If a body at `27^(@)C` emits `0.3` watt of heat then at `627^(@)C`, it will emit heat equal to -

Options

A. (a)24.3 W
B. (b)0.42 W
C. (c)2.42 W
D. (d)0.9 W

Answer

To solve the problem of determining the heat emitted by a body at `627°C`, given that it emits `0.3 watts` at `27°C`, we can use Stefan's Law of radiation. Here’s a step-by-step solution:

### Step 1: Convert Temperatures to Kelvin
First, we need to convert the given temperatures from Celsius to Kelvin.

- For `27°C`:
\[ T_1 = 27 + 273 = 300 \, K \]

- For `627°C`:
\[ T_2 = 627 + 273 = 900 \, K \]

### Step 2: Apply Stefan's Law
According to Stefan's Law, the power radiated by a body is directly proportional to the fourth power of its absolute temperature. This can be expressed as:
\[ \frac{P_1}{P_2} = \left(\frac{T_1}{T_2}\right)^4 \]
Where:
- \( P_1 = 0.3 \, W \) (power at \( T_1 \))
- \( P_2 \) is the power we want to find at \( T_2 \)

### Step 3: Rearranging the Formula
Rearranging the formula to solve for \( P_2 \):
\[ P_2 = P_1 \cdot \left(\frac{T_2}{T_1}\right)^4 \]

### Step 4: Substitute the Values
Now we can substitute the values we have:
\[ P_2 = 0.3 \cdot \left(\frac{900}{300}\right)^4 \]

### Step 5: Simplify the Ratio
Calculating the ratio:
\[ \frac{900}{300} = 3 \]
So,
\[ P_2 = 0.3 \cdot (3)^4 \]

### Step 6: Calculate \( 3^4 \)
Calculating \( 3^4 \):
\[ 3^4 = 81 \]

### Step 7: Final Calculation
Now substituting back:
\[ P_2 = 0.3 \cdot 81 = \frac{243}{10} = 24.3 \, W \]

### Conclusion
Thus, the heat emitted by the body at `627°C` is:
\[ \boxed{24.3 \, W} \]

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