Specific heat capacity and concentration

[jemamarbinay]

Hello. I am doing a research paper on the relationship of specific heat capacity and refractive index of liquids. I am doing this by finding the relationship between specific heat capacity and concentration and refractive index and concentration. With this I can find a general trend and conclude a relationship between them.

I originally hypothesized that there is a positive relationship between specific heat capacity and concentration; as you increase concentration, specific heat capacity increases because there are more molecules to heat up per given volume. However, this is not the case. With the use of varying concentrations of NaCl and sucrose, I found that there is an inverse relationship between these concentration and specific heat capacity. I also proved myself wrong mathematically as it also showed an inverse relationship.

According to this forum: https://socratic.org/questions/how-does-salt-change-the-specific-heat-capacity-of-water

The reason why specific heat capacity decreases is because of the water molecules forming a rigid cage around the ions. Which decreases the energy/heat required to raise its temperature, hence decreasing specific heat capacity. But why? Why does the rigid cage lower the energy required to raise it by 1C?

Thank you so much

PS. I found out that there is an inverse relationship between SHC and refractive index

 

[drvrm]

The reason why specific heat capacity decreases is because of the water molecules forming a rigid cage around the ions. Which decreases the energy/heat required to raise its temperature, hence decreasing specific heat capacity. But why?

Perhaps the answer is that for each translational degree of freedom we get ½ R contributing to the heat capacity. The molecule can move in x, y or z; and in each direction.
The other degrees of freedom are rotation/vibration. A common sense answer is that as you constrain a system you are reducing degrees of freedom and Formation of rigid structures may be doing that...