Specific latent heat

In a nutshell

Transferring thermal energy to or from a substance may cause it to change state. The heat responsible for changing the state of a substance is called the latent heat.

Equations

Variable definitions

Changing state

If heating a substance causes it to change state, the heat transferred into the system (from the surroundings) will not increase its temperature. Instead, the energy goes into breaking the bonds between the particles, which increases the internal energy of the system without changing its temperature. 

Likewise, if cooling a substance causes it to change state, the heat released from the system (to the surroundings) does not change the temperature of the substance. Instead, the energy released allows new bonds to form between particles, which changes the internal energy of the system without changing its temperature.

Flat lines in the heating graph below represent the time during which the substance is being heated but remains at a constant temperature. This is therefore when the state of the substance changes.

Specific latent heat

Definition

Specific latent heat is the thermal energy responsible for changing the state of $$1kg$$ of a substance. 

During heating, latent heat goes into the system, breaking the bonds between the particles, causing melting or boiling. During cooling, latent heat is released from the system, allowing new bonds to form between the particles, causing either freezing or condensing. 

The formula for specific latent heat is:

​$$thermal \space energy \space transferred = mass \space \times \space specific \space latent \space heat \\ \ \\ E = m \times L$$​​

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where the variables $$E$$, $$m$$ and $$L$$ are defined above.  

Definition

The specific latent heat for changing between a solid and a liquid (either freezing or melting) is called the specific latent heat of fusion. The specific latent heat for changing between a liquid and a gas (either boiling or condensing) is called the specific latent heat of vaporisation. 

Example

A block of ice of mass $$50\,g$$ is heated at $$0^{\,o}C$$. The specific latent heat of fusion for water is $$334\,000\, J/kg$$. How much heat is required to completely melt the block of ice?

Write down the relevant information provided in the question (converting to base units where appropriate): 

$$L=334\,000\,J/kg \\ \ \\ m=50\,g=0.05\,kg$$​

Write down the relevant formula: 

$$E=m\times L$$

Substitute the relevant information into the formula:

$$E=0.05\times334\,000 \\ \ \\ E=16,700\,J\\ \ \\ E=\underline{16.7\,kJ}$$

So $$\underline{16.7 \, kJ}$$ of heat is required to completely melt a $$50\,g$$ block of ice.