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

Hint:

Latent heat is energy per unit mass, so its dimensional formula is derived by dividing energy (\( [M L^2 T^{-2}] \)) by mass (\( [M] \)), giving \( M^0 L^2 T^{-2} \).

Answer 1

The Correct Option is C

Step 1: {Define latent heat}
Latent heat (\( L \)) is defined as the quantity of heat energy (\( Q \)) required to alter the phase of a substance per unit mass:\[L = \frac{Q}{m}\]Step 2: {Determine the dimensional formula of \( Q \)}
Heat energy (\( Q \)) is a form of energy; its dimensional formula is identical to that of work:\[[Q] = [M L^2 T^{-2}]\]Step 3: {Determine the dimensional formula of \( L \)}
Given that mass (\( m \)) has the dimensional formula:\[[m] = [M]\]the division yields:\[[L] = \frac{[Q]}{[m]} = \frac{[M L^2 T^{-2}]}{[M]}\]\[= M^0 L^2 T^{-2}\]Step 4: {Verify the options}
Comparison with the provided options indicates that the correct answer is (C) \( M^0 L^2 T^{-2} \).