User:FrankP/Drafts/ABV

Prediction of alcohol content
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Practical estimation of alcohol content
During the production of wine and beer, yeast is added to a sugary solution. During fermentation, the yeasts consume the sugars and produce alcohol. The density of sugar in water is greater than the density of alcohol in water. A hydrometer is used to measure the change in specific gravity (SG) of the solution before and after fermentation. The volume of alcohol in the solution can then be estimated. There are a number of empirical formulae which brewers and winemakers use to estimate the alcohol content of the liquor made.

Specific gravity is the density of a liquid relative to that of water, i.e if the density of the liquid is 1.05 times that of water it has a specific gravity of 1.05. In UK brewing usage it is customary to regard the reference value for water to be 1000, so the specific gravity of the same example beer would be quoted as 1050. The formulas here assume that the former definition is used for specific gravity.

Wine
The simplest method for wine has been described by English author C.J.J. Berry:

$$ABV \approx 136 \times \left( \mathrm{Starting~SG} - \mathrm{Final~SG} \right)$$

Beer
One calculation for beer is :

$$ABV = 131 \times \left( \mathrm{Starting~SG} - \mathrm{Final~SG} \right)$$

For higher ABV above 6% many brewers use this formula :

$$ABV = \frac{1.05}{0.79} \times \left( \frac{\mathrm{Starting~SG} - \mathrm{Final~SG}}{\mathrm{Final~SG}} \right) \times 100$$

removed content
It is derived in this manner:

''1.05 is the ratio (by mass) of ethanol molecules produced for every molecule of CO2 produced (46.07 g/mol C2H6O / 44.01 g/mol CO2 = 1.0468) from a single molecule of glucose. The number 0.7936 is the specific gravity of a 100% ethanol solution . Both are unit-less measurements. The difference between the starting SG and the final SG measures the specific gravity lost to CO2 release.''
 * $$ABV = \frac{\rho_{C2H5OH}}{\rho_{CO2}} \times \frac{\rho_{H2O}}{\rho_{C2H5OH}} \times \frac{\rho_{CO2}}{\rho_{H2O}} \times 100$$
 * $$ABV = \frac{\rho_{C2H5OH}}{\rho_{CO2}} \times \frac{\rho_{H2O}}{\rho_{C2H5OH}} \times \frac{\rho_{OG}-\rho_{FG}}{\rho_{H2O}} \times 100$$
 * $$ABV = \frac{\rho_{C2H5OH}}{\rho_{CO2}} \times \frac{\rho_{H2O}}{\rho_{C2H5OH}} \times \left( \mathrm{Starting~SG} - \mathrm{Final~SG} \right) \times 100$$
 * $$ABV = \frac{46.0684}{44.0095} \times \frac{1.0}{0.78934} \left( \mathrm{Starting~SG} - \mathrm{Final~SG} \right) \times 100$$
 * $$ABV = \frac{1.04678}{0.78934} \times \left( \mathrm{Starting~SG} - \mathrm{Final~SG} \right) \times 100$$
 * $$ABV = 133.62 \times \left( \mathrm{Starting~SG} - \mathrm{Final~SG} \right)$$