The value of Stefan's constant is `sigma =5.76xx 10^(-8) J s^(-1) m^(-2)K^(-4).` Find its value in cgs system.

Explanation

To convert Stefan's constant from the SI system (MKS) to the CGS system, we need to follow these steps:

### Step 1: Write down the given value of Stefan's constant in SI units.
The value of Stefan's constant is given as:
\[ \sigma = 5.76 \times 10^{-8} \, \text{J s}^{-1} \text{m}^{-2} \text{K}^{-4} \]

### Step 2: Convert the units from SI to CGS.
In the CGS system, the units are as follows:
- 1 Joule (J) = \(10^7\) ergs
- 1 meter (m) = \(10^2\) centimeters (cm)
- Temperature (Kelvin) remains the same in both systems.

### Step 3: Substitute the unit conversions into the equation.
We need to convert the units in the expression for \(\sigma\):
\[ \sigma = 5.76 \times 10^{-8} \, \text{J s}^{-1} \text{m}^{-2} \text{K}^{-4} = 5.76 \times 10^{-8} \, \text{J} \cdot \text{s}^{-1} \cdot \text{m}^{-2} \cdot \text{K}^{-4} \]
Substituting the conversions:
\[ = 5.76 \times 10^{-8} \cdot (10^7 \, \text{erg}) \cdot \text{s}^{-1} \cdot (10^{-2} \, \text{cm})^{-2} \cdot \text{K}^{-4} \]

### Step 4: Simplify the expression.
Now we simplify the expression:
\[ = 5.76 \times 10^{-8} \cdot 10^7 \cdot \text{s}^{-1} \cdot 10^{-4} \, \text{cm}^{-2} \cdot \text{K}^{-4} \]
\[ = 5.76 \times 10^{-8 + 7 - 4} \, \text{erg s}^{-1} \text{cm}^{-2} \text{K}^{-4} \]
\[ = 5.76 \times 10^{-5} \, \text{erg s}^{-1} \text{cm}^{-2} \text{K}^{-4} \]

### Step 5: Final result.
Thus, the value of Stefan's constant in the CGS system is:
\[ \sigma = 5.76 \times 10^{-5} \, \text{erg s}^{-1} \text{cm}^{-2} \text{K}^{-4} \]

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