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This is probably a stupid question, but why do different materials have different specific heat capacities?

To better understand my question let's say that I have $1$ kg of copper and $1$ kg of water. The amount of heat required to raise the temperature of the water by $1$ degree is about $10.8$ times that of copper (see footnote). Where is this extra energy that's required to increase the water's temperature by one degree compared to the copper "stored"?

Moreover, suppose if I have $1$ kg of ice and $1$ kg of liquid water where both substances are made up of the same molecules. Even though it is the same "substance" they still have different specific heat capacities. Is it simply because the numbers of atoms per kg in the substances are different?

Footnote: $C_{\text{Cu}}=385$ J/(kg K), $C_{\text{H$_2$O}}=4.19\cdot 10^{3}$ J/(kg K).

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Primarily because 1 kg of water has more atoms than 1 kg of copper.

For ordinary solids at or above room temperature, the molar heat capacity is approximately the same (Dulong and Petit's law), three times the gas constant, about 25 J/K. It is because the sum of potential and kinetic energy per atom is $3k_BT$ in the harmonic approximation.

Hydrogen in water or ice is a bit different. It is so light that quantum effects come inte play, equipartition does not apply.

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  • $\begingroup$ Waddup Pieter, when you say 'Primarily because 1 kg of water has more atoms than 1 kg of copper.' is that molar heat capacity or specific heat capacity? $\endgroup$ – Fred Weasley Apr 18 at 11:53
  • $\begingroup$ @FredWeasley It is my answer on the OP's question: the specific heat capacity per unit weight. And I added that the heat capacity per mole or per atom is approximately the same for solids at or above room temperature. $\endgroup$ – Pieter Apr 18 at 13:34
  • $\begingroup$ so the element's atom mass matter right? for example the amu for copper is 63.5 and the amu for gold 197 and the specific heat capacity for each of the element is 376 and 126 respectively. Can you please explain why is that? why does it take less energy to heat up a greater mass? Thank you and sorry for bothering you Pieter master $\endgroup$ – Fred Weasley Apr 18 at 13:49
  • $\begingroup$ i looked up heat capacity at wikipedia and it said 'specific heat capacity ... depends on degree of freedom' and then it adds on "larger the number of degrees of freedom available to the particles .... larger will be the specific heat capacity for the substance" if copper has more mass, isnt that means it harder to speed it up and shouldn't it then has a lower specific heat? $\endgroup$ – Fred Weasley Apr 18 at 13:53
  • $\begingroup$ I had linked to Dulong and Petit's law. They discovered already two centuries ago that ratios of specific heats are as the ratios of their atomic masses. In the case of gold and copper 3:1. The reason is that each atom has the same thermal energy. $\endgroup$ – Pieter Apr 18 at 17:58

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