Statement-1: When the temperature of a black body is doubled from` t^(@)C` to `2t^(@)C`, the radiant power becomes 16 times.
Statement-2: The radiant power of a body is proportional to fourth power of absolute temperature.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Answer

To solve the question, we need to analyze both statements regarding the radiant power of a black body and the relationship between temperature and radiant power.

### Step-by-step Solution:

1. **Understanding Statement 2**:
- The radiant power \( P \) of a black body is given by the Stefan-Boltzmann Law, which states that \( P \propto T^4 \), where \( T \) is the absolute temperature in Kelvin.
- This means that if the temperature of a black body increases, the radiant power increases with the fourth power of the temperature.

**Hint**: Remember that the relationship between temperature and radiant power is exponential, specifically to the fourth power.

2. **Converting Celsius to Kelvin**:
- The temperature in Celsius must be converted to Kelvin for the calculations. The conversion formula is:
\[ T(K) = T(°C) + 273.15 \]
- If we denote the initial temperature as \( t \) degrees Celsius, the absolute temperature \( T_1 \) in Kelvin is:
\[ T_1 = t + 273.15 \]
- When the temperature is doubled, the new temperature \( T_2 \) in Celsius is \( 2t \) degrees Celsius, which converts to:
\[ T_2 = 2t + 273.15 \]

**Hint**: Always convert Celsius to Kelvin before using the temperature in any physical equations.

3. **Comparing the Temperatures**:
- To find out how the radiant power changes, we need to compare \( T_1 \) and \( T_2 \):
\[ T_2 = 2t + 273.15 \]
\[ T_1 = t + 273.15 \]
- The ratio of the temperatures is:
\[ \frac{T_2}{T_1} = \frac{2t + 273.15}{t + 273.15} \]
- This ratio is not equal to 2, hence \( T_2 \) is not simply double \( T_1 \).

**Hint**: Use the ratio of temperatures to understand how the power changes, rather than assuming a direct doubling.

4. **Calculating the Radiant Power**:
- Since the radiant power is proportional to the fourth power of the absolute temperature, we can express the change in power as:
\[ \frac{P_2}{P_1} = \left( \frac{T_2}{T_1} \right)^4 \]
- Since \( T_2 \) is not exactly double \( T_1 \), we cannot conclude that \( P_2 \) is 16 times \( P_1 \).

**Hint**: Remember that the relationship is based on the fourth power of the temperature ratio.

5. **Conclusion**:
- Statement 1 is false because the radiant power does not become 16 times when the temperature in Celsius is doubled.
- Statement 2 is true as it correctly states the relationship between radiant power and absolute temperature.

### Final Answer:
- **Statement 1**: False
- **Statement 2**: True