Shulou(Shulou.com)11/24 Report--

In 1854, a German scientist named Rudolf Clausius pointed out that absorbing less heat at lower temperatures was equivalent to absorbing more heat at higher temperatures. Therefore, he called the change in heat divided by temperature the "equivalent value."

By 1862 Clausius had discovered that a decrease in the equivalent value of one object required an increase in the equivalent value of another. For any process in a closed system, the sum of equivalent values must be greater than or equal to zero. In 1865 Clausius renamed the equivalent entropy and designated it with its German initials S.

Molecular motion goes back to 1857, three years after Clausius introduced entropy in his first paper, when he wrote a paper on the significance of temperature for molecular motion. In this treatise Clausius studied the rotation, vibration, and linear motion of molecules and found that they moved at incredible speeds. For example, hydrogen molecules at 0 degrees Celsius should move at a speed slightly higher than five times the speed of sound.

After reading Clausius 'paper, another scientist raised the objection: If the molecules move so fast, why doesn't the smoke from the firewood fill the room immediately? Clausius thought this was a very interesting objection, but he did not deny his theory. Clausius thought that although the gas molecules moved very fast, they did not travel very far, so the smoke from the firewood did not immediately fill the room.

In other words, a gas has a large number of molecules moving in all directions, but they are quickly bounced and redirected by another molecule, so that even if the individual gas molecules move very fast, the gas itself diffuses very slowly. Clausius later developed the concept of molecular mean free path, which represents the distance a molecule jumps between two collisions.

Pexels Probability and Entropy Coincidentally, an English scientist named Frederick Guthrie was a fan of Clausius and also spoke German. Guthrie translated Clausius's work into English and published it in February 1859. Three months later, James Clerk Maxwell, a 27-year-old Scottish scientist, wrote to a friend that Clausius 'paper had inspired him. Between 1860 and 1866 Maxwell published a series of articles on what he called the theory of gas dynamics. Maxwell also published several papers on electricity and magnetism, the results of which are known as Maxwell's equations.

Clausius, however, had some minor complaints about Maxwell's theory. But there was another German scientist who was fascinated by Maxwell's theory. His name was Ludwig Boltzmann. Boltzmann translated Maxwell's paper and also published his own paper on gas theory, three years after which he received his doctorate in gas dynamics theory. Maxwell's and Boltzmann's work on thermodynamic statistics resulted in the Maxwell-Boltzmann distribution equations, which are probability equations describing the velocities of different gases.

Boltzmann wrote in 1872 that the molecules of a body are indeed so numerous and move so rapidly that we can perceive only their average value, so that the problem of the mechanical theory of heat is also a problem of probability theory. In 1877 Boltzmann began to study the relationship between probability and entropy. Boltzmann ended up writing more than 50 pages of material containing dense equations that broke down the energy of molecules into different parts and predicted the probability of different situations eventually occurring. Applying this to the second law, we can use the probability of the condition in question to determine the amount of entropy.

Quantum mechanics and entropy In 1879 Planck received his doctorate in the second law of thermodynamics. Planck, however, preferred Clausius 'entropy theory, never Boltzmann's statistical theory, believing that the principle of entropy increase was as valid as the principle of conservation of energy, whereas Boltzmann treated the principle of entropy increase only as a law of probability.

Planck, meanwhile, turned to a new subject. In 1894 William Wien developed an equation describing the radiation distribution of a blackbody. However, there is a problem with this law. It does not work at low energies. Planck concocted a new equation that applied to both low and high frequencies, and the high frequencies looked like Wien's Law. Experimentalists were pleased, but Planck was upset: theorists should not just guess equations from experimental data, they should derive equations from basic ideas.

Pixabay So after weeks of intense work in "Despair," Planck turned to Boltzmann's entropy statistical method. Boltzmann's paper at the time proved S ∞ logW, while Planck added a constant k, simply assuming S=k logW. It means that entropy has an absolute value that can be calculated from the properties of the molecules in matter. Although not as easily measured as temperature, entropy has a definite value for any arrangement of molecules.

The more complex the molecular arrangement, the greater the entropy of the object. Planck encountered a problem: if energy is continuous, then it can be divided into an infinite number of permutations, so the probability will be infinite, and the entropy will be infinite. Planck thus confined energy to small packets equal to a constant h times frequency. This is the origin of quantum mechanics, so Boltzmann entropy equation can be said to start the quantum revolution.

This article comes from Weixin Official Accounts: Vientiane Experience (ID: UR4351), by Eugene Wang

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