A spherical body of area A and emissivity `e=0.6` is kept inside a perfectly black body. Total heat radiated by the body at temperature T

Options

A. `0.4sigmaAT^(4)`
B. `0.8sigmaAT^(4)`
C. `0.6sigmaAT^(4)`
D. `1.0sigmaAT^(4)`

Explanation

To find the total heat radiated by a spherical body of area \( A \) and emissivity \( e = 0.6 \) kept inside a perfectly black body at temperature \( T \), we can use the Stefan-Boltzmann law. Here’s a step-by-step solution:

### Step 1: Understand the Stefan-Boltzmann Law
The Stefan-Boltzmann law states that the power radiated per unit area of a black body is directly proportional to the fourth power of its absolute temperature. The formula is given by:
\[ P = \sigma A T^4 \]
where:
- \( P \) is the power (total heat radiated per unit time),
- \( \sigma \) is the Stefan-Boltzmann constant,
- \( A \) is the area,
- \( T \) is the absolute temperature.

### Step 2: Modify the Law for Non-Black Bodies
For a body that is not a perfect black body (like our spherical body with emissivity \( e \)), the formula is modified to:
\[ P = e \sigma A T^4 \]
where \( e \) is the emissivity of the body.

### Step 3: Substitute the Given Values
In this case, the emissivity \( e \) is given as \( 0.6 \). Thus, we can substitute this value into the modified Stefan-Boltzmann law:
\[ P = 0.6 \sigma A T^4 \]

### Step 4: Conclusion
The total heat radiated by the spherical body at temperature \( T \) is:
\[ P = 0.6 \sigma A T^4 \]

This is the final expression for the total heat radiated by the body.