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

Latent heat is the energy exchanged during a phase transition at constant temperature. It is quantified as heat energy per unit mass.

The relationship is expressed as: \(L = \frac{Q}{m}\), where \(L\) is latent heat, \(Q\) is heat energy, and \(m\) is mass.

The dimensions of heat energy (\(Q\)) are \([M^1 L^2 T^{-2}]\), and the dimensions of mass (\(m\)) are \([M^1]\).

To find the dimensional formula for latent heat (\(L\)), we divide the dimensions of \(Q\) by the dimensions of \(m\):

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

Simplification yields:

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

The dimensional formula for latent heat is thus: \([M^0 L^2 T^{-2}]\).