Unit of Stefan's constant is

Options

A. 1. Watt-`m^2`-`K^4`
B. 2. Watt-`m^2`/`K^4`
C. 3. Watt/`m^2`–K
D. 4. Watt/`m^2K^4`

Answer

To find the unit of Stefan's constant (σ), we start with the formula that relates power (energy per unit time) to Stefan's constant:

1. **Understand the formula**: The formula for the power radiated by a black body is given by:
\[ P = \sigma \cdot E \cdot A \cdot T^4 \]
where:
- \( P \) is the power (in watts),
- \( \sigma \) is Stefan's constant,
- \( E \) is the emissivity (dimensionless),
- \( A \) is the area (in square meters),
- \( T \) is the absolute temperature (in Kelvin).

2. **Identify the units**: We know that:
- The unit of power \( P \) is watts (W).
- The unit of area \( A \) is square meters (m²).
- The unit of temperature \( T \) is Kelvin (K).

3. **Rearranging the formula**: To isolate Stefan's constant \( \sigma \), we rearrange the formula:
\[ \sigma = \frac{P}{E \cdot A \cdot T^4} \]

4. **Substituting the units**: Since emissivity \( E \) is dimensionless, we can ignore its units. Thus, we substitute the units into the equation:
\[ \sigma = \frac{W}{m^2 \cdot K^4} \]

5. **Final expression for units**: Therefore, the unit of Stefan's constant \( \sigma \) is:
\[ \sigma = \frac{W}{m^2 \cdot K^4} \]

6. **Conclusion**: The final unit of Stefan's constant is:
\[ \text{Watt per meter square per Kelvin to the power 4} \quad \left( \frac{W}{m^2 \cdot K^4} \right) \]

Now, let's identify the correct option from the choices provided in the question. The correct option is:
- **Option 4**: Watt per meter square per Kelvin to the power 4.