Physics Rediscovered #13: The death of caloric
And the birth of modern thermodynamics
Are you hot? You’re reading this, so I think you’re a 10/10.
Regardless, you should feel hot, because we are going deeper down the rabbit hole of thermodynamics and that brings us closer to the core of how we understand it today.
Right now, however, we seem to be stuck in the 19th century, without hopes of getting out. Everyone’s insisting on this magical fluid of heat - the caloric. People do that because it’s too good of an idea. It explains so much and almost makes sense. Sure it has its flaws, but also many successes.
On that note, in the previous episode we witnessed how Sadi Carnot used caloric to create the standard for the perfect engine that we still use to this day. Perhaps, without fully realizing it, he also did something profoundly smart and surprisingly wrong. His insight and his blunder, if you can call it that, laid the foundations of modern thermodynamics and much more.
All of this will become clear, but first, I need to take you on a trip to Indonesia (called the Dutch East Indies back then). Since it’s in our imagination, its all inclusive.
Here we go.
Blood never lies
I’m glad you agreed to take this journey with me.
What I didn’t mention is that the trip is on a 19th century 3-masted vessel, with cramped quarters, full of sick sailors and constantly clogged toilets. Too late to back out now. Oh, but the ship also has a doctor, who’s trying to do his best to help the diseased men onboard, so there’s that.
Keep in mind that 19th century medicine was a total mess. Physicians were still trying to treat people by balancing their humors in various ways. For example, dubious, untested and often dangerous drugs were a new fad, since chemistry was a rapidly evolving domain. However, the all time classic was bloodletting. It was the go to procedure for the treatment of many, if not most maladies.
That is what the good doctor offered the sailors who came to see him, coughing their lungs out. One by one, the men went to the doctor to “let their veins breathe“ as bloodletting was referred to.
While the blood was flowing, doctor Julius Mayer, for that was his name, noticed something peculiar about it. The blood seemed to be bright red, almost like arterial blood. His experience from practicing in Europe told him that venous blood should be much darker. Additionally, he noticed that the seamen were consuming less food, while sailing in the tropics, in contrast to colder environments.
All this had to mean something, surely.
Cogs started turning rapidly in Mayer’s head and a question has emerged: what if all of this has something to do with the heat of the climate? Going even deeper, what if the abundant presence heat in an environment, demanded less heat production by organisms in that environment?
Mayer wanted to make sense of all this.
By his time people were fairly familiar and accepting of the existence of oxygen and its role in combustion, courtesy of Lavoisier. Combustion of, say hydrogen or gunpowder, generated heat with the added bonus of fireworks. Burning food in the body seemed to be similar if more controlled, which is a shame. I wouldn’t mind breathing some fire now and then.
In this context, less demand for heat could mean a lower rate of “food oxydation”. A lower rate of burning would mean that there is less “ash“ produced in the sailor’s body, preventing the venous blood from turning dark.
So that’s ok, but body heat production was nothing new. However, it’s the amount of heat produced depending on that of the environment that got Mayer digging for more. There was something about that balance…
Let’s take it further and ask: what if that sailor then start’s rubbing his hands, lifting things, climbing and whatever it is sailors do? Where do they get the energy to do all that? It must be from that same food, right? I mean, what else?
But why stop there? All that work, that the sailors are doing, can be used to generate heat anew. It seemed that heat and work, and work, and heat were interchangeable.
All that thinking led Mayer to conclude that the heat of a body and the work done by a body are both aspects of the same “indestructible“ quantity, which we will NOT call energy, to keep with the spirit of the times.
For someone living in the 19th century, this was a groundbreaking revelation. Mayer knew he was onto something monumental and rushed to let people know.
Unfortunately, he was not a trained physicist and was pretty awkward in his delivery. For all you masochists out there, here’s an example:
If two bodies find themselves in a given difference, then they could remain in a state of rest after the annihilation of that difference if the forces that were communicated to them as a result of the leveling of that difference could cease to exist; but if they are assumed to be indestructible, then the still-persisting forces, as causes of changes in relationships, will again re-establish the originally present difference.
It took him a few rejections and help from a physicist friend to get his statements to an acceptable level. To make it a bit easier on the mind, he provided a number of examples about interchangeability of heat and work. Here’s an example in the context of gravity:
If falling force and motion are equivalent to heat, heat must also naturally be equivalent to motion and falling force. Just as heat appears as an effect of the diminution of bulk and of the cessation of motion, so also does heat disappear as a cause when its effects are produced in the shape of motion, expansion, or raising of weight.
In the 19th century, that’s a heavy-hitting statement. Here’s one more, this time a more practical one:
A locomotive engine with its train may be compared to a distilling apparatus ; the heat applied under the boiler passes off as motion, and this is deposited again as heat at the axles of the wheels.
With an outline of a theory all that was left to do is to quantify it. If heat and work are indeed interchangeable, then he needed to state the conversion rate between both.
Based on various measurements available to him a the time, he eventually ended up saying that to heat water of a certain weight, from 0° C to 1° C, that same weight would need to be dropped from 365 meters. That’s not exactly right, but it’s the idea that matters.
This is not the end of this story, but I totally forgot that we are still on that rat infested ship, heading to Jakarta. Time to get off this thing. Let’s see what’s happening on English land, for a change.
Hold my beer
The good thing about England is the beer. English breweries are capable of producing great beer, but also great physicists.
One of those was James Prescott Joule.
Born into a family business of brewing beer, it seemed he would be destined to become a master brewer himself. Not a terrible perspective, if you ask me, but the Universe had other plans.
From a young age, Joule’s mind was set on a different trajectory, than that of others. Among his teachers was the famous John Dalton. Today, he is considered the father of the atomic theory of matter and I’m sure he filled Joule’s mind with all kinds of heresies of little particles vibrating and bouncing around.
Now, brewing, at the time, made use of steam engines like almost every industry in the 19th century. As Joule took to running the family brewing business, he got interested in maybe throwing these things out. The engines were pretty crap in terms of efficiency and running them was burning not only coal but also cash. Perhaps he could make things better somehow.
However, his motivation quickly evolved beyond just the bottom line. Soon, he would also go down the same rabbit hole Mayer did and start thinking about converting heat to work and work to heat.
On that journey, Joule got really interested in count Rumford’s experiments. We’ve already seen the count’s exploits here. If you recall, Rumford was boring cannons in order to demonstrate that heat can be constantly generated through friction alone. In the, then prevailing, theory of heat as a substance called caloric, this would mean an infinite supply of the thing, which was ridiculous.
Rumford’s work should’ve been enough to make caloric go away forever, but he wasn’t rigorous enough with his experiments. This left room for people to rationalize his results away and so they did.
Joule thought that maybe he can do better. He devised an experiment, which we can summarize like this:
Take a can of water and make sure the can is really good at isolating the water from the outside.
Put a set of paddles into the water and allow them to rotate, churning the water as they go, but don’t touch anything yet.
Take something heavy, of known weight, and drop it some known distance.
Before you do that, however, make sure that the heavy thing is connected to the paddles, so as the weight drops, the paddles turn.
Finally, stick a thermometer up your can of water and observe what happens.
The experiment is fairly simple and Joule did it over, and over again, like a good scientist, leaving nothing to chance. With that, he was able to show that raising the temperature of water by some amount requires a certain specific amount of falling, every time.
This was a spectacular result. We didn’t burn any coal, there was no fire applied and no caloric was transferred. The heat come from the motion of the paddles alone and with a specific value. Joule just proved what Rumford couldn’t.
What’s that value exactly? I’m glad you’ve asked. It’s 770 foot-pounds of force per British thermal units. Don’t you just love imperial units?
Fortunately, we’ve since established less insane units of measurements. To honour Joule’s contribution we named the unit of energy after him and the aforementioned value became 4140 Joules, initially, to be refined later by the man himself.
Ok, so this is some groundbreaking stuff. Joule just disproved a century worth of nonsense. Here’s a historically accurate depiction of how other scientists reacted to this revelation:
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So anyway, what about that caloric, right?
You might be wondering what is happening right now. How was it that Joule just broke the world, at about the same time that Mayer did and nobody has noticed?
That’s because there was a technical problem, as well as a social one.
You don’t like Carnot, so I don’t like you
“Vibrating particles and non-academics are considered trespassers and will be sho…uhhm… ridiculed on sight,” would’ve be the sign hanging at the entrance of the British Royal Society at the time, if they made signs like that.
Both Mayer and Joule were not academics. Sure, they were literate in math and physics (Joule probably a bit more than Mayer, who was doctor after all), but they didn’t mingle around in academic circles.
Mayer wrote up his findings in 1842 and Joule just shortly after in 1843. However, they had real trouble getting published in respected journals and get the recognition they deserved. At the face of it, its just two guys, who nobody knows, coming out of nowhere and proposing something that breaks a centuries-old tradition.
In stories like this it is often instinctive to favor the underdog. Understand though, that anyone can claim that they’ve figured it all out (as people still do), but that doesn’t mean they necessarily deserve attention.
On top of that, Mayer came across as too amateurish, while Joule made claims of unprecedented precision of measurement, which didn’t sound plausible at the time. But all that paled in comparison to the main concern everyone had. For context, take this quote from Joule (source here):
“And indeed when we consider heat not as a substance, but as a state of vibration, there appears to be no reason why it should not be induced by an action of a simply mechanical character…”
Not only did these results required a new and unproven look at matter, as made of vibrating particles, they also violated what Carnot found about 20 plus years before.
We’ve recently examined Carnot’s work here, so you might want to check back on that. TLDR; in his mind, Carnot was building the perfect engine, all on the idea of caloric. The way it works is: you put caloric/heat into an engine, it does some useful work, like moving some wheels and you get caloric/heat back at the end. Since caloric was considered indestructible but transferable, he proposed that we get as much heat out of an engine as we put into it. In other words, no caloric is lost/destroyed during the engine’s operation.
Now, Mayer and Joule come in and say that heat (or caloric, for stubborn minds) is actually converted to work, so Carnot’s picture doesn’t… work.
This unfortunately, was too bad for the doctor and the brewer.
Oh save us, Thermodynamics Man
The struggle continued, both Mayer and Joule weren’t taken seriously enough. However, in a contest of who’s the least known and influential physicist, Mayer won, therefore he lost. Joule simply was more persistent in making noise about himself and eventually it worked. Slowly but surely, Joule’s accomplishments became more recognized and accepted.
Joule was winning, so much so, that at certain point his works came across the desk of Rudolf Clausius, a giant in physics, at the time. Clausius looked at Joule’s results and they made a lot of sense to him. He also looked at Carnot’s results and they made equal sense, thought both seemed incompatible. However, he was set on resolving this tension.
If you recall, at the very beginning of this episode, I wrote that Carnot “blundered“. He said that he could get the same amount caloric (heat) out of an engine, as he put it, plus the engine would do some work. All that Clausius needed to do to fix it was to state that it’s not caloric that’s conserved, but energy.
Easier said than done, but here’s one way to look at it.
In the first stage Carnot proposed isothermal heating. You put heat in (let’s call the flow of heat ΔQ), the temperature doesn’t change, the gas expands a bit. This expansion does work and let’s call that ΔW. All the heat goes into work and he could say that:
ΔQ = ΔW
So far, so good. Now, for the next stage.
Here Carnot says, that if you leave the gas alone and prevent any heat transfer, then the gas will expand and do some work. Wait, that doesn’t make sense, does it? If ΔQ = 0, then ΔW = 0, but I see work being done…
Something is missing and we need to introduce one more element for all that make sense. Instead of saying ΔQ = ΔW, let’s say:
ΔQ = ΔU + ΔW
where ΔU is something we will call internal energy.
Ok, let’s try that again. In the first stage (expansion at constant temperature) we need ΔU to be zero and that’s fine. The gas expands, but the internal doesn’t change and that would suggest that it doesn’t really care about changes in volume.
Now for the second stage, which is expansion without heat exchange. ΔQ is zero, so this is a bit scary, but this time ΔW = -ΔU. However, Joule converted work to heat. So, if we would like Joule’s principle of interchangeability of heat and work to hold, then we must extend our thinking. We must be converting energy to work and vice versa.
Also, during this second stage expansion, the temperature of the gas changes and so does the internal energy. That must mean that temperature change is the thing that make it tick.
You might be asking yourself, why didn’t Carnot figure this out in the first place? Well, the problem was that his intuitions were based on his experiences with steam engines. These were terrible at converting heat to work. It was so bad that very little work was done in relation to the heat that was fed to the engine. As a result almost an equal amount of heat was coming out the other end. Carnot might’ve simply not noticed the difference.
Anyway, there you have it. Clausius saved Carnot and Joule, while stating the first law of thermodynamics in mathematical form:
All of this is a very diminished rendition of Clausius’ thinking and if you want the original, you can find it here.
This version of conservation of energy was based on mechanical intuitions so that’s where all this talk of heat, work and engines come from. However, this would prove to be a profound statement, finding applications is so much more than just choo choo’s.
The death of caloric
OMG, what a mess this whole thermodynamics story was.
Over 200 years of struggle and confusion, aaand I haven’t even mentioned how much everyone was pissed off by heat transfer through radiation. Thankfully, we can finally say that caloric and all kinds of magical heat fluids are bullshit.
Joule’s interchangeability of heat and work, and Clausius' showing that both are just different measures of energy was the final blow. We can finally start thinking about thermodynamics in modern terms, so as of molecules just having a constant rave party.
Note that all this time I’m going on about Joule, but what about Mayer?
Years passed and, although technically first, Mayer was about to be ignored and forgotten forever. Losing to Joule, enduring tragedies in his personal life and having his work ruthlessly ridiculed by several academics, turned Mayer into a wreck of a man. However, an unlikely rescue was on the horizon.
A physicist by the name of John Tyndall wanted to do some research of heat transfers and asked Clausius for references on the work done so far. Among papers at Clausius’ disposal was also Mayer’s work.
Clausius told Tyndall that he could send him the paper, but that nothing worthwhile was in it. However, he decided to take one more look at Mayer’s work and once he looked, Clausius did a 180.
He immediately wrote Tyndall, telling him that he takes everything back and that Mayer’s work is full of wonderful ideas.
Tyndall, went around Europe, spreading word of Mayer’s work and annoyed the hell out of a lot of Brits, with the fact that a German was first to the prize.
Mayer was saved and eventually recognized, and praised, so some amount of justice was done.
You might ask, why would I go through all the trouble of telling Mayer’s and Joule’s story, instead of just starting here.
Well, first of all that would go against the spirit of Physics Rediscovered, where the thing we care most about is the evolution of ideas and not bare facts.
Second, it’s a story of two, very different minds arriving at the same conclusions, starting from seemingly very disconnected intuitions. Although the final truth is singular, there are a multitude of ways of finding it. I think that it is fascinating and if you made it this far into the episode, then perhaps so do you.
Fashionable motion
Now, with caloric out of the picture, people could finally focus on heat and work, and energy in general as being the result of motion of microscopic particles.
As matter, especially gases, were pictured as little angry balls speeding through space and bouncing around, a kinetic understanding of their behavior started to emerge.
Before we end, only one thing remains.
We have already addressed Carnot’s surprising “error“, with the conservation of caloric. Clausius handled that one like a boss.
Now, for Carnot’s groundbreaking discovery. In his own words:
The production of motive power in a steam engine is therefore not due to a consumption of the caloric, but to its transfer from a hotter to a colder body…
Or in, a less archaic paraphrasing, heat flows only from hot to cold, unless you work really hard on reversing it.
This is the essence of the second law of thermodynamics.
What Carnot or Clausius probably didn’t anticipate was how consequential this law would be. It would apply to silly steam engines as well, as to the entirety of the Universe and everything in it, including black holes. If someone forced me to say what is the most important piece of physics ever, then this would be it.
Clausius called this phenomenon the ever increasing entropy and in the next episode we will figure out, what the hell does that even mean.
Until then.