# Dimensions of Latent Heat

## Dimensional Formula of Latent Heat

The dimensional formula of latent heat is given by,

[MLT-2]

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Latent heat (L) = Heat × [Mass]-1 . . . . . . (1)

The dimensional formula of mass = [M1 LT0] . . . . (2)

Also, the dimensions of heat = dimensions of energy = dimensions of work

Since, work = force × displacement . . . . (3)

And, the dimensional formula of,

Displacement = [MLT0] . . . (5)

Force = m a = [MLT-2] . . . (4)

On substituting equation (4) and (5) in equation (3) we get,

Work = [MLT-2] × [L1]

Therefore, the dimensions of work or heat = [MLT-2] . . . . (6)

On substituting equation (2) and (6) in equation (1) we get,

Latent heat (L) = Heat × [Mass]-1

Or, L = [MLT-2] × [MLT0]-1 = [MLT-2].

Therefore, latent heat is dimensionally represented as [M0 LT-2].