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I homebrew my own beer and I'm looking for way to cheaply monitor the specific gravity of my brew during the fermentation process. I came across this thread that seems to indicate capacitance may be used to determine specific gravity. Is there a direct relationship between the dielectric constant and/or capacitance of a liquid and its specific gravity?

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Can't you float it in something? –  Ron Maimon Aug 21 '11 at 19:30
    
I could float a hydrometer in there and attempt to measure that with some sort of optical or buoyancy reading but the problem with that approach is that the liquid level changes during the different stages of fermentation. –  Eric Ryan Aug 21 '11 at 22:03
    
I think this is a great example of engineering vs. physics actually. If we're talking about a process, we can't exactly put limits on the scope of material values it will change, but we can't guarantee it either. I don't doubt that such measurement methods could be successful, but it would depend on a litany of situation-specific things. –  AlanSE Aug 21 '11 at 22:12
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2 Answers

In general, no. Specific gravity refers to the density of a substance - how heavy a liter of it is. Dielectric constant refers to the response of the substance to an electric field, which depends on the chemistry of the substance. They are not physically related in any obvious way. It is possible to find two liquids with very similar densities and different dielectric constants or very similar dielectric constants and different densities.

It may be possible to find useful correlations between dielectric constant and density if you already know a lot of other information about the substances involved, as you might with beer. The nature of the correlation would probably need to be empirically determined (i.e. sample many batches of beer, measure explicitly both dielectric constant and density, and search for a correlation.)

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Good answer. One addendum: If the goal is just to know when fermentation is over, this measurement may work anyway. Even if you don't know the exact relation between the measured quantity and density (or anything else), it may be the case that the measured quantity varies significantly during fermentation, and it's pretty definitely the case that it stops varying after fermentation is over. So measuring this quantity and seeing when it stops changing would probably tell you when fermentation's over. But if it's important to know density in particular, then Mark's right that you need more. –  Ted Bunn Aug 21 '11 at 18:42
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I would agree with mark. There most likely is a correlation for any specific liquid. If you track the specific gravity and the capacitance for one batch it may provide a relationship for the future. However I would imagine the constant to relate the two would even vary between different beers.
Im meeting with someone today who has done postdoctoral work in Organic Chem. Ill ask her.

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Yeah she agreed there should be a correlation but no way to discover it except experimentally. She told me she would ask her husband if the relationship should be linear or quadratic or what. I'll keep you posted. –  Grey Aug 22 '11 at 14:06
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