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Does anybody know an algorithm or a calculator to compute thermal expansion of worts?

Most of the time in homebrewing materials, it is said that in volume calculations one should account for 4% expansion of water from 20C to 100C (on standard pressure). More precise expansion can be calculated based on volumetric expansion coefficients.

However, because my volume measurements of wort do not add up (as if some wort is mysteriously vanished), I'm thinking whether the calculation is correct.

Isn't the thermal expansion of sugar solution different than the one for water?



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I don't know the formula, but I can gather that it is a very complex one given heat, quantity, density of sugars in the solution, even the height and diameter of your boil kettle, not to mention any modifications made to the inside (ridge along the bottom, submerged immersion chiller, etc). Heck, I'd imagine one would even have to take into consideration the barometric pressure of your given altitude. – Scott May 20 '14 at 12:21
I agree with Scott. You need to figure out what is right for your system over time with experience. To start with, measure it using a marked stick or rod as the boil completes, and compare that with the volume after chilling. Most systems lose some wort too (left with the hops, inside a chiller, etc). You can measure it when close to finishing the boil, and adjust if necessary (add more water if too little or increase the intensity or length of the boil if too much). – jalynn2 May 20 '14 at 17:07
Thanks for your help! I've actually measured and calibrated everything but there is still quite some loss that I'd like to explain somehow. But it seems quite difficult to find any research or physics materials explaining how sugar solutions affect volume. – jbv May 20 '14 at 20:54
Are you accounting for the proteins and trub left in the bottom of your kettle when you go to rack out of your boil kettle for fermentation? If not that, are you using an immersion chiller? That would displace wort if you measured while it was in the kettle. – Scott May 21 '14 at 20:27

For temperature coefficients of sugar solutions, this article empirically determines expansion coefficients for grape juice. For 22% brix, density at 20°C is 1.097 vs 1.065 at 80°C - which corresponds to a volume in increase of 3%. At 100°C the figure is closer to 4% as expected.

The difference between using 4% and the actual temperature coefficients of various sugars is going to be small - a fraction of a percent. I doubt the volume scale on your kettle is this precise or accurate, so your losses are more likely to come from somewhere else and not specifically with discrepancies in thermal expansion calculations.

There are many places you lose wort volume during boiling:

  • absorption by dry hops (these absorb ca 5 times their dry weight in wort)
  • loss to trub, hot and cold break
  • losses in hoses, chiller
  • losses in deadspace in the kettle
  • evaporation

All but the last are real losses - you will see a reduction in the density*volume figure - here, you are specifically losing volume and some quantity of dissolved solids. With evaporation, density*volume remains the same, so it's not a real loss, but just a concentration of the solids that are there.

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Thanks mdma. I didn't see immediate answer so I researched further and also found that same article. I also further found a calculator (see at the bottom of that page): sugartech.com/density/index.php I came to same conclusion that it's so minor difference but the puzzling part is that all the rest of the variables were already under control so I still don't know where the error came from. – jbv Jun 4 '14 at 14:32

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