In a dark room with ambient temperature `T_(0)`, a black body is kept at a temperature `T`. Keeping the temperature of the black body constant (at `T`), sunrays are allowed to fall on the black body through a hole in the roof of the dark room. Assuming that there is no change in the ambient temperature of the room, which of the following statements (s) is/are correct ?

Options

A. (a)The quantity of radiation absorbed by the black body in unit time will increase
B. (b)Since emissivity = absorptivity, hence the quantity of radiation emitted by black body in unittime will increase
C. (c)Black body radiates more energy in unit time in the visible spectrum
D. (d)The reflected energy in unit time by the black body remains same

Answer

To solve the problem, we need to analyze the situation of a black body in a dark room with ambient temperature \( T_0 \) and at a constant temperature \( T \) while sunrays are allowed to fall on it. We will evaluate each statement provided in the options to determine their correctness.

### Step-by-Step Solution:

1. **Understanding Black Body Radiation**:
A black body is an idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. It also emits radiation in a characteristic spectrum that depends solely on its temperature.

2. **Effect of Sunrays on the Black Body**:
When sunrays fall on the black body, the amount of radiation absorbed by the black body increases. Since the black body is in a dark room and is kept at a constant temperature \( T \), it will absorb more energy from the sun.

**Conclusion for Option A**:
The quantity of radiation absorbed by the black body in unit time will indeed increase. **(Correct)**

3. **Emissivity and Absorptivity**:
According to Kirchhoff's law of thermal radiation, for a body in thermal equilibrium, the emissivity (the ability to emit radiation) is equal to its absorptivity (the ability to absorb radiation). Since the black body is at a constant temperature \( T \), the increase in absorbed radiation will also lead to an increase in emitted radiation.

**Conclusion for Option B**:
The quantity of radiation emitted by the black body in unit time will also increase. **(Correct)**

4. **Energy Radiation in the Visible Spectrum**:
A black body radiates energy across all wavelengths, including the visible spectrum. As the temperature \( T \) remains constant, the energy radiated in the visible spectrum will also increase due to the increase in total emitted radiation.

**Conclusion for Option C**:
The black body radiates more energy in unit time in the visible spectrum. **(Correct)**

5. **Reflective Energy**:
A perfect black body has zero reflectivity, meaning it does not reflect any incident radiation. Therefore, the reflective energy per unit time remains zero and does not change regardless of the incident radiation.

**Conclusion for Option D**:
The reflective energy per unit time by the black body remains the same (zero). **(Correct)**

### Final Conclusion:
All statements (A, B, C, and D) are correct.