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, we start with the formula for Stefan's constant itself:

\[ \sigma = \frac{E}{A \cdot t \cdot T^4} \]

Where:
- \(E\) is energy,
- \(A\) is area,
- \(t\) is time,
- \(T\) is temperature.

### Step 1: Write the dimensional formula for energy
The dimensional formula for energy is given by:

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

### Step 2: Write the dimensional formula for area
The dimensional formula for area is:

\[ [A] = [L^2] \]

### Step 3: Write the dimensional formula for time
The dimensional formula for time is:

\[ [T] = [T] \]

### Step 4: Write the dimensional formula for temperature
The dimensional formula for temperature is:

\[ [T] = [K] \]

### Step 5: Substitute the dimensional formulas into the equation for Stefan's constant
Now we can substitute these into the equation for Stefan's constant:

\[ [\sigma] = \frac{[E]}{[A] \cdot [t] \cdot [T^4]} \]

Substituting the dimensional formulas:

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

### Step 6: Simplify the expression
Now we simplify the expression:

\[ [\sigma] = \frac{[M][L^2][T^{-2}]}{[L^2][T][K^4]} = [M][L^2][T^{-2}] \cdot [L^{-2}][T^{-1}][K^{-4}] \]

This simplifies to:

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

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

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