Starting this to somewhat un-hijack another thread:

http://www.greenbuildingforum.co.uk/forum114/comments.php?DiscussionID=7085&page=2#Item_2

Posted By: CleanEnergiesI see what you are saying Ed Davies, and am aware of the facts you outlined above albeit not in as much detail as you have provided." alt="" src="http:///forum114/extensions/Vanillacons/smilies/standard/bigsmile.gif" >

When I said; 'so I always presumed it was because the weight COULD remain a constant' I was implying and presuming as stated, that if we are talking about a mass of water in a vessel (sealed for e.g) as the temperature rises the volume will increase (taken up by expansion vessel for example) whereas the weight would remain the same (weight decreases but volume increases?) so a kg of water would be greater than 1 litre but the overall weight of the mass in question (within the sealed vessel) would remain the same?

Or am I wrong (and perfectly happy to accept that) and the mass in question would physically weigh less than the same mass at a lower temperature in such test conditions?

I am interested to hear the answer as you say, normally you have to apply some kind of benchmark to work off, particularly in my line of work were the effects are negligible in reality.

Thanks, Sam

First of all, there's no point in involving weight in this discussion at all. Apart from stopping water floating out of a vented system and very slightly compressing nearly-incompressible water it makes no difference at all. We might as well just think about masses (measured in kg) and ignore weight (measured in newtons, it's a force).

A fixed mass of water, say 1 kg, will always have the same weight in a fixed gravitational field. E.g., on Earth near the equator it'll have a weight of about 9.78 newtons whereas near the poles it'll weigh about 9.832 N. Heating it up will increase its volume (hence reduce its density) but will not affect its weight.

https://en.wikipedia.org/wiki/Gravity_of_Earth#Latitude

Secondly we have to be consistent about what we're keeping constant. We can think about a fixed mass of water. For example, we can think about the water in the tank to start off with. As we warm it (above 4°C) it expands (volume increases and density decreases) and some of it flows out into the expansion vessel. If we consider the water that's flowed out to still be in the game then we're thinking about a fixed mass.

On the other hand, if we only ever consider the water in the vessel so that which has flowed out into the expansion vessel has retired from the game then we're considering a fixed volume. In that case, warming the water reduces not just the density but also the mass (and, incidentally, the weight even if the gravitational field has remained constant in the mean time).

Whatever, we're agreed that the specific heat capacity (i.e., the heat capacity per unit mass) varies over the temperature range. CleanEnergies' original comment (first quote in my posts above) sort of speculates that maybe it's the volumetric heat capacity that remains constant. I tried to show qualitatively that this couldn't be right (because density and specific heat capacity have different minimum points) so let's try it quantitatively. From:

http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html

at 20°C water has a specific heat capacity of 4.183 kJ/(kg·K) and density of 998.3 kg/m³. Therefore it has a volumetric heat capacity of the product of these values: 4175.8889 kJ/m³ (4.175'888'9 kJ/litre).

At 80°C the SHC is 4.203 kJ/(kg·K) and density 972 kg/m³ so the volumetric heat capacity is 4085.316 kJ/m³ (4.085'316 kJ/l).

So, nope, the change in specific heat capacity with temperature is not just “compensation” for a fixed volumetric heat capacity as the density changes.

Posted By: CWattersWater is strange stuff..
http://www.lsbu.ac.uk/water/explan4.html" >http://www.lsbu.ac.uk/water/explan4.html

doesn't mention that water actually gets denser (a sample shrinks in volume) as its temp rises to 4C (the 'anomaly point'); above 4C it gets less dense (expands)with increasing temp, like 'normal' substances.

Plus lots more on the wacky side, which I won't mention just now - except ... Schauberger!

Is the specific heat capacity of the water greater at the bottom or the top of my thermal store :-)

Funny you should mention that Jeremy, just been doing some stats to explain 'degrees of freedom'. It is where the 10% is located that makes a difference. At the lower temperature/energy bins it makes little difference, at the higher ones it makes a lot. But guess that is why we use STP as the baseline and work from there.
We can blame Newton for this.

Posted By: JSHarris

Posted By: CWattersIs the specific heat capacity of the water greater at the bottom or the top of my thermal store :-)

And does it really matter?

Given the wide variation in heating demand we have to deal with, due to factors like unusually warm or cold seasons, there's no merit in getting overly precise with heating or energy storage calculations . I'd argue that getting within 10% is plenty good enough for thermal storage calculations.

Exactly.