Solids with very large specific heats

Looking at the table of specific heat capacities on Wikipedia, there is quite a wide range of heat capacities for the solids listed and many are much less that $1~mathrm{kJ}~mathrm{kg}^{-1}~mathrm{K}^{-1}$. The Dulong-Petit law provides an approximate limit of $25~mathrm{J}~mathrm{mol}^{-1}~mathrm{K}^{-1}$ for the molar heat capacity of atomic crystals (and as you can see, predicts the molar heat capacities of many metals pretty well), but makes no statements about mass heat capacity.

As far as solids with very high specific heat capacities go, try long chain hydrocarbons (paraffin and polyethylene are listed) or water ice, as well as anything that has a lot of water in it. For volumetric heat capacities, metals become competitive because of their typical high densities.

I know of nothing which has a higher specific heat than water (though I won't be dogmatic about water being the highest). For a high specific heat solid, look for something like ice or another substance which is solid and has high water content at the temperature of interest.

Solids have high density due to compact arrangement of constituent particles.The energy possessed by them is not used for their motion.Opposite to this, gaseous and liquid have very lose arrangement . The constituent particles can move freely by using their energy.hence energy is not stored in them resulting low specific heat capacity.

Here is the list. It has solid, liquid and gas. You can sort by Specific Heat.

https://www.engineeringtoolbox.com/specific-heat-capacity-d_391.html