Mage? Magic Engineer!-Chapter 50 - 47: Shattering the Caloric Theory

Heat and work are both forms of energy, measured in the same units.

This was common knowledge—common knowledge for an engineer like Rorschach, that is. It was not the mainstream view in this Otherworld! 𝒇𝙧𝙚𝓮𝔀𝓮𝒃𝙣𝓸𝒗𝒆𝒍.𝙘𝒐𝒎

In ancient times, Casters and Alchemists had discovered that matter could be continuously divided into tiny particles. By observing celestial bodies, dust, and steam, a Master of Arcane Magic named Leukippos, who lived before the Old Empire Era, had already posited a theory: Elements and Ether are composed of the smallest possible units. These units drift and swirl through space and the world behind the veil, coalescing to form all things and all Magic.

"The primordial god used His great Divine Power to bind the tiny elements together, creating all things. Just as we mix fine clay particles with water to shape pottery."

Thus, the smallest unit of an element—or of matter itself—was named the "element-particle." After the transition from the Old Empire to the new era, the term was translated by the Shanshi people. By the time it made its way back to the Main Continent, "element-particle" had been corrupted into "atom."

Discovering the atom was a great step. However, the Casters, and the Alchemists in particular, had a bad habit of over-extrapolating. They figured that if physical objects were made of particles, then everything else must be too—just particles so small they were impossible to touch.

The idea that Ether was a particle? Rorschach didn’t understand it well enough to comment. The idea that light was a particle? He’d grant them partial credit for that. But the notion of particles called the ’Flammable Element’ and ’caloric’...’Today, I will overthrow the Caloric Theory!’ On the surface, Rorschach smiled cheerfully at Kano and promised to make revisions. The moment he turned away, however, he began to plot his "mechanical equivalent of heat" experiment with grim determination.

Modern people from his original world might find it hard to grasp, but assuming heat was a type of particle called "caloric" wasn’t entirely baseless. The hypothesis provided a simple analogy that could explain some heat transfer phenomena.

For instance, one could imagine temperature as a measure of the quantity of "caloric," or as a measurement of the potential at which "caloric" is stored within an object. With this model, the transfer of heat from a hot object to a cold one could be vividly analogized to water spilling from a high place and flowing downward.

When paired with its heavyweight counterpart, the theory of the Flammable Element, it was a match made in heaven. An accumulation of caloric would activate the Flammable Element, which would then degrade back into caloric and be released during combustion.

But there were also phenomena it couldn’t explain.

There was once an Alchemist, a staunch believer in the Caloric Theory, who lived in the icy lands of the Northern Continent. He had two friends—a Dwarf and a Polar Elf—as well as an apprentice.

First, the apprentice brought two identical large copper pots, one filled with oil and the other with water. He then took equal weights of ice and placed them into each pot. After the ice had completely melted, the apprentice measured the temperatures and discovered something odd.

"Teacher, why is it that the oil and water lost the same amount of caloric, but their temperatures dropped by different amounts?"

"Different substances have different capacities for accepting or losing caloric. Clearly, caloric from the surroundings must have replenished the caloric in the colder liquid, which is what allowed all the ice to melt."

Then, his Polar Elf friend asked him why rubbing one’s hands together generates heat. He answered that in the process of rubbing your hands, you were unconsciously activating Magic, causing Ether to transform into caloric.

The Elf told him to use a Mage’s Hand to rub two blocks of ice together, claiming the ice would melt. "Can blocks of ice perform Magic?" the Alchemist asked, telling the Elf to stop teasing him.

Finally, his Dwarf friend sent him a letter. While manufacturing a cannon barrel, he had submerged a solid iron rod in water to bore it out. After two and a half hours of drilling, the water had actually started to boil. This left him very confused. ’Is caloric a type of mineral that can be drilled out?’ The Alchemist replied: The metal rod contains caloric, and more caloric is released during the process of creating the iron shavings.

Then the Dwarf wrote again: If caloric is distributed evenly throughout the material, then drilling with a sharp bit produces more iron shavings but less heating of the water. Drilling with a dull bit produces fewer shavings but much more heating. Isn’t that a contradiction?

Rorschach finished the story of the Alchemist who lived at the Pole.

"And then what happened?" Pascal asked with a yawn, using a piece of bread to mop up the last of the creamy mushroom soup in his bowl.

"Then, thoroughly exasperated, he reported the Dwarf to the Imperial authorities for illegally manufacturing heavy firearms." After speaking, Rorschach cut off a piece of duck and popped it into his mouth. "Let’s head over to the Alchemy Department after we’re done eating. Oh, by the way, Teacher Kano wants you to bring the liqueur from his office to the research lab on Prairie Avenue."

"You’re going too? Another experiment?"

"Don’t worry. We’ll have people from the Alchemy Department helping us this time."

On the first floor of the Alchemy Department, Master Snow had already arrived, along with a few other men. Two apparatuses were set up in a space that had been cleared out in the storeroom. Both had glass tanks containing an equal mass of water.

One apparatus had a paddlewheel submerged in the water. Its axle was wrapped with a rope, which was tied to a large weight at one end. Clearly, as the weight fell, it would drive the paddlewheel, stirring the water.

In the other, a falling weight would drive the smallest rotary generator the Alchemy Department could find. Part of the electrical circuit was coiled into a spring-like shape and submerged in the water.

Master Snow looked pained. "Rorschach Mage, this isn’t a destructive test, is it? The resistance wire you requested is an iron-aluminum alloy!" In a world without electrolysis, the Alchemy Department had even tried to develop Magic to refine aluminum—that dull gray stuff was priced a little higher than gold.

"Don’t worry, it’s not. Have the mechanical parts been lubricated? I want as little friction as possible." Rorschach inspected the apparatuses. "Both weights need to be level at the same height. Record that height. What’s the current room temperature? It should be the same as the water temperature..."

Finally, the weights on both apparatuses were released. The paddlewheel in the first apparatus began to spin, and the rotor in the second began to turn.

The weights hit the floor. "Quick, record the water temperature readings!"

"And then? That’s it? The experiment is over?" Pascal was baffled. ’It’s that simple? This is nothing like the other experiments I’ve helped with.’

"Yes." ’A simple experiment and a genius insight are all it takes to reach a grand conclusion... This was the work of the great Joule, after all.’

Master Snow took the data from the man who had recorded it. "They’re almost identical! Rorschach Mage! The water really did heat up, and to the same temperature!"

Rorschach nodded. "If we could completely eliminate the wire’s resistance and all friction, the results would be identical. That said, our thermometers aren’t precise enough to measure such a tiny difference anyway."

Pascal still didn’t understand. "What are you trying to prove with these experiments?"

"In the experiment designed by the Rorschach Mage, the temperature of everything was the same at the start. According to theory, there should have been no transfer of caloric. But after the weights were released, kinetic energy made the water heat up! Two different apparatuses transferred kinetic energy and, without any intervention from the Ether, raised the water to the same temperature..."

"It proves that heat and work are interchangeable," Rorschach finished. "If you view heat as ’caloric,’ this is very difficult to explain. Our devices have no Magic Circuits, after all. But if you view heat as a form of energy that, when transferred into a substance, causes its particles to undergo minute movements, then we can see it plainly with the first apparatus. Macroscopic motion is converted into microscopic motion within the substance, and the result is a rise in temperature."

’Heat is not a substance, but a phenomenon of motion in microscopic particles, equivalent and convertible with macroscopic mechanical motion. I can explain everything the Caloric Theory explains, and I can explain everything it *cannot*. This is the Kinetic Theory of Heat!’

He then walked over to the generator apparatus. "The second device proves that the kinetic energy of macroscopic motion, electrical energy, and heat are also interchangeable. If we were to raise both apparatuses to increase the falling distance of the weights, we should see the water reach an even higher temperature. Furthermore, if we know the mass of the weight, the height of the fall, and the mass of the water, we can calculate the relationship between the temperature and the kinetic energy."

And so, they began multiple rounds of experiments. The resulting series of data made it easy to see that the falling height of the weight was directly proportional to the rise in temperature.

"You were right, Rorschach Mage! Heat and work can be measured with the same units! I have no reason to doubt your theories of energy conservation and equivalence any longer!"

"And electrical energy, Mr. Snow."