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Here and here it states that water is at its highest density around $4^\circ$ Celsius. I know very little physics and a Google search has left me without an answer. I am teaching an ODE class in the math department. I have a student that heard the above stated in a physics course. She is wondering whether this is an appropriate project for my class. So, does this fact come from some differential equations?

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Hi Joe - no offense, but your question sounds kind of "rambly." What is it exactly that you want to ask? Is it how one can derive the fact that water is at its densest at 4 degrees? Are you just asking whether there is a differential equation involved in determining this, which you could use as an example in class? Or something else? – David Z Feb 5 '13 at 20:49
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Here is a link which discuses this problem in some depth. I do not think that this would be a good project for an ODE class because temperature and density are not differentially related to each other i.e. one is not a differential form of the other.

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