Question

Derive the dimensional formula for latent heat.

Answer 1

Answer:

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Answer 2

Answer:

dimensional formula for latent heat is given by,

[M0 L2 T-2]

Where,M = Mass, L = Length, T = Time

Explanation:

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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