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:
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].