The surface area of a black body is `5xx10^(-4) m^(2)` and its temperature is `727^@C` . Energy radiated by it per minute is (Take `sigma =5.67xx10^(-8) "J m"^(-2) s^(-1) K^(-4)` )

Options

A. `1.7xx10^3J`
B. `2.5xx10^(2)J`
C. `3xx10^4 J`
D. `2.7xx10^(4)J`

Answer

To solve the problem of calculating the energy radiated by a black body per minute, we will use Stefan's Law, which states that the power radiated per unit area of a black body is proportional to the fourth power of its absolute temperature.

### Step-by-step Solution:

1. **Identify Given Values**:
- Surface area (A) = \(5 \times 10^{-4} \, m^2\)
- Temperature (T) = \(727^\circ C\)
- Stefan's constant (\(\sigma\)) = \(5.67 \times 10^{-8} \, J \, m^{-2} \, s^{-1} \, K^{-4}\)

2. **Convert Temperature to Kelvin**:
- To convert Celsius to Kelvin, use the formula:
\[ T(K) = T(°C) + 273 \]
- Thus,
\[ T = 727 + 273 = 1000 \, K \]

3. **Apply Stefan's Law**:
- The power (P) radiated by the black body can be calculated using the formula:
\[ P = A \sigma T^4 \]
- Substitute the known values:
\[ P = (5 \times 10^{-4}) \times (5.67 \times 10^{-8}) \times (1000)^4 \]

4. **Calculate \(T^4\)**:
- Calculate \(1000^4\):
\[ 1000^4 = 10^{12} \]

5. **Substitute and Calculate Power**:
- Now substitute \(T^4\) in the power equation:
\[ P = (5 \times 10^{-4}) \times (5.67 \times 10^{-8}) \times (10^{12}) \]
- Calculate:
\[ P = 5 \times 5.67 \times 10^{-4} \times 10^{-8} \times 10^{12} \]
\[ P = 5 \times 5.67 \times 10^{12 - 4 - 8} = 5 \times 5.67 \times 10^{0} = 5 \times 5.67 = 28.35 \, J/s \]

6. **Convert Power to Energy per Minute**:
- Since we need energy per minute, multiply the power by the number of seconds in a minute (60 seconds):
\[ E = P \times 60 = 28.35 \times 60 \]
- Calculate:
\[ E = 1701 \, J \approx 1.7 \times 10^{3} \, J \]

### Final Answer:
The energy radiated by the black body per minute is approximately \(1.7 \times 10^{3} \, J\).