Theory for Hydrometer Temperature Correction
This article describes the theory that makes it possible to use an ethanol hydrometer at temperatures other than the calibration temperature. This theory is used in the hydrometer temperature correction calculator built into the computer program AlcoDens. This calculator allows you to make rapid and accurate measurements of alcohol strength in the plant or laboratory without having to heat or cool the sample to the exact calibration temperature. See the calculator in action here.
In order to correct a reading taken at a particular temperature with an hydrometer that is calibrated for a different temperature there are three factors that have to be taken into account. These are :
- The expansion coefficient of the liquid solution
- The relationship between the density of the ethanol solution and its strength
- The expansion coefficient of the hydrometer itself
The information for the first two factors is built into AlcoDens and the expansion of the hydrometer follows a simple formula, so once we understand the theory it is a simple calculation.
The best way to clarify the theory behind this, is to break the process down into separate concepts, and to understand each one individually. Once each concept has been understood by itself, they can be combined into an understanding of the total process.
Concept 1 - Required Information
If we have a solution of ethanol and water we must know the SG and the temperature to be able to determine the strength. If we have the SG and temperature we can use alcohol tables, or graphs or AlcoDens to get the strength in Vol%. This is a simple concept and needs no further explanation.
Concept 2 - Hydrometer Calibration
Let us imagine that we have a solution of ethanol-water which we know has a strength of 20.0 Vol% and is at 15ºC. From AlcoDens or alcohol tables we know the SG of this solution is 0.97613. Also, we have an uncalibrated hydrometer. We put the hydrometer into the solution (everything is at 15ºC) and we make a mark on the hydrometer at the liquid level. What value would we allocate to this mark? We could write SG = 0.97613, or we could write Vol% = 20.0. If a manufacturer was making an alcometer rather than a general hydrometer he would mark it "Vol% = 20.0".
Concept 3 - Other liquids
Now imagine that we put this hydrometer with just the single calibration point into some other solution, say methanol and water at 15ºC, and it floats with the calibration mark exactly at the liquid surface. What does this tell us? We cannot say that its strength is 20.0 Vol% because the density of methanol is different from that of ethanol. But we can say that the SG of this methanol-water solution is 0.97613 because if we had calibrated it for SG rather than strength, this is what we would have written on the hydrometer scale.
Concept 4 - Ethanol-Water at Other Temperatures
Let us imagine a similar situation to Concept 3, but instead of an unknown solution (or a methanol solution) we know that we have a solution of ethanol and water, although we do not know its strength. But the temperature of this solution is 25ºC. We put our hydrometer into the solution and it also floats with its single calibration mark exactly at the liquid surface. Again, we cannot say that the strength of this solution is 20.0 Vol%, even though the hydrometer floats at exactly the 20.0% mark, because the hydrometer was calibrated for 15ºC solutions. But we can say that the SG of this alcohol solution is 0.97613 (just as we did in Concept 3), corrected for the very slight expansion of the hydrometer glass. The formula that describes the expansion of the glass is :
SG(true) = SG(indic) x [ 1.0 - 0.000025[ T(act) - T(calib) ]]
where
SG(true) is the corrected, true SG
SG(indic) is the SG indicated by the hydrometer
T(act) is the actual temperature of the alcohol solution and the hydrometer in ºC
T(calib) is the temperature at which the hydrometer was calibrated in ºC
this makes SG(true) = 0.97613 x ( 1.0 - 0.000025(25-15) )
= 0.97613 x 0.99975
= 0.97589
Back to Concept 1 - Required Information
For the alcohol solution in Concept 4 - we know the SG is 0.97589 and we know the temperature is 25ºC, so we can certainly get the strength from AlcoDens or alcohol tables. This tells us the strength is 17.20 Vol% at 25ºC. If we want to know the strength at any other temperature (i.e. other than at the sample temperature) we can simply use the conversion routine built into AlcoDens.
Summary
The way to look at it is that we have a solution of alcohol at (say) 25ºC and in order to know its strength we need to know its SG (Concept 1). But we do not have an SG hydrometer. All we have is a 15ºC alcometer. So we need a way to use the 15ºC alcometer as an SG hydrometer. AlcoDens allows us to do this because if we take a reading using the 15ºC alcometer we can convert that reading from a Vol% at 15ºC to an SG. We should correct this SG for the slight expansion of the glass using the formula above. Now we have the true SG and the temperature so it is a simple matter to get the strength from AlcoDens or from alcohol tables.