Dimensional Formula of Latent Heat
The dimensional formula of latent heat is given by,
[M0 L2 T-2]
Where,
- M = Mass
- L = Length
- T = Time
Derivation
Latent heat (L) = Heat × [Mass]-1 . . . . . . (1)
The dimensional formula of mass = [M1 L0 T0] . . . . (2)
Also, the dimensions of heat = dimensions of energy = dimensions of work
Since, work = force × displacement . . . . (3)
And, the dimensional formula of,
Displacement = [M0 L1 T0] . . . (5)
Force = m a = [M1 L1 T-2] . . . (4)
On substituting equation (4) and (5) in equation (3) we get,
Work = [M1 L1 T-2] × [L1]
Therefore, the dimensions of work or heat = [M1 L2 T-2] . . . . (6)
On substituting equation (2) and (6) in equation (1) we get,
Latent heat (L) = Heat × [Mass]-1
Or, L = [M1 L2 T-2] × [M1 L0 T0]-1 = [M0 L2 T-2].
Therefore, latent heat is dimensionally represented as [M0 L2 T-2].
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