The temperature of a body is increased from −`73^(@)C" to "327^(@)C`. Then the ratio of emissive power is

Options

A. `1//9`
B. `1//27`
C. 1/27
D. 1/81

Answer

To solve the problem step by step, we need to find the ratio of the emissive power of a body when its temperature is increased from -73°C to 327°C.

### Step 1: Convert temperatures from Celsius to Kelvin
The first step is to convert the given temperatures from Celsius to Kelvin, as the emissive power is calculated using absolute temperatures.

- For the first temperature:
\[ T_1 = -73°C + 273 = 200 \, K \]

- For the second temperature:
\[ T_2 = 327°C + 273 = 600 \, K \]

### Step 2: Use the Stefan-Boltzmann Law
According to the Stefan-Boltzmann Law, the emissive power \( E \) of a body is directly proportional to the fourth power of its absolute temperature:
\[ E \propto T^4 \]

### Step 3: Set up the ratio of emissive powers
We can express the ratio of the emissive powers \( E_1 \) and \( E_2 \) using their respective temperatures:
\[ \frac{E_1}{E_2} = \left(\frac{T_1}{T_2}\right)^4 \]

### Step 4: Substitute the temperatures into the ratio
Substituting \( T_1 \) and \( T_2 \) into the equation:
\[ \frac{E_1}{E_2} = \left(\frac{200}{600}\right)^4 \]

### Step 5: Simplify the fraction
Simplifying the fraction:
\[ \frac{200}{600} = \frac{1}{3} \]

### Step 6: Calculate the fourth power
Now we calculate the fourth power:
\[ \left(\frac{1}{3}\right)^4 = \frac{1}{81} \]

### Step 7: Write the final ratio of emissive powers
Thus, the ratio of the emissive powers \( E_1 \) to \( E_2 \) is:
\[ \frac{E_1}{E_2} = \frac{1}{81} \]

### Conclusion
The final answer is:
\[ E_1 : E_2 = 1 : 81 \]