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We know that denser objects have lower specific heat capacity. Since water is more dense than ice, water must have lower specific heat capacity than ice but we know that water's heat capacity is $4.200\,\text{J/(gK)}$ and ice's specific heat is $2.100\,\text{J/(gk)}$.

Why is this apparently the wrong way around?

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    $\begingroup$ The general rule that there is an inverse correlation between a solid's mass density and its specific heat capacity (considered on a per-mass basis) is only an approximate one. Also, as far as I'm aware, it applies only to solids (while you're making a liquid-to-solid comparison). Also, it really only applies to comparisons of different materials, not two different phases of the same material. Look up the argument that goes into deriving this general rule and note what assumptions are made. $\endgroup$ – Samuel Weir Oct 4 '15 at 7:29
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    $\begingroup$ "Pro Tip" : never ever start out a question with "We know that" . It's almost always wrong. If you can quote a specific law or link to a tech page, that would be acceptable. $\endgroup$ – Carl Witthoft Oct 4 '15 at 17:06

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