Question

The dimensional formula of latent heat is:

• A. \([M^0 L T^{-2}]\)
• B. \([M L T^{-2}]\)
• C. \([M^0 L^2 T^{-2}]\)
• D. \([M L^2 T^{-2}]\)

Answer 1

The Correct Option is C

To determine the dimensional formula for latent heat, we need to understand what latent heat refers to. Latent heat is the heat absorbed or released by a substance during a phase change (such as melting or boiling) without a change in temperature. It is usually expressed in energy per unit mass.

The formula for latent heat (L) is:
\(L = \frac{Q}{m}\)where \(Q\) is the total heat absorbed or released, and \(m\) is the mass.

The dimensional formula for heat energy \((Q)\) is: \([M^1 L^2 T^{-2}]\). Mass \((m)\) has the dimensional formula \([M^1]\).

Since \(L = \frac{Q}{m}\), the dimensional formula of latent heat will be calculated as:

\([L] = \frac{[M^1 L^2 T^{-2}]}{[M^1]}\)

After simplifying, we get:

\([L] = [M^0 L^2 T^{-2}]\)

Therefore, the correct dimensional formula for latent heat is: \([M^0 L^2 T^{-2}]\).

Answer 2

Latent heat is the energy absorbed or released during a phase change per unit mass. Hence, it is specific energy:

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

The dimensional formula of energy is:

\[ \text{Energy} = [ML^2T^{-2}]. \]

Divide by mass:

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

Final Answer: \([M^0L^2T^{-2}]\).