The dimensional formula for latent heat is

Options

A. `M^(2)L^(2)T^(-2)`
B. `MLT^(-2)`
C. `M^(0)L^(2)T^(-2)`
D. `ML^(2)T^(-1)`

Answer

To find the dimensional formula for latent heat, we can follow these steps:

### Step 1: Understand the Definition of Latent Heat
Latent heat is defined as the amount of heat energy required to change the state of a unit mass of a substance without changing its temperature. Mathematically, it can be expressed as:

\[ \text{Latent Heat} = \frac{\text{Energy}}{\text{Mass}} \]

### Step 2: Identify the Dimensional Formula for Energy
The dimensional formula for energy (work done) is derived from the formula for kinetic energy or potential energy. The dimensional formula for energy is:

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

### Step 3: Identify the Dimensional Formula for Mass
The dimensional formula for mass is simply:

\[ [M] = M^1 L^0 T^0 \]

### Step 4: Substitute the Dimensional Formulas into the Latent Heat Formula
Now, we can substitute the dimensional formulas for energy and mass into the equation for latent heat:

\[ \text{Latent Heat} = \frac{[E]}{[M]} = \frac{M^1 L^2 T^{-2}}{M^1 L^0 T^0} \]

### Step 5: Simplify the Expression
When we divide the dimensional formulas, we subtract the exponents of the same base:

\[ \text{Latent Heat} = M^{1-1} L^{2-0} T^{-2-0} = M^0 L^2 T^{-2} \]

### Step 6: Write the Final Dimensional Formula
Thus, the dimensional formula for latent heat is:

\[ \text{Latent Heat} = L^2 T^{-2} \]

### Conclusion
The final answer is:

\[ \text{Dimensional Formula for Latent Heat} = L^2 T^{-2} \]