Temperature: What It Means and How We Measure It
Almost nothing happens in the universe without there being a difference of temperature between two places. This suggests that most energy changes are associated with a temperature difference.
Temperature key to understanding energy processes
Electric currents flow with associated Seebeck and Peltier effects. Chemical reactions are associated with exothermal and endothermal changes. Thermal energy itself ‘flows’ from hot to cold places. Heat engines would not work without a temperature difference. Wind turbines require that temperature differences move masses of air. Hydroelectric dams require temperature differences to raise masses of water in the gravitational field. We cannot escape the idea that temperature difference is key to understanding energy processes, which is why it is so important for understanding climate change. Masses falling in gravitational fields and phase changes, such as melting and evaporating, take place at constant temperature. But how was the mass raised, and how does thermal energy flow into or out of a fluid at the phase change point?
Motions of atoms and electrons
Given that our current school level understanding of temperature is that it is the motions of atoms and electrons, it is easy to see that kinetic energy changes reflect temperature changes. From high school physics we have
KE of a molecule= 3kT
where k is Boltzmann’s constant and T is the absolute temperature. More on this later.
Change from order to disorder
Once all particles in the universe are at the same temperature, nothing further will ever happen. This is the so-called heat death of the universe, when the mean temperature will be very close to absolute zero. It is clear therefore that temperature is related to entropy, the change from order to disorder. Entropy is always steadily increasing as energy is shifted from one form to another. Indeed,
ΔU = TΔS …
which states that an energy change ΔU is given by T multiplied by the entropy change ΔS. This is our modern understanding of the concept of temperature, T= dU/dS.
History of modern understanding of temperature
The concept may seem obvious to us today, but it was not so in the past. It has taken more than two thousand years to develop our modern understanding of temperature, so let’s look a little further back in time. We owe it to doctors for those first attempts to make sense of hotness and coldness. Here I deliberately do not refer to heat, but to temperature and have avoided using the word heat when I mean hot. I have picked three great figures from the field of medicine who have influenced our thinking over the millennia: Hippocrates, Galen and Vesalius.
Hippocrates (460–370 BCE)
An ancient Greek, Hippocrates used thermographs made by laying a blanket soaked with mud over a patient and then watching to see which areas dried first. He identified four humours (384–322 BCE) and suggested that these humours — melancholy, choleric, sanguinity and phlegmatism — had to be in balance, otherwise illness results. There was no concept of temperature; a patient was simply hot or cold from touch.
Galen (130–220 CE, ancient Greek in the Roman Empire)
Five hundred years later, Galen comes on the scene. He adds to Hippocrates’ hot or cold by including four levels of sensation either side of a neutral temperature, eight levels in all. Galen achieved a neutral temperature by mixing equal amounts of boiling water and ice. He then described four degrees of cold and four degrees of hotness either side, none of it being measured. Galen used the humours developed by Hippocrates and associated each with an Aristotelian Element. Earth with melancholy, etc. It was a question of balancing temperature and humidity through adjusting the humours. In those days, many people were guided by astrology, and Galen was no exception.
It is quite extraordinary that Galen’s ideas were used for the next 1,400 years and more without anybody questioning them. Your sense of touch had to be very good to differentiate these levels, something you might want to try with your students.
Thirteen hundred years after Galen, Vesalius decides to be more scientific about his work and questions everything that Galen has written. This is the principle reason why he is so important and why I mention him here. Vesalius was strong on observation and the rejection of previous ideas, in particular those of Galen. But he still did not have a practical device for measuring temperature. Notions of temperature and heat were still in their infancy. It was still another 200 years before Fahrenheit’s mercury thermometer appeared. The first instruments for showing hotness or cold were called thermoscopes, and even these were 100 years away. They were simply bulbs with an open tube, the open end being inserted into water.
Santorio Santori (1561–1636)
An Italian, Santori made a thermoscope around 1612, possibly after a design by Galileo. These thermoscopes suffered from being barometers as well! Measurements were not at all repeatable.
J. Leurechon first used the word thermometer, 1620, in ‘Récréation Mathématiques’ — clearly an early STEM contributor! His was a calibrated thermoscope showing eight degrees, probably following the teachings of Galen. The patient kept the bulb in their mouth, driving air out. After a while, the patient removed their mouth and water would rise up in the thermoscope showing the temperature.
First sealed glass thermometer
The first sealed glass thermometer (1629) is possibly due to Joseph Delmedigo, a student of both Galileo and Santori, but he gets no credit for this from the still infant scientific society. Huygens suggested (1665) using freezing and boiling water as fixed points and received much support for this by the year 1700.
Eventually Daniel Gabriel Fahrenheit (1686–1736), a German who lived in the Netherlands, designs the first standardised thermometer scale in 1724. He used mercury and chose fixed points of freezing brine (0° F), freezing water (30° F) and body temperature (90° F). He later modified this to read 0 - 32 - 96 to make 64 degrees between 32 and 96, making scale marking easier. The scale was inscribed on the glass by a machine which kept halving the distance between the fixed points. Sixty-four is easily halved in this way all the way to a one-degree interval. Your younger students might have fun putting such a scale on a line using only a compass. The scale was further redefined so that freezing water to boiling water was exactly 180 degrees. This led to body temperature being 98.7° F.
Réaumur (1683–1757, French) and Celsius (1701–1744, Swedish)
There were others who wanted to make their mark. Réaumur built an alcohol thermometer in 1730 and devised his scale as follows. He chose one fixed point, freezing water. Then the scale was marked for each 1/1000 of volume of bulb containing the alcohol up to the zero mark. Of course, because alcohol boils at 77° C the boiling point of water was predicted to be 80° R , but I like to think that he was a little bit of a follower of Galen. Users of this thermometer and scale fixed the boiling point of water to be 80° R, regardless. This was called the octagesimal scale, as distinct from the finally successful centigrade scale of Anders Celsius.
Celsius’ original scale, 1742, which went from 0 boiling water to 100 melting snow was inverted for its modern form.
William Thomson or Lord Kelvin (1824–1907)
The Kelvin scale was proposed in 1848, 0 K being absolute zero and 273.15 being the melting point of ice. This was to bring it in line with the Celsius scale. However, in 1967 the triple point of water was used as the fixed point as it was a unique point rather than the melting point of ice which depended on pressure. The triple point of water is 0.01° C.
In 1967, the scale ranged from 0–273.16. 0 K being absolute zero and 273.16 K being the defined triple point of water. The use of the word degree has been dropped, so the units are simply kelvins.
Post 2019, the international committee on weights and measures has decided to link all the base units to defined constants of nature. This makes them all, in principle, perfectly reproducible. For temperature, the Boltzmann constant was defined exactly which means that the triple point of water has an experimental uncertainty.
k= 1.380649×10−23 J⋅K−1 exactly so that the triple point of water is now approximately 273.16001.
Now all the base units of physics are defined in terms of universal constants.
This is the Boomerang Nebula
It has a temperature of 0.5 K while the background temperature of the universe is about 2.7 K. The calculations are due to Richard Hawking and are connected with Hawking radiation. At the centre of this galaxy is a supermassive black hole with a temperature very close to 0 K but quite zero due to the Hawking radiation.
A black hole the size of the moon has a temperature around 1 K, as the temperature of a black hole is inversely proportional to its mass. This is the very antithesis of the Big Bang which started out as a phenomenally high temperature singularity. Now black holes are the modern singularity with a phenomenally low temperature. So maybe there is a connection between gravity and temperature after all, with masses moving from higher temperature regions to lower temperature regions?
The connection to the T³ network?
The king of the probes is the temperature probe. There is so much that can be done in any science or maths classroom. It is the most useful tool for many biological, chemical and physical situations. The sensitive element is a resistor in the tip of a stainless-steel tube which can be connected to a TI-Nspire™ Lab Cradle or directly to a TI-Nspire™ handheld using a Vernier EasyTemp® sensor.
Alternatively, Grove sensors, either negative or positive temperature coefficient sensors, can be connected to the TI-Innovator™ Hub which can be programmed from the TI-84 Plus CE-T family of graphing calculators or TI-Nspire™ handhelds.
Check out these classroom activities:
- Activities using temperature scales
- Simply recording temperature as a function of time is an essential feature of so many experiments, like:
- Activities on phase changes and alarms
- Mathematicians may want ways of introducing students to exponential change and Newton’s Law of Cooling
- Forensics activities using Newton’s Law of Cooling
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