# Why the specific heat capacity of the same substance is different in its different phase (state of matter)?

Concise Physics ICSE Volume II page 265 mentions the following:

The specific heat capacity of the same substance is different in its different phases. The specific heat capacity of water is 4200 J kg^-1 K^-1, of ice is 2100 J kg^-1 K^-1 and of steam is 460 J kg^-l K^-l.

After reading the text I searched some other books and the internet. But I couldn't get a convincing answer which explains why the same substance's specific heat capacity differs in different state of matter(phases). So could anyone plz explain why it happens so?

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• The specific heat capacity of steam is about $2\,\rm kJ \, kg^{-1}\, K^{-1}$. Jan 8, 2022 at 13:05
• Yeah thanks I searched on the internet you are right it's ~2kJKg^-1K^-1. The books must have got it wrong Jan 8, 2022 at 13:11

An increase in temperature means that the average kinetic energy of molecules has increased.

Adding heat to ice increases the average vibrational kinetic energy of the water molecules (the temperature rises).
The liquid state of water in more complex in that some of the ordered lower density structure of ice still exists in the liquid phase which explains the anomalous behaviour of water resulting in a maximum density at around $$4^\circ \rm C$$.
Applying heat to water thus has two effects. It increases the kinetic energy of the molecules (the temperature rises) whilst also braking down the bonds which are in the ordered lower density structure.

Once in the vapour phase with little bonding between the water molecules the heat which is supplied increases the translational kinetic energy of the water molecules (the temperature rises). Note that for a vapour which expands a greater deal more than a liquid for a given temperature rise the specific heat capacity will differ if the steam is a constant pressure as oppose if it is a constant volume.
The tables in Engineering Toolbox illustrate the dependence of specific heat capacity on external factors.

• (+1) but I have questions. Leaving the steam out of the discussion for a while, what is the key reason behind water having more specific heat capacity as compared to ice? is it the breaking of bonds or is it the addition of kinetic energy to the water molecules? Jan 8, 2022 at 19:57
• Judging by the similarity of the specific heat capacities of ice and steam I expect it to be breaking of the bonds. Jan 8, 2022 at 20:09

You need to look at it from an intermolecular bond strength angle. More intermolecular strength means more specific heat capacity because the heat you are supplying needs to overcome the intermolecular forces in order to raise the temperature. Certainly, the forces will be different for different states of matter and that explains one part - specific heat capacity depending on the state of matter.

Now, intuitively, you might think that solid will have higher forces as compared to liquid and gases and specific heat capacities should show a similar trend i.e. specific heat capacity of ice > water > steam.

However, water is an exception due to the strong hydrogen bonding present in its liquid state. These forces are stronger than the forces of the solid state. That's why specific heat capacity of water > ice > steam.

• However, water is an exception due to the strong hydrogen bonding present in its liquid state. These forces are stronger than the forces of the solid state. The bonding of water molecules in ice is due to the same hydrogen bonds as exist in liquid water. Jan 8, 2022 at 13:23
• @farcher - thanks for your comment. I am wondering, isn't the bond structure and thus overall bond energy less in case of ice? a longer bond length resulting in lower density of ice as compared to water? Kindly correct me if I am missing something here. :) Jan 8, 2022 at 13:39
• The increased separation of the molecules is because the more "open" ordered structure of water molecules making the average separation of water molecules greater than in the liquid pahse.. Image. Jan 8, 2022 at 13:44