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].

⇒ Check Other Dimensional Formulas:

• Dimensions of Gravitational Constant
• Dimensions of Magnetic Flux
• Dimensions of Impedance
• Dimensions of Boltzmann Constant
• Dimensions of Gravitational Potential Energy