# Water density / volume

Water density at 0 C is 990 kg/m3.
Water density at 100 C is 1030 kg/m3 - 1 m3 of water "loses" about 4 % of its mass.
Water expansion rate is 1.0002 for each 1 C increase in temperature - 2 % for the above rise from 0 C to 100 C..
How comes that water density decreases 4 % but its volume increases just 2 % ?

SteamKing
Staff Emeritus
Homework Helper
Water density at 0 C is 990 kg/m3.
Water density at 100 C is 1030 kg/m3 - 1 m3 of water "loses" about 4 % of its mass.
Water expansion rate is 1.0002 for each 1 C increase in temperature - 2 % for the above rise from 0 C to 100 C..
How comes that water density decreases 4 % but its volume increases just 2 % ?

It's one consequence of dealing with too little information. The density-temperature relation for liquid water between 0 C and 100 C is a curve, with the maximum density occurring at about 4 C. Plot the values from the density table referenced by DrClaude.

I mistakenly put it otherwise so, more precisely - according to the reference - it should be :
0.999808 at 0 °C
0.958593 at 100 °C - about 4 % of the initial value
But the volume will increase just 2 %
Maybe there is square root relation ?

russ_watters
Mentor
I mistakenly put it otherwise so, more precisely - according to the reference - it should be :
0.999808 at 0 °C
0.958593 at 100 °C - about 4 % of the initial value
But the volume will increase just 2 %
Maybe there is square root relation ?
Again: the relationship isn't linear.

Let it be it, but I refer to the exactly 2 points (on the "curve") between which there is the 4% decrease in density for, as it seems, 2% increase in volume
Square root ?

DrClaude
Mentor
Let it be it, but I refer to the exactly 2 points (on the "curve") between which there is the 4% decrease in density for, as it seems, 2% increase in volume
Square root ?
But as Russ said, the relationship is not linear. In other words, you can't use the same expansion coefficient at all temperatures.

Water expansion rate is 1.0002 for each 1 C increase in temperature
This is only true around 20°C.

russ_watters
Mentor
Please have a look at the link DrClaude gave you in post #2. You may even try dropping the data into a spreadsheet and calculating the coefficient at different temperatures. You will find that it varies substantially from 2%.

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But will % of expansion = % of decrease in density ?

Chestermiller
Mentor
The product of density and specific volume is 1. So there is no square root relation involved.

Chet

Thank you.