The Specific Heat Capacity of Solids and Water

Matter can be divided broadly into three states—solid, liquid, and gaseous. Their physical states can be interchanged by providing the required temperature and pressure. Their equilibrium points can also be changed the same way.

To increase or decrease the temperature of any kind of matter, it needs an external source of energy. When gases are heated, the temperature change is minimal, but there is a prominent change in other factors. These factors are pressure and volume.

The specific heat capacity can be defined as the amount of energy provided to a unit mass of a substance to raise its temperature by one degree Celsius.

Specific heat capacity of solids

Solids are forms of matter having characteristics like strong forces of intermolecular interaction, rigidity, proper shape, structure, etc. Solids can be heated, so the capacity of specific heat for solids can be determined. The SI unit of specific heat capacity is J/Kg/K. 

The specific heat capacity of solids is defined as the amount of energy provided to a unit mass of any solid substance so that its temperature is raised by 1°C. 

To determine the specific heat capacity, we will have to make use of the law of equipartition of energy. This law states that for a system in thermal equilibrium, there will be a certain amount of average energy for each degree of freedom a molecule has.

For example, a gas molecule moving in three-dimensional space has three coordinates, so the value of the degree of freedom for that molecule would be 3.

Let us consider any solid having N atoms. Each atom is allowed to move freely but only in one coordinate axis or 1D space. The expression for the total energy U is given as:

U = 3kbTNA= 3RT

We will use the equation for the first law of thermodynamics given below:

                                                               ΔQ =   ΔU+P ΔV    

The first law states: “Energy cannot be created or destroyed, it can only be converted from one form to another.” 

Here, PV can be eliminated as the volume change is negligible for solids. 

 Therefore, the expression for molar specific heat capacity (heat capacity calculated for one mole of solid) will be:

C=   ΔQ / ΔT=   ΔU   /ΔT

C = 3R = 24.94 J/K-1 mol -1 

 C here is the molar specific heat capacity

Q is the heat given and ∆T is the temperature change. 

Heat capacity is more or less an intrinsic property. This means that it is an attribute of any particular substance. The heat capacity is calculated with the help of a Calorimeter. The bomb calorimeter always indicates constant volume values. Another type of calorimeters known as the coffee cup calorimeters is associated with finding heat capacity at constant pressure. 

Specific heat capacity of water

Liquids like water have fewer forces of intermolecular attraction compared to solids. Liquids do not have a definite shape but they take the shape and size of the container they are in. The concept of equipartition of energy is used to calculate the expression for the specific heat capacity of water.

The specific heat capacity of water is defined as the amount of energy required that is given to a unit of any liquid so that the temperature of the liquid is increased by 1°C.

The chemical constituents of water include two components, namely hydrogen and oxygen, which are present in the ratio 2:1. The ratio specifies that one molecule of water will have two atoms of hydrogen and one atom of oxygen making a total of three atoms. So, these three atoms will be free to move across three dimensions.

Hence, we will have to find the total energy associated with one mole of water.

 The total energy becomes:

U =3 3kbTNA= 9RT                                          

Now, the expression for molar specific heat capacity [C] becomes:

C=   ΔQ /  ΔT=   ΔU   /ΔT= 9R

C= 98.31 J mol-1K-1

C = 74.7 J mol-1K-1                                

Comparison of Molar Heat Capacity and Specific Heat Capacity 

Molar Heat Capacity and specific heat capacity can be a bit confusing. Let’s have a look at their major differences for your understanding of this topic. 

The molar heat capacity of a given matter is calculated according to the value of moles. It is per mole. 

On the other hand, specific heat capacity is calculated according to the mass of the matter. Specific heat capacity also goes by the name specific heat. 

Conclusion

The three states of matter, namely solid, liquid and gas, and their equilibrium points can be interchanged when the required temperature and pressure are applied. The specific heat capacity can be defined as the amount of energy provided to a unit mass of a substance to raise its temperature by one degree Celsius. To increase or decrease the temperature of any kind of matter, it needs an external source of energy. When gases are heated, the temperature change is minimal, but there is a prominent change in other factors. These factors are pressure and volume. The law of equipartition of energy states that the molecules present in any thermal equilibrium are said to possess the average energy that becomes associated with their degree of freedom. For this law, we derive the average kinetic energy.