Thermometers, Barometers, and Vacuums¶
Introduction¶
Before thermodynamics could even begin, it was imperative that we discover a way to accurately measure temperature. Along with this, we needed to understand vacuums and barometers.
Critical Concepts¶
In order to build a functioning thermometer, the following are needed:
A way to measure the temperature, specifically, the effect temperature has on matter.
Understanding that things (gasses, liquids, especially) expand when their temperatures rise.
A way to calibrate temperatures such that two thermometers will agree on the calibration points.
A way to subdivide thermometers such that different types of thermometers will agree on temperatures in between.
A barometer relies on the following critical insights:
That vacums can be created (easily.)
That vacuums do not suck. Air pressure pushes.
Classical Greeks¶
Empedocles in “On Nature” wrote about how the universe is composed of four atomic elements and two forces. These forces he called “love” and “strife” and either brought the elements together into beautiful and complete harmony or drove them apart into isolation from one another. It is said that early ideas about how the volume of a gas relate to the temperature are connected here. Perhaps Empedocles would say that temperature is the amount of “strife” and that is what causes the gas to expand.
Aristotle is also highly valued for his thoughts, which included the following:
That hot and cold are not substances, but attributes of the four classical elements (along with dry and wet).
That vacuums can’t exist because ‘nothing’ is a contradiction of itself.
That the air has no pressure because it has no weight.
After the classical period, we meet one Hero of Alexander, a famous inventor. Among his inventions is not found the thermoscope (which we will describe later), but is found mention of the fact that rising temperatures causes gasses to expand. This is the core operating principle behind the thermoscope.
Galileo and the Thermoscope¶
No one can say exactly who invented the thermoscope or when it was first made, but Galileo Galilei takes credit for himself. The date for the construction of the first thermoscope is 1593, although it isn’t clear if Santorio Santorio invented or created it first. Regardless, in Galileo’s day, you could buy a thermoscope at the markets.
A thermoscope is a rather simple device. A glass bulb with a long neck is filled with a little water and then inverted into a reservoir of water. As the temperature rises, the gas expands (while the water changes very little) and the water falls. As the temperature drops, the gas contracts (and the water changes very little) and the water rises.
If you want to measure freezing temperatures, that’s rather easy. Add alcohol to the water, or just use red wine, and you can not only easily see the water level, but it won’t freeze in sub-zero conditions.
Althought this device does record temperature, it also records the air pressure. If the temperature remains the same but the pressure rises, then the water level will rise as well, which looks like the temperature is falling. Conversely, if the pressure drops then the water will fall, which looks like the temperature is rising.
At this time, no concern over this flaw was made because everyone “knew” that there was no air pressure because air had no weight. Aristotle had proven that a long time ago. It’s a simple experiment, just grab and empty glass of air and weight it against another empty glass of air, and air weighs nothing.
Throughout the early 1600s, people were making various thermoscopes and some even started to mark the glass tube to note how the temperature was changing. No effort, however, was made to calibrate these thermoscopes with each other.
The first clear diagram of a thermoscope is courtesy Giuseppe Biancani in 1617. It was Robert Fludd in 1638 who added a scale to the long tube in his drawing, although Francesco Sangredo or Santorio Santorio are reported to have added scales to theirs in either 1611 or 1613.
In 1629, Joseph Solomon Delmedigo, under Galileo, drew a diagram and explained a new type of thermoscope that was sealed at both ends, and thus isolated from the atmospheric pressure, though he didn’t take credit for the idea. (It wouldn’t be until 1644 that anyone would propose that there was any atmospheric pressure at all.) I don’t know if Delmedigo was simply trying to build a consistent thermoscope but I doubt he knew that the air pressure would vary from time to time and day to day.
Vacuums¶
In the late summer of 1630, Giovanni Battista Baliani wrote the famous Galileo Galilei reporting that he was unable to create a siphon that could lift water over a certain height.
A siphon is a child’s trick. Take a hose, fill it with water, and water can flow from a greater height to a lower height. This can be an ideal solution to, say, drain a mine, or the foundation of a building before the foundation is laid.
Siphons do work, to a point. If you lift the middle part of the siphon too high, it will no longer work. The reason why, we know today, is because a vacuum is created when the water reaches a height of about 30 feet.
Troubled by this phenomena, and unable to find a way to avoid it, Baliani begged Galileo for help. He needed to move water over a hill that was too tall for the siphon to work. Surely Galileo would know what to do!
Galileo, educated and familiar with the ancient philosophers, reported that it was horror vacui that caused water to rise to fill the vacuum created by the siphon, an idea reported by Aristotle 2,000 years earlier. Galileo surmised that perhaps vacuums couldn’t suck beyond a certain limit, that their strength was thus limited. So Galileo did correctly report that a vacuum was being created, but he didn’t quite grasp the concept of how vacuums worked.
Eight years later, in Rome, Raffaele Magiotti and Gasparo Berti undertook the challenge to create a better vacuum, this time without siphons. With Magiotti’s ideas, Berti created a long tube of glass, sealed at one end. Filling it with water, submerging it in a tub of water, when you put the sealed end up, and allowed the water to flow out the other end, it would create a vacuum. The water would sit at a precise height above the water level, and no higher, no matter how you arranged the sealed end.
Torricelli correctly reasoned in 1644 that it wasn’t that vacuums sucked; it was that the atmosphere created pressure to push the water up the tube. His ideas were revolutionary. Aristotle and Galileo both believed that air had no weight, and thus there was no pressure. At a suggestion of Galileo, Torricelli did his experiments with mercury, to keep it hidden from the public, due to accusations of sorcery and witchcraft. You’d need a large building to do the experiments with water, but with mercury, only need a few feet.
The debate about what exactly was created at the top of the tubes were raging at the time. Those who were sure Aristotle was right asserted that there was no vacuum, just vaporized air. It was Blaise Pascal in 1646, along with Pierre Petit, who took Torricelli’s experiment on to prove the Aristotleans wrong. Inviting them to make a prediction of whether wine or water would rise higher or lower, they predicted that wine would rise lower, due to its spiritous nature. Pascal performed the experiment, and they both rose to the same height. This showed that the vacuum was not evaporated water or wine – it was nothing at all.
Pascal wrote to his brother-in-law Florin Perier, who lived near the mountain Puy de Dome, asking him to perform the same experiment, carefully measuring the height of the mercury, as he ascended the slopes. If the atmosphere did indeed have weight, and it was pressure that caused the mercury to rise, then he predicted that the mercury would be lower at higher elevations. After carefully performing the experiment in 1646, Perier reported to Pascal that he was right.
This device – the barometer – is still used today, and you can create your own rather easily. I encourage you to take Pascal’s challenge, and calculate for yourself the pressure at various elevations.
In order to create a barometer, you’ll need mercury, but any liquid will do, provided you have enough vertical height. Create a tube that is rigid and won’t collapse on itself. PVC pipe can work, but so can glass tubes. Fill the pipes or tubes with water, then seal one end off. Being careful not to allow any air inside, keep the open end at the bottom in a reservoir where the excess liquid can pour into or flow in from.
You should see the liquid will rise to a specific height. Raising or lowering the tubes or pipes will not change the level to which it rises. It will always be the same height over the reservoir.
Blaise Pascal takes credit for convincing the world that vacuums do exist and that vacuums don’t suck. It is the air pressure pushing the liquid up the tube.
1646 is an important year: Not only do we have accurate barometers, but we know that vacuums exist and they do not suck.
Back to Thermometers¶
In either 1641 or 1654, Ferdinando Il de’ Medici created the first completely sealed thermometer. This thermometer didn’t change depending on the high and low pressures of the day, or the elevation of the thermometer. It truly measured only temperature. As temperatures rose, the liquid expanded. As it fell, it contracted.
Putting the liquid into a bulb and having a narrow tube meant that tiny changes in volume could easily be noted. More volume means a tiny change in the fraction of the volume is larger than with a smaller volume. And a narrow tube means that tiny changes in volume translate to large changes in height.
Now that thermometers could be built independent of atmospheric pressure, the race was on to build more and more accurate ones, and develop a standard scale.
In 1665, Christiaan Huygens proposed using the melting and boiling points of pure water as a standard. In 1694, Carlo Renaldini suggested fixing them to a scale. In 1701, Isaac Newton proposed a scale of 12 degrees between the melting point of water and body temperature. In the same year, Ole Christiansen Romer proposed his own scale with 7.5 degrees the melting point of pure water and 60 degrees the boiling point.
It wasn’t until 1714 that Daniel Gabriel Fahrenheit was able to manufacture accurate and reliable thermometers. His thermometers used mercury, rather than water or alcohol. In 1724 he proposed the Fahrenheit scale. Building on Romer’s work, he invented his own scale, calibrated to the coldest temperature obtainable (0 degrees for melting salt water) and the human body temperature.
Fahrenheit chose 180 degrees between the melting point and boiling point of water because 180 is a highly divisible number. Note that at this time we were thinking of “degrees” the same way we think of angles and times of day. I don’t think Fahrenheit conceived of the notion that the temperature scale had an absolute zero at this time.
1714 is an important year in thermodynamics. It marks the beginning of the era of precision thermometry.
Not long after, Anders Celsius proposed a scale with 0 at the boiling point and 100 the melting point of water – exactly opposite of the scale that bears his name today. In 1743 Jean-Pierre Christin independently suggested the opposite – 0 at the melting point, and 100 at the boiling point. After Celsius passed in 1774, Carl Linnaeus reversed Celsius’ scale. Since then, we have called it “centigrade”. In 1948, we renamed it “Celsius” in his honor.
Why did Celsius propose 100 as the freezing point and 0 as the boiling point? This seems silly to us today but remember that Celsius grew up with thermoscopes. Thermoscopes measured the expansion and contraction of a gas at the top of the device, and so a lower reading meant a higher temperature.
Calibrating In Between¶
It’s not immediately clear why we’d need consistent marking points between 0 and 100 on a thermometer. Just measure things out neatly, and there you go, right?
However, not all things expand proportionally the temperature over all temperatures. Notably, water expands right before it freezes.
Thankfully, mercury (and glass) are relatively constant over the temperature ranges we’re considering. This fact meant that Fahrenheit’s thermometers were much more accurate for the in-between temperatures than the water or alcohol thermometers. Note that Fahrenheit wasn’t just calibrating his thermometers between two points, he was using several points, which helped him to better calculate consistency for a wider variety of temperatures.
If you want to calculate the thermal expansion of mercury, it’s impossible to do so with a thermometer. Instead, you have to measure the mercury as various amounts of heat are added in a carefully controlled environment. This is a topic that goes beyond this video and into calorimetry and other fundamental concepts in thermodynamics.
It’s lucky that we live in a temperature range where mercury is so consistent and effective. Had it not been so, I think thermodynamics would’ve taken a lot longer to figure out.
Absolute Zero¶
The temperature scales we have seen so far are completely arbitrary. There is no physical phenomena that applies to all substances in the same way.
In order to get there, we need to find “absolute zero”, the minimum temperature that can exist in the universe. anything below this temperature is ridiculous and insane, a contradiction just like dividing by zero.
Robert Boyle in 1665 published “New Experiments and Observations Touching Cold.” In this work, he discusses the idea of primum frigidum, the idea that there is an ultimate cold. Based on Aristotle’s ideas, cold is assigned to water and earth, so it was a matter of debate whether water or earth was colder. Using logical and rational reasoning, he concluded that there must be some ultimately cold object from which all cold flows, a sort of “anti-sun”.
In 1702, Guillarme Amontons, investigating his own thermometer measuring temperature with the expansion of a gas, theorized that there was an absolute zero, a point at which the gas would have zero volume and zero pressure. His instruments were very inaccurate but he was able to estimate where this temperature lie – at minus 240 celsius according to his estimates in his notation. Although Amontons knew it was silly to try and create absolute zero, and thus never attempted to calculate it, we can derive his estimates based on his notes.
In 1740, George Martins estimated absolute zero to lie at -431 Fahrenheit, which is close but still off by a large amount. In 1779, Johann Heinrich Lambert estimated -270 C, which is off by only a few degrees.
Others were making their own estimates, and they were off by a huge amount. In 1780, Pierre-Simon Laplace and Antoine Lavoisier wrote that it lie at about -1500 C or -3000 C, but definitely below -600 C, a ridiculous value with today’s understanding. In 1808, John Dalton gave ten calculatiosn for absolute zero, and arrived at -3000 C as his best estimate.
William Thomson, later made Lord Kelvin, combining the findings of Joule and Carnot and careful observations by Regnault, arrived at the remarkably accurate -273 C. Although this was not accepted, since his time the various estimates by various people put it between -271 C and -274 C, and this debate raged into the 1900s! It wouldn’t be until 1954 that Thomson’s work was accepted and we created a new scale in his name, Kelvin.
1848 is also an important year. It marks when we first accurately calculated absolute zero.
Other Temperature Scales¶
There are other scales proposed but forgotten. I won’t mention them here. If you use them, then you should know how to convert between it and Celsius, but oftentimes this is unnecessary as you can simply buy a thermometer with the right units if you need it.
Today¶
Today, we make thermometers out of all sorts of things. Nowadays we use infrared sensors to calculate temperature based on blackbody radiation. We also use thermocouples which rely on the fact that there is a small voltage between two different kinds of metals that relates to the temperature.
Without accurate thermometers and barometers, further research into thermodynamics is impossible. It is thanks to these early pioneers who figured how to make accurate and reliable thermometers and understood the principles behind them that we were able to get to where we are today.
