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 that 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 evaporates at a 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 affect 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 being 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:

\[M^{0}L^{2}T^{-2}\]

Where,

M represents Mass

L represents Length

T represents Time


Derivation of Formula

Latent heat (L) = \[ Heat \times Mass^{-1}\] ….(i)

The dimensional formula of mass =  \[M^{1}L^{0}T^{0}\]----(ii)

Also, the dimensions of heat is the 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 =  \[M^{0}L^{1}T^{0}\] . . . (v)

Force = m a = \[M^{1}L^{1}T^{-2}\] . . . (iv)

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

Work =  \[M^{1}L^{1}T^{-2} \times L^{1}\]

Therefore, the dimensions of work or heat = \[M^{1}L^{2}T^{-2}\]. .. . (vi)

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

Latent heat (L) = \[ Heat \times Mass^{-1}\]

Or, L = \[M^{1}L^{2}T^{-2} \times M^{1}L^{0}T^{0-1}= M^{0}L^{2}T^{-2}\].

Therefore, the latent heat dimension formula is represented as \[M^{0}L^{2}T^{-2}\].

FAQs on Dimensions of Latent Heat

1. What is the latent heat of vaporization?

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 the 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 unit for the latent heat of fusion or vaporisation is J/kg.

2. What is the specific latent heat of a material?

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 vaporization, and latent heat of sublimation respectively.

3. What is latent heat?

The energy given out or taken in by a body or a thermodynamic system during a constant-temperature process usually a first-order phase transition is called latent heat (also known as latent energy or heat of transformation).


Latent heat is energy that is provided or removed in a concealed form to affect the state of a substance without changing its temperature. Phase transitions, such as a substance condensing or vaporizing at a specific temperature and pressure, are examples of latent heat of fusion and latent heat of evaporation. 


Joseph Black, a British scientist, coined the name around 1762. It comes from the Latin word latere (to lie hidden). The term was first coined by Black with regards to calorimetry, in which a heat transfer produced a change in volume in a body while the temperature remained the same. Sensible heat, in contrast to latent heat, is energy transferred as heat with a temperature change in a body. Click here for more information.

4. What is the latent heat of fusion?

The heat taken in or given out when matter melts, shifting state from solid to fluid-structure at a constant temperature, is called the latent heat of fusion.


As the heat energy expected to transform the substance from solid to fluid at air pressure during softening is the latent heat of fusion, and the temperature remains constant during the procedure, the 'enthalpy' of fusion is latent heat. The enthalpy change of any measure of substance as it dissolves is the latent heat of fusion.


When the heat of fusion is expressed in terms of a unit of mass, it is called the specific heat of fusion, whereas the molar heat of fusion refers to the enthalpy change per mole of a substance.

5. What are some real-life examples of latent and sensible heat?

Some of the examples of latent and sensible heat are:

  • Warm vitality from the heating component is transferred to the pot and hence to the water, resulting in bubbling water on a stove. Fluid water grows from water fumes and water bubbles when enough vitality is provided. When water bubbles form, a massive amount of vitality is released. It's not difficult to be burnt by steam because water has such a high heat of vaporization.

  • As a result, converting fluid water to ice in a cooler requires a large amount of energy. The cooler dispels heat energy, allowing the stage to progress. Because water has a high latent heat of combination, turning it into ice takes more energy per unit gram than freezing fluid oxygen into solid oxygen.

6. What is meant by specific latent heat?

When a body encounters a steady temperature process, specific latent heat is defined as the amount of heat energy (heat, Q) that is consumed or emitted.

The following is the formula for specific latent heat:

Q/m = L

Where:

The specific latent heat is implied by the letter L.

The heat retained or expelled is denoted by Q.

The mass of material is m.


Stage shifts, such as liquefying, solidifying, vaporization, or accumulation, are the most well-known types of continuous temperature forms. The energy is considered to be "latent" since it is essentially safeguarded inside the atoms until the change of stage happens. The joules per gramme and kilojoules per kilogram units of specific latent heat are the most well-known.


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