Chapter the Fourth
A Matter of Work
"This place is a mess," exclaimed Mendel late the following evening. For the past hour the three scientist monks had been taking samples of contaminated wine and serially diluting them into small flasks of sterile water. At several different dilutions, one tenth of a milliliter of the water, and the rods floating in it, had been carefully withdrawn and placed onto the surface of the solid broth in the bottles. They had watched as the drop of liquid spread over the surface and then been absorbed. Now all the bottles were on their sides, in rows, on shelves near the stove, and Brother Gregory had turned his attention to the state of their laboratory.
He began to tidy up, and the other two reluctantly joined him in his efforts, but when it came to moving a series of packing cases back against a wall, their combined strength was not enough.
"Huff," grunted Klacel, "what's in these things?"
But the ever practical Mendel had already found a long metal bar, the tip of which he placed under one side of the case, and was busy levering the offending wooden box out of the way.
Klacel went in search of some fresh bottles of monastery wine, and when he returned he found that Brother Joseph and Brother Gregory had successfully moved all the cases .
"Here, let's take a break," he said, opening the first bottle of uncontaminated wine they had seen in a week. He filled three glasses and pulled the most comfortable chair up to the table.
"You know," he said after the first few sips of wine had started the mellowing process, "how did you do that?"
Brother Gregory and Brother Joseph just looked at him. "What do you mean?" they asked.
"How did you move those packing cases?" Brother Matthew insisted, "A moment ago the three of us pushing together could not dislodge a single box, but Mendel here - not the strongest person in the world - suddenly moved the heaviest box all by himself. How?"
You are not getting philosophical again?" Brother Joseph said with a groan. Klacel's tendencies towards Naturphilosophie were legendary in the monastery, and had resulted in more than one embarrassing incident. But Mendel took the question with his usual seriousness.
"I used this bar as a lever," he said, pointing to the instrument now resting by the wall. "I put the tip of the bar under the case, pushed down on my end and the case moved. It is a well known principle."
"But why did the bar help you?" was the next question, "Certainly you were no stronger than you were before, when you could not move the case, and the bar did not add to your strength, so what changed?"
"Please ...!" pleaded Brother Joseph, "I'm tired, let's not start a discussion now." But his pleas were ignored. Neither Klacel or Mendel could resist the opportunity to talk about science.
"That is easy," said Brother Gregory with a grin, totally ignoring Brother Joseph and responding to Klacel's question. "
- A lever, which, incidentally comes from the Latin word meaning 'to lift', is a means of transferring force from one place to another. I push down on my end of the lever - a force - and that force is transmitted along the bar, to the box, which then moves."
"But wait," said Klacel, "you cannot get something for nothing in this world. Let us say your body creates one unit of force, but we already know that one unit of force applied directly to the box will not move it. How come, when you use the bar, that one unit of force suddenly becomes, say, the ten units of force that will move the box?"
Brother Joseph groaned, it was happening, but he could not help himself, "It is the principle of - 'multiplying force'," he said, "Mendel pushes down and moves his body and his end of the bar a distance of about a meter, while at the other end of the bar the tip only moves the box a few centimeters. What is important is that when you multiply the force by the distance moved, the two numbers come out the same at each end of the bar."
Mendel drew out the equation on a piece of paper; force multiplied by distance equals work. "At both ends of the bar," he said, "the amount of work that is done remains the same. If I generate one unit of force over a two meter distance, that means I have done two units of work. But at the other end of the bar, the tip has only moved 2 centimeters, that means, if the work is still only two units, a hundred units of force have been exerted on the box; more than enough to move it."
"When you said earlier that 'you cannot get something for nothing' you were talking about 'work'," Brother Joseph said, thoughtfully. "Work is done when a force moves an object through a distance. A lever is a type of machine which changes the numbers in the equation. The amount of work being done is the same at both ends of the lever, but if the distances are different then the force is different. But the important principle here is that the amount of work is always constant. The machine cannot create more work than Mendel generated. The machine only changed the way that work was used."
"So Mendel was able to move that heavy box, using a pathetic amount of work on his part, by shifting the box in small distances across the floor," Klacel conceded. "That part I understand; work into the process has to equal the work out of the process, but, all you have done is contradict yourself."
Brother Joseph looked puzzled, so Klacel went on, "You say that in all processes taking place on this planet, the amount of work put into the process has to be the same as the amount of work produced by the process."
"Call it a 'law of conservation', said Mendel, helpfully.
"Very well," pounced Klacel, "if you cannot get something for nothing, where did all that work come from originally? If the amount of work in the world is constant, like you say, why was Brother Gregory here, suddenly able to generate from his body the work needed to move the box. Answer that one!"
"I suppose that work is somehow stored in the human body," Brother Joseph admitted. "I seem to remember Gottfried Wilhem Leibnitz calling this stored work vis viva - 'living force' - over a hundred years ago."
"But what about ships or steam locomotives? They are not alive and could not have a 'living force' but they do the same as Mendel and apparently generate work and force out of nowhere," Klacel was remorseless.
"There you are wrong," Brother Gregory could not help adding, "the Englishman Thomas Young solved this problem in a more general way some time ago. He proposed that any kind of 'stored work' be called energy, from the Greek words meaning 'work-within'. I believe most physicists use that term nowadays."
"So, even when the good Brother Gregory is sitting there, sipping his wine, he is still full of this 'work-within' or 'energy'?" said Klacel.
"Yes."
"And when he gets up and presses down on that lever, the stored energy in his body is released and used to do work?"
"Correct."
"And all work involves motion, since an object has to be moved a distance for work to be done?"
"Yes."
"So, anything that moves contains energy?"
"That is what the English physicist William Thomson said about nine years ago (1856), when he introduced the term kinetic energy. The word 'kinetic' is Greek for 'motion'," Brother Gregory said.
"But when Brother Gregory is not in motion, he still has energy. What form does that take?"
"It was the Scottish engineer, William Rankine, that solved that one," Mendel said, "he suggested in 1853 that we called this 'stored energy' potential energy."
" - And the 'potential energy' and 'kinetic energy' are interchangeable?"
"So it appears. Which is why the 'law of conservation' really works. It is the mechanical energy that is conserved, either in its 'stored' form or in its 'motion' form. No matter what form it takes, the amount of energy is always the same."
"Hummm," mused Klacel, reluctant to give up the argument, "it's all too neat. Nature is never that simple."
"In this case it is," Brother Joseph assured him, "the total amount of energy in a system is always the same at the end of a process as it was at the beginning of a process. All Brother Gregory did when he moved the box was transfer energy from his body into the work of moving the box. The world, the universe, stayed the same."
Perhaps it was the wine, but Klacel felt there was a flaw somewhere in this all-to-simple 'law of energy conservation'. While his friends reluctantly got to their feet and continued clearing up the temporary laboratory for their next day's efforts, he cast his eye around the room and his mind around the problem. It was when he saw the iron bar that his attention suddenly focused; iron, force, movement, energy, the ideas and concepts spun through his brain. Move the bar, and convert potential energy to kinetic energy and the box moves - but ...
"Wait a minute!" he shouted, startling his fellow philosophers, "there is something wrong here." He jumped up and collected the bar of iron from the wall. He rested one end of the bar on the table and picked up a piece of rough sacking cloth in his other hand. "Watch," he said, and began rubbing the bar vigorously with the cloth. "Just as Mendel did a few moments ago, I am taking this mysterious 'potential energy' from my body and converting it to movement. My hand is moving the cloth up and down on the bar. So kinetic energy is being produced, right?"
Cautiously Brother Gregory and Brother Joseph agreed.
"But where is that energy going?" Klacel asked in triumph, the bar is not moving and no packing case is being moved by a force, what is happening to all that energy?"
Brother Gregory looked at Brother Joseph and a smile appeared on both their mouths at the same time. "Are you going to tell him, or should I?" asked Brother Joseph.
"Let me," said Mendel, and he took the iron bar from Klacel. "Feel his, he said, holding out the bar. Klacel took it in his hands. "What do you feel?"
"The bar is warm," Brother Matthew said after a few moments.
"Exactly; while you were rubbing the bar with the cloth, the friction between the two surfaces generated heat, which warmed up the bar. Heat is another form of energy. Your potential energy has been converted into heat energy."
"Wait a minute," expostulated Klacel, "that's not fair, you cannot go on inventing - different forms of energy just to make the theory correct."
"That seems to be the way it is," Brother Gregory told him, "an English brewer by the name of James Prescott Joule has measured the heat produced by a wide variety of causes, everything from squeezing gas to turning paddle wheels, and about 20 years ago found that there were many different types of energy and that one kind could be converted into another kind, but that in all his exchanges no extra energy was ever produced and none of the energy that was there in the beginning was ever lost."
"But," Brother Joseph was quick to add, "it was a good German scientist Herrmann von Helmholtz who has put the law of conservation of energy into the form most people accept it today. As far as we can tell, this is one of the most fundamental laws of the whole world, if not the universe. It seems to hold true for all the systems tested so far, and will probably hold true when humans venture beyond our small world and visit those beyond the stars."
Klacel just snorted.