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For this question, assume all things not mentioned are perfectly controlled, all at 14.7lbs of atmospheric pressure, and water is 100% pure of anything not mentioned, with no dissolved air.

Given a quantity of water that is 1 liter at 20°, what would the volume be when heated to 30°?

Secondly, the same question, except the water being heated is fully saturated with salt.

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up vote 7 down vote accepted

The volumetric expansion of a liquid is given by the following equation $$\ce{\Delta V = V_o~ \beta~ \Delta T}$$ where $\ce{\beta}$ is the coefficient of thermal expansion and $\ce{\Delta T}$ is the change in temperature in degrees K.

Here's a link to a nice table containing coefficients of expansion for water, both pure and salinated. Wikipedia shows the maximum solubility of salt in water to be around 36% (w/w)

From the first link we find that

$\ce{\beta}$ for pure water at $\ce{25^{o}C~ =~ 257*10^{-6}/^{o}K }$

$\ce{\beta}$ for water with 35% $\ce{NaCl}$ dissolved at $\ce{25^{o} C~ =~ 297*10^{-6}/^{o}K }$

Now you should be able to calculate the values you are interested in.

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Thanks so much. This is very interesting. For whatever reason, this morning I came up with a theory that perhaps more of the see rise we are experiencing is due to expansion than is due to new water in the oceans. Immediately after asking this question, I Googled and found that this theory is nothing new, and that expansion might actually account for 70% of sea rise. – orokusaki Aug 25 '14 at 15:24
You're welcome, and nice thinking! – ron Aug 25 '14 at 15:29

So did you try to find any information to address this question at all?

For a starting point I would suggest although this will not help much on the 'saturated' end of things since the salinity values in the tables do not reach the 20C saturation values. I leave finding the saturation value to the requester, since google brings it up quite easily.

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