The MKS unit of Stefan's constant is

Options

A. Watt/ `m^2-K^4`
B. Watt `m^2- K^4`
C. Watt/ `m^2 - K`
D. Watt/`m^2`

Answer

To determine the MKS unit of Stefan's constant (σ), we will analyze the formula derived from Stefan's law.

### Step 1: Understand Stefan's Law
Stefan's law states that the power radiated by a black body per unit area is proportional to the fourth power of its absolute temperature. The formula can be expressed as:
\[ P = \sigma E A T^4 \]
Where:
- \( P \) = Power radiated (in Watts)
- \( \sigma \) = Stefan's constant
- \( E \) = Emissivity (dimensionless, no units)
- \( A \) = Area (in square meters, \( m^2 \))
- \( T \) = Temperature (in Kelvin, \( K \))

### Step 2: Rearrange the Formula
To isolate Stefan's constant \( \sigma \), we rearrange the formula:
\[ \sigma = \frac{P}{E A T^4} \]
Since emissivity \( E \) is dimensionless, it does not affect the units.

### Step 3: Substitute Units
Now, we substitute the units into the equation:
- Power \( P \) is measured in Watts (W), where \( 1 \, W = 1 \, \text{J/s} = 1 \, \text{kg m}^2/\text{s}^3 \)
- Area \( A \) is measured in \( m^2 \)
- Temperature \( T \) is measured in Kelvin \( K \)

Thus, we can express the units of \( \sigma \):
\[ \sigma = \frac{W}{A T^4} = \frac{\text{kg m}^2/\text{s}^3}{m^2 K^4} \]

### Step 4: Simplify the Units
Now, we simplify the units:
\[ \sigma = \frac{\text{kg m}^2}{\text{s}^3} \cdot \frac{1}{m^2 K^4} = \frac{\text{kg}}{\text{s}^3 K^4} \]

### Conclusion
The MKS unit of Stefan's constant \( \sigma \) is:
\[ \sigma = \frac{\text{kg}}{\text{s}^3 \text{K}^4} \]