In MKS system, Stefan's constant is denoted by `sigma`. In CGS system multiplying factor of `sigma` will be

Options

A. 1
B. `10^(3)`
C. `10^(5)`
D. `10^(2)`

Explanation

To find the multiplying factor of Stefan's constant (σ) when converting from the MKS (Meter-Kilogram-Second) system to the CGS (Centimeter-Gram-Second) system, we can follow these steps:

### Step 1: Identify the units of Stefan's constant in the MKS system.
In the MKS system, Stefan's constant (σ) is expressed in the units of:
\[ \text{Joules} \, \text{m}^{-2} \, \text{s}^{-1} \, \text{K}^{-4} \]

### Step 2: Convert the units from MKS to CGS.
We need to convert each component of the units from MKS to CGS:
- **Joules (J)**: In CGS, 1 Joule = \(10^7\) ergs.
- **Meters (m)**: In CGS, 1 meter = \(10^2\) centimeters.
- **Seconds (s)**: The unit of time remains the same in both systems.
- **Kelvin (K)**: The unit of temperature also remains the same in both systems.

### Step 3: Substitute the conversions into the unit of σ.
Now we can substitute the conversions into the unit of σ:
\[ \sigma = \frac{\text{Joules}}{\text{m}^2 \cdot \text{s} \cdot \text{K}^4} = \frac{10^7 \, \text{ergs}}{(10^2 \, \text{cm})^2 \cdot \text{s} \cdot \text{K}^4} \]

### Step 4: Simplify the expression.
Now we simplify the expression:
\[ \sigma = \frac{10^7 \, \text{ergs}}{10^4 \, \text{cm}^2 \cdot \text{s} \cdot \text{K}^4} = \frac{10^7}{10^4} \cdot \frac{\text{ergs}}{\text{cm}^2 \cdot \text{s} \cdot \text{K}^4} \]
\[ \sigma = 10^{7-4} \cdot \frac{\text{ergs}}{\text{cm}^2 \cdot \text{s} \cdot \text{K}^4} = 10^3 \cdot \frac{\text{ergs}}{\text{cm}^2 \cdot \text{s} \cdot \text{K}^4} \]

### Step 5: Determine the multiplying factor.
From the simplification, we find that the multiplying factor when converting σ from MKS to CGS is:
\[ 10^3 \]

### Conclusion
Thus, the multiplying factor of σ in the CGS system is \(10^3\).

---