## Wednesday, January 23, 2013

### How to measure thermometer drift to compensate for calibration

Every measurement device has some inherent error.

An oven thermometer that I purchased recently was off by five degrees!  This doesn't mean that it is "broken" or "bad" simply that it is not accurate.  Of course the closer the display is to actual temperature will not only make use of the thermometer easier, but it will give you confidence that it is accurate at temperatures that are harder to measure for certain.

Measuring the error

Two temperatures that are easy to recreate accurately are 32°F (0°C) and 212°F (100°C)

To measure the error, bring water to a rolling boil and measure the temperature.  The thermometer I purchased recently measured 210.0°F, or two degrees low.   At sea level, liquid water can only get to 212°F before it vaporizes, making it  impossible to heat the water too much.  If you are located significantly higher than sea level, then you will need to compensate the boiling temperature with altitude.  For every 500 feet above sea level the boiling point of water drops 1 degree Fahrenheit.

Solid ice can be colder than freezing, or 32°F. If the thermometer were placed in a freezer in a glass of water the temperature measure could be bellow 32°F.  Instead, the thermometer can be placed in a glass of ice water.  Crushed ice will ensure that more of the water is in contact with ice making the temperature closer to freezing.  Putting the glass in the freezer will also get the water closer to freezing, but you'll want to take the measurement before the water freezes.

A third temperature can be recorded that is between these two.  It's not necessary, but give you a little more data to work with and will give you an idea of the accuracy of the interpolated temperatures between.  If you don't have a fever, then your body temperature, under the tongue,  should be 98.2+/-0.7°F mid morning. (1)

The simplest approach is to use the deviation at boiling for mash temperatures and use the deviation at freezing for fermentation temperatures.

Crunching the numbers.

But if you are like me and want to really geek this out, keep reading, and don't worry, you only have to do this once. The recorded deviation at boiling and at freezing can be combined to create a reasonable guess of the deviation of temperatures measured in between.  For this we need to derive a best line fit for the boiling and freezing points, and then we can use this to check the third temperature point that was measured to get a sense of accuracy.

We know two situations and have two unknowns, so this is solvable.   I'll spare you the bore of watching me lash out the algebra, and skip to the equations:

BCF = Boiling Correction Factor
FCF = Freezing  Correction Factor
MBT = Measured Boiling Temperature
MFT = Measured Freezing Temperature
CF = Correction Factor
MT = Measured Temperature
m = slope of fit
b = y intercept of fit.

CF = m * MT + b
m = (BCF-FCF)/(MBT-MFT)
b = CF - m * MT

For example, my thermometer measured 210°F at boiling, and 33°F degrees at freezing.  My body temperature measured 98.5°F.

BCF = Boiling Correction Factor = 2
FCF = Freezing  Correction Factor = -1

m = (2-(-1))/(210-33) = 0.0169
b = 2 - 0.0169*210=-1.549

We can then use this to find the correction factor at 98.5°F

0.0169*98.5-1.549=0.1157

The actual temperature would be 98.5+0.1157=98.6157 not bad.

So that I don't have to do this math every time I use my thermometer I just made an abbreviated table with correction factors for common temperatures that I measure.

(1) http://en.wikipedia.org/wiki/Human_body_temperature

#### 4 comments:

1. I just wanted to mention one caveat about using body temperature. 98.6F is an average body temperature, but it can range anywhere between 97-100F in a normal adult and can vary even in the same person based on several factors. I agree that's a convenient point to quickly check your calibration, but if you're off by a degree or two it's not really a big deal.

1. Good point Eric. I did a little reading and it seems that the standard under the tongue measurement is 98.2+/-0.7°F mid morning. I have updated the text to reflect this.

2. Can anyone tell me about any thermometer to use in my kitchen to keep checking the temperature inside? I don't know what is that specifically called!

3. Another way to measure an intermediate temperature is to mix equal volumes of boiling and ice water, the resultant temperature should be the average of the two. To avoid heat loss to the container use a styrofoam cup, it has little mass and little thermal conductivity.

Great blog, thanks for all the work!