Chapter 191: [Entropy]

"Why?" many people can't help asking, "This doesn't violate the law of conservation of energy."

"Yes, the second type of perpetual motion machine does not violate the law of conservation of energy, but it violates another law." Ma Shao paused, "This law that has not yet been clarified is exactly the topic of my speech today - the second law of thermodynamics."

He said "has not yet been identified", not "has not yet been discovered".

Compared with other disciplines, the development of thermodynamics seems to be closer to gradualism. For example, the law of conservation of energy has long been vaguely recognized by some scientists, but it has only been clearly defined in recent years.

The same is true for the second law of thermodynamics. Some keen physicists have also been vaguely aware of the existence of this law, but they cannot explain it clearly because there is a thin layer of window paper between them.

At this point, if physicists look back and carefully examine Carnot's theorem, it will not be difficult for them to realize the existence of the second law of thermodynamics.

In fact, in the original history, two or three years later, after re-examining Carnot's theorem, Clausius and Kelvin would each give their own interpretations of this law.

But now, Clausius and Kelvin obviously don't have this opportunity, Ma Shao will explain the second law of thermodynamics thoroughly.

"The second law?" Faraday couldn't help saying, "It sounds interesting."

Ma Shao said: "The first law tells us that energy is neither created nor destroyed, but can only be transferred, while the second law talks about the rules of energy transfer - energy cannot be transferred at will."

"Nature always limits us more than we imagine," he interjected.

"The plainest statement of this rule is that it is impossible to transfer heat from a low-temperature body to a high-temperature body without causing other changes."

"After knowing the first law of thermodynamics, we look back at Carnot's theorem. It is not difficult to find that the second law of thermodynamics is actually the premise of Carnot's theorem. Only when it is established can Carnot's theorem be established..."

There was a lot of discussion in the audience.

The law of conservation of energy tells us that heat and work are equivalent and can be converted into each other, but the heat and work described by Carnot's theorem are not exactly the same. Work can be completely converted into heat, but not vice versa.

If the law of conservation of energy and Carnot's theorem are both correct, then obviously another law is needed to support this system, namely the second law of thermodynamics - although energy can be converted into each other, it is restricted in direction.

This principle is not complicated. After Ma Shao's explanation, many physicists understood it.

"I see!"

"That's right. Without this law, Carnot's theorem would not hold."

"This is really crucial, and it's definitely the second most important law of thermodynamics."

"Damn, I noticed this a while ago, but I didn't think about it!" several physicists were frustrated. "Oh my God, what did I miss!"

"What a lucky guy he is!" Some people couldn't help but say sourly as they looked at the horse whistle on the stage.

Apparently, they thought the discovery of the second law of thermodynamics was a matter of luck.

This is true. Such a rough description of the physical laws does not have much technical content and is difficult to convince people.

So Ma Shao continued: "Of course, this is just a rough description. It doesn't look like a law of physics, but more like a philosophical motto."

"Like Newton's work, physics is a combination of philosophy and mathematics... Therefore, in order to make it a real physical law, we need to express it in mathematical language, and we need to introduce a concept that can be calculated - entropy."

"Entropy?" The people in the audience were confused and tried to repeat this difficult name.

Ma Shao did not use the English name of entropy that he knew in his previous life, but used the Apache word "original disaster", a religious term of the Oracle religion, which the British naturally found difficult to pronounce.

"It's an Apache word that means 'original disaster', like original sin," he explained. "It's actually a religious word, and my people have attached some religious meaning to it."

"What religion do the Apaches believe in?" People can't help but wonder.

So Ma Shao first gave a brief introduction to the Lingyu religion, and then changed the subject: "Of course, I don't really advocate religion. I have always suggested that people follow a more rational way of thinking... Anyway, at least here, at a physics conference, let's talk less about religion."

There is no doubt that the religion described by Ma Shao aroused people's curiosity, which is what he wanted.

But he didn't say much. After all, he couldn't be a missionary, and now was not the right time for him to preach.

"Here, primordial catastrophe or entropy is a purely physical concept. The connotation of entropy is very complex. From the time I thought of it a few years ago until now, my understanding of it has been constantly revised."

"First, let's review Kano's work."

As he spoke, Ma Shao turned around again and wrote some formulas on the blackboard behind the podium.

"We can differentiate any thermal cycle and reduce it to a thermal cycle consisting of a large number of Carnot heat engines superimposed on each other. Then, based on Carnot's conclusion, we get this result..."

For many physicists here, these are familiar contents and are not difficult to understand.

Of course, this excludes those physicists who don't understand calculus - and there are such physicists.

For example, Faraday's level of calculus is very questionable, and it is highly likely that he did not understand it.

Faraday was born in poverty and had little formal education. He was far from being a physicist proficient in mathematics. His work was basically in the experimental field. It was his excellent hands-on ability and physical intuition that made him a first-class physicist.

It can be said that among physicists of the same level, Faraday's mathematical level may be the worst.

His shortcomings in mathematics were also the reason why he failed to take his research on electromagnetism further. Fortunately, the young and talented Maxwell would soon complete this mission for him.

After a moment, Ma Shao circled a variable in the formula and said, "This variable, or state function, is what I call 'entropy'."

The variable he circled was naturally Clausius entropy, which is also the earliest definition of "entropy".

"…Now, it is not difficult for us to find that for an isolated system, its entropy is a value that cannot be reduced, and the entropy change must be greater than or equal to zero. The fact that entropy cannot be reduced reflects the directionality of energy conversion."

"The inequality here is the mathematical expression of the second law of thermodynamics." He pointed to the Clausius inequality on the blackboard.

After this operation, the physicists present had to be convinced.

Although discovering the second law of thermodynamics could be attributed to luck, extracting the mathematical expression from this law is impossible without a solid foundation.

"Entropy... I think it won't be long before this word appears in all textbooks," Thomson said with emotion.

"A great discovery!" Faraday couldn't help but applaud. Although he could not understand the mathematical derivation process, with his extraordinary physical intuition, he undoubtedly felt the wonder of entropy.

"Clap, clap, clap--" Following his applause, other physicists also followed suit.

"Thank you." Ma Shao smiled and responded politely.

But then he stopped smiling and changed the subject: "However, this is not the final result of my thinking, and it is far from the true appearance of the second law of thermodynamics."

The applause quickly died down and people looked at him in silence and surprise.

In their opinion, the speech just now was a model of physics, but Ma Shao told them that this was not the result?

Facing the puzzled eyes of the crowd, Ma Shao said calmly: "We have expressed the second law of thermodynamics in mathematics, but I think you have all noticed that the concept of 'entropy' does not seem to have a corresponding actual physical meaning."

"This question has troubled me for a long time. After a long period of thinking, I got a relatively satisfactory answer. It is because of this answer that I named the variable 'entropy' - 'original disaster' in Apache language, a concept symbolizing endless disasters and tests."

After a pause, Ma Shao continued, "Next, let's explore the nature of 'entropy'."