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In a set of questions that I was solving, the answer to one of the questions asking why the density of liquid water increases from 0 to 4 degrees C had the above answer: due to an increase in entropy.

This website does explain this a bit with two thermodynamic equations, but I am unable to make sense of how entropy comes into the picture here. Please explain how the increase in density of water is due to an increase in entropy.

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    $\begingroup$ IMHO, increase of entropy is not the cause of density increase, but both are consequences of the common cause. The less dense water structure near freezing point are less random and have lower entropy. If more organized structure were more compact as usually, increasing entropy would be toward lower density. $\endgroup$ – Poutnik Feb 4 at 6:51
  • $\begingroup$ chemistry.stackexchange.com/questions/81756/… and the papers referenced in the answer (mine) suggest that entropy has a role to play (but isn't the only factor). $\endgroup$ – Jon Custer Feb 4 at 13:18
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    $\begingroup$ It's very hard to see what entropy has to do with this. The entropy of liquid water increases monotonically with temperature. So, attributing a density maximum to entropy alone does not make sense. Also, this question is unanswerable as there is no agreed upon cause of the density maximum in liquid water. $\endgroup$ – jheindel Feb 5 at 3:22
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At $0°$C, the water is not yet made of independent $H_2O$ molecules. It is still a mixture of hexagones containing 6 molecules $H_2O$. And these hexagones are separated by independent $H_2O$ molecules. There is still a certain order in the water at 0°C. These hexagones are destroyed between $0°$C and $4$°C. These hexagones are more cumbersome than 6 molecules $H_2O$, because there is a hole in the center of the hexagones. That is why the density of water at $0$°C is lower than at $4°$C.

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    $\begingroup$ This does neither answer the question, nor is it entirely correct. At least to the extend from what I understood from the page the OP linked. $\endgroup$ – Martin - マーチン Feb 4 at 11:32
  • $\begingroup$ @martin you may be right, but do you have an alternative we can upvote? $\endgroup$ – Oscar Lanzi Feb 5 at 13:35
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    $\begingroup$ @Oscar Unfortunately I can't dig further into the ressource the OP linked, even though it appears very thorough, and probably a very good read. At least the images provided there look stunning. I believe water, as a system in itself, is incredibly complex, and I would love to have someone with more experience on the matter write an answer. Or maybe someone who has the time and the passion to read and understand and excerpt the linked website. $\endgroup$ – Martin - マーチン Feb 5 at 14:05

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