A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power at given temperature.

Answer

To find the emissive power of the metal cube, we can follow these steps:

### Step 1: Understand the Given Information
We are given:
- The rate of heat radiation (Q/t) = 10 J/s
- The length of the cube = 4 cm

### Step 2: Convert Length to Meters
Since the standard unit of length in physics is meters, we need to convert the length of the cube from centimeters to meters.
\[ \text{Length} = 4 \, \text{cm} = 4 \times 10^{-2} \, \text{m} = 0.04 \, \text{m} \]

### Step 3: Calculate the Surface Area of the Cube
The surface area (A) of a cube is given by the formula:
\[ A = 6 \times (\text{side length})^2 \]
Substituting the side length:
\[ A = 6 \times (0.04)^2 = 6 \times 0.0016 = 0.0096 \, \text{m}^2 \]

### Step 4: Calculate the Emissive Power
The emissive power (E) can be calculated using the formula:
\[ E = \frac{Q/t}{A} \]
Substituting the values we have:
\[ E = \frac{10 \, \text{J/s}}{0.0096 \, \text{m}^2} \approx 1041.67 \, \text{J/(s m}^2\text{)} \]

### Final Answer
The emissive power of the metal cube is approximately:
\[ E \approx 1041.67 \, \text{J/(s m}^2\text{)} \]

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