Thunder_Chicken
Well-Known Member
Many home brewers may come to question the accuracy of their standard spirit thermometers. I just went through the process of calibrating my thermometer, which I found was quite inaccurate without a proper calibration. I wanted to share the procedure and findings so others can accurately measure their homebrew process temperatures with confidence.
The Thermometer
My thermometer is a spirit thermometer provided by Brooklyn Brewshop in their starter kits (picture below). It has a range from 0 °F to 230 °F with a resolution of 1 °F.
The Problem
I noticed that this thermometer differed from the room thermostat by as much as 4 °F, but it seemed that the thermostat temperature felt closer to right. I was concerned that my fermenter temperatures, hydrometer corrections, mash temperatures, etc. might be off, so I proceeded to calibrate my thermometer.
The Calibration
In the range of this particular thermometer there are two thermodynamic reference points that can be used, the freezing/melting point and the boiling point of water. At an atmospheric pressure of 1 atmosphere, the freezing point of water is 32 °F and the boiling point is 212 °F. These temperatures vary with pressure, so if you live at high elevations you will need to determine these temperatures at the appropriate atmospheric pressure. I live at sea level so the above temperatures are appropriate for me.
Freezing/Melting Point Reference
The freezing/melting point is defined as the temperature at which liquid water and ice are in equilibrium. A reference can be measured by putting your thermometer in an ice/water mixture. For best results use shaved ice or snow and make a slushy mixture vs. using ice cubes.
Boiling Point Reference
The boiling point is defined as the temperature at which liquid water and vapor are at equilibrium. For this reference I simply used my tea kettle. I got the water to a rolling boil and immersed my thermometer in the water, taking care to not touch the kettle itself. Note that most thermometers have a minimum immersion depth (usually marked with a line).
The Data
My measured melting/freezing and boiling point temperatures are shown below next to their reference values:
Melting Point
Measured 34 °F / Actual 32 °F
Boiling Point
Measured 226 °F / Actual 212 °F
Note that the measured boiling point was 14 °F higher than the actual value! Not the greatest thermometer in the world, but no worries, we can still correct these measurements to get accurate temperatures.
The Correction
What we want to do with the above temperatures is get an equation where you can calculate the actual temperature based on the measured temperature from your thermometer. Since we only have two points, we'll use a linear correction.
Tactual = m × Tmeasured + b
If you remember your grade school math, m is the slope (rise divided by run) of the line created by plotting the actual temperatures against the corresponding measured temperatures, and b is the actual temperature when the measured temperature would be zero.
For my data:
m = (actual difference between boiling and melting)/(measured difference between boiling and melting)
m = (212 °F - 32 °F)/(226 °F - 34 °F) = 0.9375
I can get b by plugging in m and either the actual/measured boiling points or melting points and solving for b. I'll use the melting point temperatures.
Tactual = m × Tmeasured + b
32 °F = 0.9375 × 34 °F + b
b = 32 °F - 0.9375 × 34 °F or 0.125 °F
So the correction equation for my thermometer is:
Tactual = 0.9375 × Tmeasured + 0.125°F
where all the temperatures are in °F.
All of this can also be done in Excel simply by plotting your actual temperatures against the measured values and fitting a linear trendline (see plot below). This procedure will work for Celsius thermometers as well, just remembering that the melting/freezing point is 0 °C and the boiling point is 100 °C at sea level.
So now if I measure 72 °F on my thermometer, I can determine the actual temperature by running it through the equation:
Tactual = 0.9375 × 72 °F + 0.125°F
Tactual = 67 °F
By the way, this turns out to be the difference between my thermometer and my thermostat, which was indicating closer to the true room temperature.
The Application
The above is all good, but we need to be able to hit target temperatures during the mash and aim for correct temperatures during fermentation, and we don't want to be doing math while we are mashing. So we have a reverse problem - if I want to ensure the actual temperature is Y, what number do I need Z to see on my thermometer?. To do that, we just take our correction equation and turn it on its head.
So let's say that I want the actual temperature during my mash to be 155 °F, what temperature do I need to be reading on my thermometer? Well, I just put 155 °F in as the actual temperature in my equation, do the algebra and solve for the measured temperature:
Tactual = 0.9375 × Tmeasured + 0.125°F
155°F = 0.9375 × Tmeasured + 0.125°F
Tmeasured = (155°F - 0.125°F)/0.9375 = 165 °F
So if I want to maintain an actual temperature of 155 °F, I need to be reading 165 °F on my thermometer. This is a 10°F difference which would be terrible during mash as I would be too cool by 10°F if I did not correct! You can do all this math prior to your mash. If you plot the correction equation on a graph with gridlines, you can pick these temperatures off the graph visually.
So Why Does my Thermometer Suck So Hard?
You'll notice that my thermometer readings are OK at lower temperatures and grow progressively worse at higher temperatures. Note that the correction at 0°F is only 0.125°F (which is less than the resolution), grows to 2°F at 32°F, and up to 14°F at 212°F. The reason for this has to do with how these thermometers are mass produced.
In a perfect world the bore of the thermometer would be an exact dimension, so when you heated the spirit it would expand by a fixed amount and would therefore travel a fixed distance up the stem. The scale printed on the thermometer is marked assuming this is the case.
In reality, making a bore of a consistent specified dimension is very difficult to do. In some thermometers the bore will be a little too big, some a little too small. If the bore is too big and the spirit is heated and changes volume by a fixed amount, its level won't rise as high as indicated on the scale. If the bore is too small, the level will rise higher than indicated on the scale.
This is described by the slope of the correction m. In my thermometer, the cross sectional area of the bore is approximately 0.9375 or 93.75% of the area it should be to indicate correctly with the printed scale.
Conclusion
With a simple calibration procedure possible using ice and boiling water in your kitchen and a little math you can correct the readings from truly poor and cheap thermometers to give you accurate measurements of temperature in your homebrewing endeavors.
Good luck and RDWHAHB!
The Thermometer
My thermometer is a spirit thermometer provided by Brooklyn Brewshop in their starter kits (picture below). It has a range from 0 °F to 230 °F with a resolution of 1 °F.
The Problem
I noticed that this thermometer differed from the room thermostat by as much as 4 °F, but it seemed that the thermostat temperature felt closer to right. I was concerned that my fermenter temperatures, hydrometer corrections, mash temperatures, etc. might be off, so I proceeded to calibrate my thermometer.
The Calibration
In the range of this particular thermometer there are two thermodynamic reference points that can be used, the freezing/melting point and the boiling point of water. At an atmospheric pressure of 1 atmosphere, the freezing point of water is 32 °F and the boiling point is 212 °F. These temperatures vary with pressure, so if you live at high elevations you will need to determine these temperatures at the appropriate atmospheric pressure. I live at sea level so the above temperatures are appropriate for me.
Freezing/Melting Point Reference
The freezing/melting point is defined as the temperature at which liquid water and ice are in equilibrium. A reference can be measured by putting your thermometer in an ice/water mixture. For best results use shaved ice or snow and make a slushy mixture vs. using ice cubes.
Boiling Point Reference
The boiling point is defined as the temperature at which liquid water and vapor are at equilibrium. For this reference I simply used my tea kettle. I got the water to a rolling boil and immersed my thermometer in the water, taking care to not touch the kettle itself. Note that most thermometers have a minimum immersion depth (usually marked with a line).
The Data
My measured melting/freezing and boiling point temperatures are shown below next to their reference values:
Melting Point
Measured 34 °F / Actual 32 °F
Boiling Point
Measured 226 °F / Actual 212 °F
Note that the measured boiling point was 14 °F higher than the actual value! Not the greatest thermometer in the world, but no worries, we can still correct these measurements to get accurate temperatures.
The Correction
What we want to do with the above temperatures is get an equation where you can calculate the actual temperature based on the measured temperature from your thermometer. Since we only have two points, we'll use a linear correction.
Tactual = m × Tmeasured + b
If you remember your grade school math, m is the slope (rise divided by run) of the line created by plotting the actual temperatures against the corresponding measured temperatures, and b is the actual temperature when the measured temperature would be zero.
For my data:
m = (actual difference between boiling and melting)/(measured difference between boiling and melting)
m = (212 °F - 32 °F)/(226 °F - 34 °F) = 0.9375
I can get b by plugging in m and either the actual/measured boiling points or melting points and solving for b. I'll use the melting point temperatures.
Tactual = m × Tmeasured + b
32 °F = 0.9375 × 34 °F + b
b = 32 °F - 0.9375 × 34 °F or 0.125 °F
So the correction equation for my thermometer is:
Tactual = 0.9375 × Tmeasured + 0.125°F
where all the temperatures are in °F.
All of this can also be done in Excel simply by plotting your actual temperatures against the measured values and fitting a linear trendline (see plot below). This procedure will work for Celsius thermometers as well, just remembering that the melting/freezing point is 0 °C and the boiling point is 100 °C at sea level.
So now if I measure 72 °F on my thermometer, I can determine the actual temperature by running it through the equation:
Tactual = 0.9375 × 72 °F + 0.125°F
Tactual = 67 °F
By the way, this turns out to be the difference between my thermometer and my thermostat, which was indicating closer to the true room temperature.
The Application
The above is all good, but we need to be able to hit target temperatures during the mash and aim for correct temperatures during fermentation, and we don't want to be doing math while we are mashing. So we have a reverse problem - if I want to ensure the actual temperature is Y, what number do I need Z to see on my thermometer?. To do that, we just take our correction equation and turn it on its head.
So let's say that I want the actual temperature during my mash to be 155 °F, what temperature do I need to be reading on my thermometer? Well, I just put 155 °F in as the actual temperature in my equation, do the algebra and solve for the measured temperature:
Tactual = 0.9375 × Tmeasured + 0.125°F
155°F = 0.9375 × Tmeasured + 0.125°F
Tmeasured = (155°F - 0.125°F)/0.9375 = 165 °F
So if I want to maintain an actual temperature of 155 °F, I need to be reading 165 °F on my thermometer. This is a 10°F difference which would be terrible during mash as I would be too cool by 10°F if I did not correct! You can do all this math prior to your mash. If you plot the correction equation on a graph with gridlines, you can pick these temperatures off the graph visually.
So Why Does my Thermometer Suck So Hard?
You'll notice that my thermometer readings are OK at lower temperatures and grow progressively worse at higher temperatures. Note that the correction at 0°F is only 0.125°F (which is less than the resolution), grows to 2°F at 32°F, and up to 14°F at 212°F. The reason for this has to do with how these thermometers are mass produced.
In a perfect world the bore of the thermometer would be an exact dimension, so when you heated the spirit it would expand by a fixed amount and would therefore travel a fixed distance up the stem. The scale printed on the thermometer is marked assuming this is the case.
In reality, making a bore of a consistent specified dimension is very difficult to do. In some thermometers the bore will be a little too big, some a little too small. If the bore is too big and the spirit is heated and changes volume by a fixed amount, its level won't rise as high as indicated on the scale. If the bore is too small, the level will rise higher than indicated on the scale.
This is described by the slope of the correction m. In my thermometer, the cross sectional area of the bore is approximately 0.9375 or 93.75% of the area it should be to indicate correctly with the printed scale.
Conclusion
With a simple calibration procedure possible using ice and boiling water in your kitchen and a little math you can correct the readings from truly poor and cheap thermometers to give you accurate measurements of temperature in your homebrewing endeavors.
Good luck and RDWHAHB!
