Dimensional formula for stefan’s constant is: (here K denotes the temperature)

Options

A. `ML^(2) T^(-3)K^(-1)`
B. `MT^(-3)K^(-4)`
C. `MLT^(-2)K^(-4)`
D. `MLT^(-2)K^(-2)`

Explanation

To find the dimensional formula for Stefan's constant (σ), we can start from Stefan's law, which states that the power radiated per unit area of a black body is proportional to the fourth power of its absolute temperature. The formula is given by:

\[ P = \sigma A T^4 \]

Where:
- \( P \) is the power (in watts, W)
- \( \sigma \) is Stefan's constant
- \( A \) is the area (in square meters, m²)
- \( T \) is the absolute temperature (in Kelvin, K)

### Step 1: Write down the dimensions of power (P)
Power (P) is defined as energy per unit time. The dimensional formula for energy is:

\[ [E] = M L^2 T^{-2} \]

Since power is energy per time, we have:

\[ [P] = [E] \cdot [T^{-1}] = M L^2 T^{-2} \cdot T^{-1} = M L^2 T^{-3} \]

### Step 2: Write down the dimensions of area (A)
Area is given by:

\[ [A] = L^2 \]

### Step 3: Write down the dimensions of temperature (T)
The dimensional formula for temperature (T) is represented as:

\[ [T] = K \]

### Step 4: Substitute the dimensions into the Stefan's law equation
From the equation \( P = \sigma A T^4 \), we can rearrange it to find the dimensions of σ:

\[ \sigma = \frac{P}{A T^4} \]

Substituting the dimensional formulas we found:

\[ [\sigma] = \frac{[P]}{[A] [T^4]} = \frac{M L^2 T^{-3}}{L^2 (K^4)} \]

### Step 5: Simplify the expression
Now, simplify the expression:

\[ [\sigma] = \frac{M L^2 T^{-3}}{L^2 K^4} = M T^{-3} K^{-4} \]

### Final Result
Thus, the dimensional formula for Stefan's constant (σ) is:

\[ [\sigma] = M T^{-3} K^{-4} \]

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