# Dimensions of Latent Heat

## What is Latent Heat?

Also known as the heat of transformation, latent energy is the energy released or absorbed by a thermodynamics system or body. It occurs during a constant-temperature process and it’s usually a first-order phase transition. It is the energy which can be understood as the energy in hidden form. It is supplied or extracted to change the state of a substance without the temperature change. Some of the examples include latent heat of vaporization and latent heat of fusion when a substance condenses or vapourises at specific temperature and pressure. The term ‘latent heat’ was introduced by British chemist Joseph Black in 1762.

### Specific Latent Heat

It is expressed as the amount of energy in the form of heat, denoted by Q, which is required to completely effect a phase change of a unit of mass (m), usually 1 kg of a substance as an intensive property.

L=Q/m or Q=mL

Here, Q = Amount of energy released or absorbed during the change of phase of the substance (in KJ or BTU)

m= mass of the substance (in kg or lb), and

L= specific latent heat for a particular substance (KJ/kg or BTU/lb)

Latent heat of fusion is the required energy for melting 1 kg of a solid at its melting point. It arises while melting a solid; the temperature remains constant. However, the extra heat energy obtained when melting the substance will help to break the attractive bonds of the molecular structure of a substance that keeps it in a solid-state, thus able to liquefy it. Melting ice into water is an example of latent heat of fusion.

### Dimensional Formula of Latent Heat

The dimensional formula for latent heat is as follows:

[M⁰L² T⁻²]

Where,

• M represents Mass

• L represents Length

• T represents Time

### Derivation of Formula

Latent heat (L) = Heat × [Mass]⁻¹ ….(i)

The dimensional formula of mass = [M¹L⁰ T⁰]----(ii)

Also, the dimensions of heat is same as that of dimensions of energy and also to the dimensions of work

As we know, work = force × displacement . . . . (iii)

And, the dimensional formula of

Displacement = [M⁰ L¹ T⁰] . . . (v)

Force = m a = [M¹ L¹ T⁻²] . . . (iv)

On substituting equation (iv) and (v) in equation (iii) we get,

Work = [M¹ L¹ T⁻²] × [L¹]

Therefore, the dimensions of work or heat = [M¹ L² T⁻²] . .. . (vi)

On substituting equation (ii) and (vi) in equation (i) we get,

Latent heat (L) = Heat × [Mass]⁻¹

Or, L = [M¹ L² T⁻²]  × [M¹L⁰ T⁰]⁻¹ = [M⁰ L² T⁻²].

Therefore, the latent heat dimension formula is represented as [M⁰ L² T⁻²].