A body is kept inside a container the temperature of the body is `T_(1)` and the temperature of the container is `T_(2)` the rate at which body absorbs the energy is `alpha` The emissivity of the body is e The radiation striking the body is either absorbed or reflected
At what rate of body will absorb the radiant energy .

Options

A. `alpha," but " alpha!=e`
B. `(T_(1)-T_(2))//t`, where t is the time
C. e, but e = `alpha`
D. None of above

Answer

To solve the problem step by step, we need to analyze the situation involving the body and the container, and how energy is absorbed and emitted.

### Step 1: Understand the System
We have a body with temperature \( T_1 \) placed inside a container with temperature \( T_2 \). The body absorbs radiant energy from the surrounding environment (the container) and also emits energy due to its temperature.

**Hint:** Identify the temperatures involved and the relationship between them.

### Step 2: Define Emissivity
The emissivity \( e \) of the body is a measure of how effectively it emits energy compared to a perfect black body. A perfect black body has an emissivity of 1, while a body with lower emissivity emits less energy.

**Hint:** Recall that emissivity affects the rate of energy emission from the body.

### Step 3: Rate of Absorption and Emission
The rate at which the body absorbs energy from the container is denoted as \( \alpha \). According to the principles of thermal equilibrium, for the body to maintain a constant temperature, the rate at which it absorbs energy must equal the rate at which it emits energy.

**Hint:** Think about the condition for thermal equilibrium.

### Step 4: Set Up the Equation
Since the body is in thermal equilibrium, we can set the rate of absorption equal to the rate of emission:
\[ \alpha = e \cdot \sigma \cdot A \cdot (T_2^4 - T_1^4) \]
where:
- \( \sigma \) is the Stefan-Boltzmann constant,
- \( A \) is the surface area of the body,
- \( T_2 \) is the temperature of the container,
- \( T_1 \) is the temperature of the body.

However, for the sake of this problem, we can simplify our understanding by stating that the body absorbs energy at a rate \( \alpha \) and emits at a rate proportional to its emissivity.

**Hint:** Relate the absorption and emission rates using emissivity.

### Step 5: Conclusion
To maintain a constant temperature, the rate of absorption \( \alpha \) must equal the rate of emission, which is influenced by the emissivity \( e \). Therefore, we conclude:
\[ \alpha = e \]

Thus, the rate at which the body absorbs radiant energy is equal to its emissivity.

**Final Answer:** The rate at which the body will absorb radiant energy is \( \alpha = e \).