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].

FAQs (Frequently Asked Questions)

Q1. What is the Latent Heat of Vaporization?

Ans: Latent heat of vaporisation is the energy needed to vaporise 1 kg of a liquid at its boiling point. It arises when a liquid is boiling and the temperature remains constant. The extra heat energy acquired when boiling the substance helps in breaking all bonds of the substance. It frees the atoms and transformation of the liquid to gas takes place. The example for the latent heat of vaporisation is boiling water for producing water vapour (boiling is not the same thing as evaporation).

Latent heat of fusion or latent heat of vaporisation is obtained with rearrangement of the equation E=mL, where L can be latent heat of fusion or vaporisation. The units for the latent heat of fusion or vaporisation is J/kg.

Q2. What is the Specific Latent Heat of a Material?

Ans: Specific latent heat is denoted by L and it is a measure of the heat energy (Q) per mass (m) released or absorbed during a phase change. It can be defined through the formula: Q=mL and its SI unit is Joule per kilogram (J/kg). There are three kinds of latent heat known depending on specific phase changes that include solid-liquid, liquid-gas and solid-gas namely latent heat of fusion, latent heat of vaporisation and latent heat of sublimation respectively.