This week we’ll be taking a break from data science to have some fun looking at measurement again. Other posts in this series include rice cups that come with rice cookers, paper measurements, and rulers.
Autumn is rapidly coming to NYC and the weather is getting noticeably chillier with each passing day. With that increasing sense of cold, I started pondering about temperature — specifically, how are thermometers all around the world reliably calibrated to the same scale.
Temperature is one of the most important measures in the world. It’s obviously important in weather, but also medicine, food preparation, chemistry, manufacturing, and tons more. We take it for granted that we can buy a thermometer for practically no money and it’ll give a usable temperature. Spend a tiny bit more and you can have very accurate temperature for things like cooking or checking our body temperature.
But how is temperature defined in terms of measurement? How do we know our thermometers are accurate and can rely on the readings? How do we know that my 25 degrees Celsius is the same as everyone else’s?
This is relevant even today because sometimes, despite how thermometers are ubiquitous, measurement errors matter. My most favorite example comes from 2013, when the record for hottest temperature recorded on Earth (56C, 136.4F from El Aziza, Libya on Sept 13, 1922) was invalidated after an investigation by meterologists looking at records from the site and also from surrounding areas. It’s a good story about data quality verification, thermometer standards from the 1800s.
The record was then given to Death Valley, California at 54.6C, 134F, recorded in July 10, 1913. (Though Wikipedia states that there’s an investigation in the 1913 record as to whether irregularities exist in THAT reading too.)
tl;dr — Someone analyzing temps from surrounding weather stations at the time noticed that the record didn’t seem right. Further investigation, including finding the original handwritten records, showed that someone inexperienced at recording weather data made numerous mistakes in the data entry — most importantly they misread the markings on the thermometer giving a 2 centigrade boost to all high temperature readings
Calibration starts simple…
I’m sure clever readers might remember their high school chemistry classes and realize that there is a very common way to calibrate a typical thermometer in the comfort of our own homes — use the phase changes of water. Specifically, if we boil water, or make ice water, we have ready access to 2 reference points on the Celsius scale.
Due to how phase changes work in materials, water that is boiling stays at 100C until it has all converted to steam, and ice water stays at 0C until it has all frozen or all the ice melts. This property creates what are called fixed points that we can use to reference our thermometers. Stick a thermometer with no markings into boiling water and whatever reading it settles at is (well, should be) 100 degrees Celsius. Take the same thermometer and stick it into a bucket of ice water, and that reading is 0 degrees Celsius. Take the two marks that you have, divide it evenly into 100, and you have a Celsius scale. You can also extend the evenly spaced markings above and beyond your fixed points. Note that when you do this, you are making a very important assumption that your thermometer works linearly between the two fixed points.
With all that done, you’ve got a functioning thermometer. By setting two points and filling in all the measurements in between, we’ve actually gone beyond calibrating the thermometer, which is comparing it to a standard, to realising a temperature scale. Our realisation isn’t nearly as good as the one made in a metrology lab, but it’s still very usable.
Then, water gets complicated…
But let’s say we want to get Even More Serious(tm) about realising our temperature scale. We want to get it as close as we can to what scientists around the world use. How would we go about it?
If you recall even more chemistry or physics, you might’ve spotted the white lie in the calibration story above. The boiling and freezing points of water change depending on conditions like the purity of the water and the ambient air pressure. This is why we salt our roads in the snow and have to adjust cooking procedures at high altitude. Our “fixed” points aren’t really fixed.
So instead of merely specifying a standard pressure, temperature calibration using water relies on the “triple point” of water, a specific combination of temperature and pressure that allows water vapor, ice, and liquid water to exist at once. Any deviations from that temperature point would push one of the states out. For pure water, this point found at 273.16 K (0.01 °C) at 0.611657 kPa (0.00603659 atm).
As for purity, the standard is an extremely specific type of pure water known as “Vienna Standard Mean Ocean Water” (VSMOW). It’s a specification of pure distilled water that has a specific ratio of rare isotypes of hydrogen and oxygen. “Vienna” comes from where the body that governed this was based. It’s called “mean ocean water” because it was made from ocean water samples collected from around the globe, thus getting an average sampling of isotopes. The reason “mean” and “ocean” need to be specified is because the ratio of isotypes vary depending on if the water is from the ocean, or in the atmosphere, or rain, not to mention the location of the earth it’s on. This is true even if the water has been highly distilled so that there’s no impurities in it. The specific balance of isotopes does actually have an effect on the triple point temperature.
Measurement of a triple point to the the exactly correct reference temperature takes a lot of work, and is usually done with the help of a triple point cell. It’s a sealed container of pure water under specific pressure that’s used to measure the triple point. A brief explanation of how to use one to get a reference temperature from NIST in a 2min video. It requires the liquid in the cell to be briefly frozen, then the layer of ice is briefly let alone just under the triple point temperature for 10 whole days to anneal. Finally, the measurement area is warmed briefly to induce the liquid phase again to find the triple point which a thermometer can be set against.
Now we need more fixed points…
Hopefully you’ve noticed that water only has one triple point (for vapor, solid, liquid states — it has other triple points for various combinations of ice and vapor phases). This means we need at least one other reference point to make our Celsius scale.
To make things even more complicated, there are many more temperatures beyond 0C and 100C. The further we get away from our reference points, the more likely very tiny deviations in the linearity of our thermometers will pile up to a measurable error. We need fixed points for a much wider range of temperatures, from down to absolute zero all the way up to when things burn and turn to plasma.
To get that, we have the International Temperature Scale of 1990 (ITS-90), a standard that (among other things) defines 14 fixed reference points for temperature, as well as defining the complicated (potentially non-linear!) formulas used to interpolate temperatures between the fixed points. It’s the guide to realizing the best temperature scale that science can offer. Inside, you can see that the next higher fixed point after the triple point of water at 0.01C is the melting point of gallium at 29.7646C.
Side note — we normally think of freezing and melting points to be the exact same thing, but ITS-90 makes them distinct. Melting point is when heat is entering the sample, and freezing point is when heat is leaving the sample. This makes it unambiguous from which direction you’re supposed to approach that point.
Oh, and we’ll need a reference thermometer too
Remember how in our the definition of the temperature scale takes the measurements of 2 fixed points and then assumes a linear interpolation for all the degrees in between the points? That means we need a thermometer that exhibits this linearity as best as possible. Not just any thermometer will do if we’re making a reference to judge all our other thermometers from.
Enter the platinum resistance thermometer and the official ITS-90 guide to realizing temperature scales using such a thermometer.
In the temperature range from the triple point of equilibrium hydrogen (13.8033 K) to the freezing point of silver (1234.93 K), the ITS-90 is defined in terms of the temperature dependence of the electrical resistance of standard platinum resistance thermometers (SPRTs). — pg. 5 “Guide to the Realization of the ITS-90, Platinum Resistance Thermometry”
These thermometers essentially work by the simple physical property that as the temperature of an material changes, its resistance changes. Platinum just happens to be a noble metal (so it resists contamination/oxidation) as well as exhibiting a very linear relationship between resistance and temperature over a very wide range (13.8K to 1234.0K!). These platinum thermometers come with a specified ohms/temperature unit rating, so in theory you can get a very accurate calibration with just one cell.
With these thermometers and the fixed point cells on hand, if we follow the procedures laid out in the guides, we have the ability to calibrate the platinum thermometer to within ~50 microKelvin (according to NIST) of the true physical triple point temperature.
That allows us to use the platinum thermometer to be our reference for other thermometers. For example if we put all the thermometers into a large even-temperature ice bath, we can compare all the values and know how much our individual thermometers deviate from the standard. (Side note, I’m somewhat sure there must be better, safer, ways to do this comparison for such expensive equipment. I just haven’t found the exact procedure yet.)
But wait, there’s STILL more! SI Units changed in 2019!
No good metrics story would be complete without a complete redefinition of everything we once believed was true.
What happened was that in 2019, the definition of the SI Units had changed. For many years, scientists have been trying to end the reliance on physical objects as the foundation for units. The platinum bar that defined the meter from 1893 to 1960 was replaced by a measurement based on a universal physical constant — the speed of light. The kilogram was the famous last holdout because it took years of work to replace the heavy chunks of platinum (that over time started drifting apart from each other in weight for an unknown reason) with a watt balance.
NIST also has a brief page w/ pictures explaining the present realisation.
The way to get rid of the artifact-based definitions, from my understanding, involves setting the definition of a specific physical constant to be a set value, thus letting the physical measurement have measurement error. This reverses the older situation where we used to say “this bar IS the meter, exactly. If we shave a centimeter off of it, then all our rulers and the Earth’s circumference changes.”. We don’t notice these changes day-to-day because the value of the constants are chosen so that it doesn’t cause noticeable changes in the practical units in life. It only really matters in high precision activities.
But in the redefinition, the Kelvin, which used to be defined specifically against the triple point of water in the old system, is now defined against the Boltzmann constant, which is defined as Joules/Kelvin and ultimately defined against the kilogram, meter, and second. So with the redefinition of the kilogram, the CGPM, the governing body of the SI units, decided to redefine temperature through the Boltzmann constant which became a fixed defined value.
This meant that the triple point of water stopped being the exact measurement that defined the Kelvin and instead became a very close realization of the “true Kelvin”. Luckily, it appears that the redefinition of the Kelvin has no practical effect on the status of ITS-90 (see pg. 4, section 4). The change seems to be within the measurement error bars of the existing standard. The new definition seems to allow for potentially better temperature definitions outside of the range of the platinum resistance thermometer in the future as technology improves.
Putting it all together
So there you have it, our everyday thermometers and even the ones used to measure the weather can be compared against reference thermometers. Those reference thermometers can ultimately trace their measurement lineage back to fixed point cells and platinum resistance thermometers that conform to ITS-90 which materialize the theoretical concept of the temperature scale. Finally, the whole system now rests upon the definition of the meter, second and kilogram, which as of 2019 are all defined against physical constants of nature that are defined exactly.
Simple!
About this newsletter
I’m Randy Au, currently a Quantitative UX researcher, former data analyst, and general-purpose data and tech nerd. The Counting Stuff newsletter is a weekly data/tech blog about the less-than-sexy aspects about data science, UX research and tech. With occasional excursions into other fun topics.
All photos/drawings used are taken/created by Randy unless otherwise noted.
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