Emission**:
- The heat emitted by an object is proportional to its emissivity and the fourth power of its absolute temperature (according to Stefan-Boltzmann law).
- Mathematically, the heat emitted (P) can be expressed as:
\[ P = e \sigma A T^4 \]
where \( \sigma \) is the Stefan-Boltzmann constant, \( A \) is the area, and \( T \) is the absolute temperature.

4. **Heat Emission Comparison**:
- Since the temperatures of A and B are the same, the heat emitted by A (P_A) and B (P_B) can be compared as:
\[ P_A = e_A \sigma A T^4 \]
\[ P_B = e_B \sigma A T^4 \]
- Since \( e_A \neq e_B \), it follows that \( P_A \neq P_B \). Therefore, the heat emitted by A is not equal to the heat emitted by B.

5. **Heat Absorption**:
- In thermal equilibrium, the heat absorbed by each body from the enclosure must equal the heat they emit.
- If \( e_A > e_B \), then body A absorbs more heat than body B, and vice versa.

6. **Conclusion**:
- Based on the above analysis, we can conclude the following:
- The heat emitted by body A is not equal to the heat emitted by body B.
- The heat absorbed by body A is not equal to the heat absorbed by body B.
- If \( e_A > e_B \), then body A absorbs more heat than body B.
- If \( e_A < e_B \), then body A absorbs less heat than body B.

### Final Answers:
- All options A, B, C, and D are correct based on the analysis.