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# Latent Heat Formula

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Last updated date: 04th Aug 2024
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## What is Latent Heat?

Latent heat is the heat used to convert a solid to a liquid or vapour phase, or a liquid to a vapour phase. The heat of condensation, the heat of vaporization, and so on are some of the names given to it depending on the different phases. The heat or energy consumed or emitted during a phase change of a material is known as latent heat. It may be from a gas to a liquid or from a liquid to a solid and back again. The heat property enthalpy is related to latent heat.

Here, we will learn about latent heat, different types of latent heat along with the formula and dimension of latent heat.

### Latent Heat Equation

The latent heat formula is given by,

L = $\frac{Q}{M}$

Where,

L = specific latent heat of a substance

Q = amount of heat

M = mass of the substance

### Latent Heat Dimensional Formula

Latent heat dimensional formula is given by,

[M⁰L²T⁻²]

Where,

M = Mass

L = Length

T = Time

### Latent Heat of Vaporization Formula

The heat absorbed or discharged as matter disintegrates, changing state from fluid to gas at a constant temperature, is known as latent heat of vaporization.

The heat of water vaporization is the most well-known. The heat of vaporization is described as the amount of heat required to convert 1 g of a fluid into a fume without changing the fluid's temperature.

### Heat of Vaporization Formula

The heat of vaporization formula can be written as based on entropy and enthalpy of vaporization, as well as their relationship.

H$_{v}$ = $\frac{q}{m}$

Where

H$_{v}$ = vaporization heat

m = mass of the substance

q = heat

We should note that the latent heat is associated with no change in temperature but a change in state. The disappearance of water has an articulated cooling effect, while the buildup has a warming effect, due to the high heat of vaporization.

The heat of vaporization is similar to the heat of fusion or melting in that it refers to the amount of heat exchanged during a stage change. It is the amount of heat (540 cal g-1) needed to convert 1 g of water to 1 g of water fume in the case of vaporization. During the conversion of 1 g water fume to 1 g water, a comparable amount of heat is exchanged or discharged.

### Latent Heat of Fusion Formula

The latent heat of fusion is the heat consumed or discharged as matter melts, changing state from solid to fluid structure at a constant temperature.

Since sea ice and brine will exist together at any temperature and melt at a temperature other than 0C when bathed in a concentrated salt solution, the content of latent heat is complex in the case of sea ice, just as it is in the walls of brine cells when brine cells migrate. The heat absorbed by the material, or the latent heat of fusion formula, is expressed as when m kg of solid converts to a fluid at a constant temperature, which is its melting point.

Q = M x L

Where

L is the substance's unique latent heat of fusion.

The heat that the material absorbs or releases is expressed as when the temperature of the substance varies from t1 (low temperature) to t2 (high temperature).

Q = mcΔt

Q = mc(t₂ - t₁)

The total amount of heat absorbed or  liberated by the material is

Q = mL + mcΔt

Since the heat energy expected to shift the material from solid to fluid at air pressure during softening is the latent heat of fusion, and the temperature remains constant during the process, the ‘enthalpy' of fusion is latent heat. The enthalpy shift of some measure of material as it dissolves is the latent heat of fusion.

The real heat of fusion is defined as the enthalpy shift per mole of the matter when expressed in terms of a unit of mass, while the molar heat of fusion is defined as the enthalpy shift per mole of matter.

The inward energy of the fluid state is greater than that of the solid-state. This means that energy must be given to the solid in order to dissolve it, and energy must be discharged from a fluid as it solidifies since the particles in the fluid have a more delicate intermolecular force and therefore have higher potential energy (a sort of bond-separation energy for intermolecular powers).

### Solved Examples:

1. If the amount of heat needed for a phase change is 300 kcal, calculate the latent heat of a 5 kg material.

Sol: Given parameters are,

Q = 300 k.cal

M = 5 kg

The formula for latent heat is given by,

L = Q / M

L = 300 / 5

L = 60 k.cal/kg

Hence latent heat value is 60 k.cal/kg

2. At 20°C, a piece of metal has a density of 60g. When immersed in a steam current at 100°C, 0.5g of the steam condenses on it. Provided that the latent heat of steam is 540 cal/g, calculate the specific heat of the metal.

Sol: Let c be the specific heat of the metal.

Heat gained by the metal

Q = mcΔt

⇒ Q = 60 x c x (100 - 20)

⇒ Q = 60 x c x 80 cal

The heat released by the steam

Q = m × L

Q = 0.5 × 540 cal

By the principle of mixtures,

Heat given is equal to Heat taken

0.5 × 540 = 60 × c ×80

c = 0.056 cal/g ⁰C

Hence specific heat value is 0.056 cal/g ⁰C

Hence, we can conclude that The specific latent heat (L) of a material:

• It is a measurement of the amount of heat energy (Q) emitted or absorbed per mass (m) during a phase shift.

• The formula Q = mL is used to describe it.

• It's commonly referred to as the material's "latent heat."

• The joule per kilogramme [J/kg] is the SI unit.

We have all three types of latent heat and dimension of latent heat. We have solved a few example problems.

## FAQs on Latent Heat Formula

1. What are Three Types of Latent Heat?

Ans: There are three different types of latent heats,

• Latent Heat of Fusion

• Latent Heat of Vaporization

• Latent Heat of Sublimation

2. What is Specific Latent Heat?

Ans: The amount of energy needed to change the state of 1 kilogram (kg) of a substance without changing its temperature is known as specific latent heat.

3. How Do You Distinguish Between Latent and Real Heat?

Ans: The amount of heat needed to increase the temperature of a material by a certain amount is known as specific heat. The amount of heat emitted during a change of state, such as the boiling of water or the melting of ice, is known as latent heat.