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

In May 1959, physicist and novelist C.P. Snow gave a speech entitled "two cultures", which caused widespread controversy. Snow believes that science and the humanities have lost contact, which makes it very difficult to solve some of the world's problems. Today, we see the same thing in denying climate change and attacking evolution. Snow is particularly dissatisfied with the declining educational standards he has seen, he said:

I have attended such gatherings many times: by the standards of traditional culture, these people are considered to be highly educated. Once or twice I was enraged, and I asked them how many people could describe the second law of thermodynamics (that is, the law of entropy). Almost no one can.

"thermodynamics" refers to the kinetics of heat. Heat can flow, it can "flow" from one location to another, moving from one object to another. Fourier wrote down the first important model of heat flow and did some mathematical calculations. But the main reason scientists are interested in heat flow is a novel and lucrative technology: the steam engine.

In about 50 BC, the Roman architect and engineer Vitruvius described a machine called a steam ball in his on Architecture. A century later, Greek mathematicians and engineers built a steam ball. It is a hollow sphere with some water in it, and two pipes stick out and bend at an angle, as shown in the following picture. When the sphere is heated, the water turns into steam, which escapes through the end of the pipe, and the reaction forces the sphere to rotate. This is the first steam engine, and it proves that it is really useful.

Watt discovered at the age of 26 that steam can be a kind of power. But the actual steam power is much earlier. The discovery of steam power is generally attributed to Italian engineer and architect Giovanni Blanca, who created the Machine in 1629 with 63 woodcut mechanisms. One of the pictures shows a paddle wheel that rotates on the shaft when steam from the pipe collides with the blade. Blanca speculated that the machine might be used for grinding flour, carrying water and chopping wood, but it may never have been built. Blanca's steam engine is just a concept machine, just like Leonardo da Vinci's aircraft.

Later, the steam engine completed various industrial tasks, the most common of which was pumping water from the mine. When the upper mineral resources are exploited, investors need to dig deeper into the ground and will inevitably encounter groundwater. At this time, either close the well and give up, or pump the groundwater. Investors are clearly reluctant to give up valuable mineral resources. Therefore, they are in urgent need of a kind of equipment (machine) to complete the pumping task. Engineers have turned to the steam engine, and the study of the steam engine has created a new branch of physics-thermodynamics. Thermodynamics reveals everything from gas to the structure of the entire universe; it applies not only to inorganic matter in physics and chemistry, but also to the complex processes of life. It is the law of conservation of energy in thermodynamics that breaks the illusion of perpetual motion machines.

One of the laws, the first law of thermodynamics, reveals a kind of energy related to heat, and extends the law of conservation of energy to the field of heat engine. Another study shows that some heat exchange methods that do not conflict with energy conservation are impossible because they must create order from disorder. This is the second law of thermodynamics.

Thermodynamics is the mathematical physics of gases. It explains how the interaction of gas molecules produces the macroscopic characteristics of temperature and pressure. Classical thermodynamics does not involve molecules (few scientists believed it at the time). Later, the law of gas was further explained, which is based on a simple mathematical model that explicitly involves molecules. Gas molecules are thought of as tiny spheres that bounce off each other like fully elastic billiards without energy loss in the collision. Although the molecule is not spherical, this model has proved to be very effective. It is called the theory of gas dynamics, and the existence of molecules is proved by experiments.

The early laws of gas developed intermittently over the past 50 years, mainly by the Irish physicist and chemist Robert Boyle, the French mathematician Jacques Alexander, and the French physicist and chemist Gelusac. In 1834, French engineer and physicist Clapeyron combined all these laws into one, the law of ideal gas, which we now write as

P is the pressure, V is the volume, T is the temperature, R is the constant. This equation shows that the pressure times the volume is proportional to the temperature. Later, physicists did a lot of research on many different gases to prove the law of ideal gas. the word "ideal" appears because real gases do not obey this law in all cases. But the assumption of an ideal gas is good enough for designing a steam engine.

Thermodynamics is encapsulated in many more general laws and does not depend on the exact form of the law of gas. However, it does require such a law, because temperature, pressure and volume are not independent of each other. There must be some connection between them, but it doesn't matter.

The first law of thermodynamics comes from the mechanical law of conservation of energy. In classical mechanics, there are two distinct kinds of energy, kinetic energy and potential energy. Neither of these energies is conserved in itself. Newton's second law of motion states that the changes of these two quantities cancel each other out, so the total energy does not change in the course of motion.

However, this is not the whole of the law of conservation. If you push a book on the table, if the table is horizontal, its potential energy will not change. But its speed has changed and will stop soon. So its kinetic energy starts with a non-zero initial value and then drops to zero. The total energy is therefore reduced, so the energy is not conserved. Where did it go? Why did the book stop? According to Newton's first law, books should continue to move unless there is an external force acting on it. This force is the friction between the book and the table. But what is friction?

There are some slight bumps on the rough surface of the book. These things come into contact with a slightly convex part of the table. They rub against each other to create a force, so the book slows down and loses energy. So where did the energy go? Maybe the law of conservation doesn't apply at all. Or this energy is still lurking somewhere. This is what the first law of thermodynamics tells us: "vanishing" energy appears in the form of heat. In the age of drilling wood to make fire, human beings have known that friction can produce heat. The first law of thermodynamics states that heat is a form of energy, and energy is conserved in the process of thermodynamics.

The first law of thermodynamics limits the efficiency of the heat engine, and the kinetic energy that can be obtained is always less than the energy input in the form of heat. Facts have proved that there is a theoretical limit to the efficiency of the heat engine in converting heat energy into kinetic energy, and only part of the energy can be converted into kinetic energy. The second law of thermodynamics turns this fact into a universal principle, which we will talk about later. In 1824, Carnot discovered this limitation in a simple model of how the steam engine works: the Carnot cycle.

To understand the Carnot cycle, it is important to distinguish between heat and temperature. In classical thermodynamics, neither of these two concepts is simple and clear. Temperature is a property of fluid, but heat is only a measure of energy transfer between fluids, not an inherent property of fluid state. In the kinetic theory, the temperature of the fluid is the average kinetic energy of the molecule, and the heat transfer between the fluid is the change of the total kinetic energy of the molecule. In a sense, heat is a bit like potential energy, which is defined relative to any reference height; this introduces an arbitrary constant, so the potential energy of a body is not uniquely defined. In short, heat transfer makes sense, while temperature is a state. The two are linked, and heat transfer is possible only when the temperature is different, which is often called the zeroth law of thermodynamics because it logically precedes the first law.

Temperature can be measured by a thermometer, which makes use of the principle of fluid expansion caused by temperature rise. Heat can be measured by its relationship with temperature. In a standard test fluid, every 1 degree increase in the temperature of 1 gram of fluid corresponds to a fixed increase in calorie content. This amount is called the specific heat of the liquid. Please note that the increase in heat is a change, not a state, which is determined by the definition of heat.

We can think of the Carnot cycle as a cylinder with a movable piston at one end. There are four steps in this loop:

The gas is heated so quickly that the temperature does not have time to change, so that the gas expands and work is done on the piston.

Let the gas expand further, reduce the pressure, and the gas cools.

Compress the gas quickly so that its temperature remains the same. The piston now does work on the gas.

Let the gas expand further and increase the pressure. The gas returned to its original temperature.

Carnot theorem proves that, in principle, Carnot cycle is the most effective way to convert heat into work. This has strict restrictions on the efficiency of any heat engine, especially the steam engine.

In the relationship between gas pressure and volume, the Carnot cycle is shown in the following figure. German physicist and mathematician Rudolph Clausius has found an easier way to visualize Carnot cycles, as shown below (right). The two axes are temperature and a new fundamental quantity, entropy. In this coordinate, the loop becomes a rectangle, and the amount of work done is the area of the rectangle.

Entropy is like heat, it is defined by the change of the state, not the state itself. Suppose the fluid changes from an initial state to a new state. Then the entropy difference between the two states is the total change of "heat divided by temperature". The transformation of entropy S can be expressed by the differential equation dS = dq / T. Entropy change is the heat change per unit temperature.

With the definition of entropy, the second law of thermodynamics is very simple. It shows that in any thermodynamic process, the entropy of the isolated system always increases, and the symbol is expressed as dS ≥ 0.

Classical thermodynamics is phenomenological. It describes what can be measured, but it is not based on the theory of any related process. Daniel Bernoulli first put forward the theory of gas dynamics in 1738. This theory provides a physical explanation for pressure, temperature, gas laws and mysterious entropy. The basic idea is that gases are made up of a large number of identical molecules that bounce around in the air and occasionally collide with each other, which was controversial at the time.

Because the molecule is small, but the size is not zero, two molecules occasionally collide. The theory of gas dynamics makes a simplified assumption that the collision between molecules is a complete elastic collision, so there is no energy loss in the collision process.

When Bernoulli first proposed this model, the law of conservation of energy had not yet been established, and complete elasticity seemed impossible. This theory has gradually won the support of a small number of scientists, who have put forward their own version and added a variety of new ideas. German chemist and physicist Auguste Kroniger assumes that molecules cannot rotate. A year later, Clausius, one of the important founders of kinetic theory, cancelled this simplification and proposed a key concept of the theory, that is, the average free path of molecules, that is, the average distance of molecules moving between successive collisions.

Both Kroniger and Clausius derived the law of ideal gas from the theory of dynamics. The three key variables are volume, pressure and temperature. The volume is determined by the container, and the "boundary condition" affects the behavior of the gas, but it is not the characteristic of the gas itself. The pressure is the average force exerted by the gas molecule when it collides with the wall of the container. It depends on how many molecules are in the container and how fast they move. Temperature depends on the speed at which the gas molecule moves, which is proportional to the average kinetic energy of the molecule.

The derivation of Boyle's law (a special case of the law of constant temperature of an ideal gas) is particularly simple. At a fixed temperature, the distribution of velocity does not change, so the pressure is determined by the number of molecules that hit the wall. If you decrease the volume, the number of molecules per cubic unit of space will increase, and the probability that any molecule will hit the wall will also increase. The smaller the volume, the greater the density of the gas and the more molecules that hit the wall. So Boyle's law has a deeper theoretical basis, based on molecular theory.

Inspired by Clausius, Maxwell wrote down the probability formula for molecules moving at a given speed (based on normal distribution), putting the theory of dynamics on the basis of mathematics. Maxwell's formula is the first law of physics based on probability. Austrian physicist Ludwig Boltzmann then proposed the same formula, now called Maxwell-Boltzmann distribution. Boltzmann reinterpreted thermodynamics with the theory of gas dynamics and established what is now called statistical mechanics. In particular, he proposed a new explanation of entropy, which links the concept of thermodynamics to the statistical characteristics of gas molecules.

Traditional thermodynamic quantities, such as temperature, pressure, heat and entropy, all refer to the macroscopic properties of gas molecules. However, macroscopic gases are made up of many molecules that rotate and collide with each other. Boltzmann distinguishes the macro state from the micro state of the system. Using this, he proved that entropy, a macro state, can be interpreted as a statistical feature of a micro state. The equation is expressed as

Here S is the entropy of the system, W is the number of different microscopic states, and k is a constant, which is called Boltzmann constant, whose value is 1.38 × 10 ^ (− 23) Joule per Kelvin. It is this public who interprets entropy as disorder. The microcosmic state corresponding to the ordered macroscopic state (Wend1) is less than that to the disordered macroscopic state (Wendy 2).

Boltzmann's ideas were not widely accepted. At the technical level, thermodynamics is plagued by conceptual problems that are difficult to understand. One is the exact meaning of "microstate". The position and velocity of molecules are continuous variables, and you can take an infinite number of values, but Boltzmann needs a limited number of microscopic states to calculate how many there are, and then take logarithms. Therefore, these variables must be "coarse-grained" to some extent, by dividing the continuous intervals of possible values into a finite number of very small intervals. Another essentially more philosophical problem is the arrow of time-a conflict between the time reversible dynamics of a micro state determined by an increase in entropy and the one-way time of a macro state. These two questions are related, which we will see soon.

However, the biggest obstacle to the acceptance of this theory is that matter is made up of tiny particles (atoms). This concept can be traced back to ancient Greece, but even around 1900, most physicists did not believe that matter was made up of atoms. So they don't believe in molecules, and the gas theory based on molecules is obviously nonsense. Maxwell, Boltzmann and other pioneers of the theory of motion were convinced that molecules and atoms were real, but for skeptics, atomic theory was just a convenient way to describe matter. Atoms have never been observed, so there is no scientific evidence of their existence. Molecules, that is, specific combinations of atoms, are also controversial. Although the atomic theory is consistent with various experimental data in chemistry, it does not prove the existence of atoms.

What finally persuaded the opponents was to use the theory of dynamics to predict Brownian motion. This effect was discovered by Scottish botanist Robert Brown. He was the first to use a microscope to discover the existence of the nucleus, which is now considered to be a repository of cellular genetic information. In 1827, Brown looked at the pollen grains in the liquid through a microscope and found smaller particles ejected from the pollen. The tiny particles swam in a random way, and at first Brown wondered whether they were some kind of tiny life form. However, experiments have shown that particles from inanimate matter have the same effect. At the time, no one knew what caused the result. We now know that the particles ejected by pollen are organelles, tiny subsystems with specific functions in cells. We interpret their random walks as evidence that matter is made up of atoms.

The connection between atoms comes from the mathematical model of Brownian motion, which first appeared in the statistical study of Danish astronomer Thorwald Tiller in 1880. Einstein put forward the physical explanation of Brownian motion: particles floating in the fluid randomly hit other particles and gave them a small force. On this basis, Einstein used the mathematical model to quantitatively predict the statistics of Brownian motion, which was confirmed by Baptiste Palin (1908-1909).

Boltzmann committed suicide in 1906, when the scientific community was beginning to realize that his theory was correct.

Entropy and Boltzmann formula provide an excellent model for many studies. It explains why the heat engine can only reach a certain level of efficiency. This applies not only to Victorian steam engines, but also to modern car engines. Engine design is one of the practical fields of thermodynamics. Power generation is another application. In coal, natural gas or nuclear power plants, heat is initially generated. The heat produces steam, which in turn drives the turbine. The turbine follows Faraday's principle and converts kinetic energy into electricity.

Therefore, the laws of thermodynamics are the basis of many things we take for granted. Interpreting entropy as "disorder" helps us to understand these laws and have an intuitive sense of their physical basis. In some cases, however, interpreting entropy as disorder seems to lead to paradoxes. This is a more philosophical area of discussion, and it is very attractive.

The arrow of time is one of the most profound mysteries in physics. Time seems to flow in a particular direction. Logically and mathematically, however, it seems that time can be turned back, and many science fiction takes advantage of this. So why can't time go back? At first glance, thermodynamics provides a simple explanation for the time arrow: it is the direction in which entropy increases. Thermodynamic processes are irreversible, such as oxygen and nitrogen will automatically mix, but will not automatically separate.

However, there is a problem here, because any classical mechanical system, such as the molecules in a room, is time reversible. In the mathematical equation, if at some point, the velocity of all particles is reversed at the same time, then the system will follow its trajectory and go back and forward in time. So why have we never seen a broken egg become complete automatically?

The usual thermodynamic answer is that broken eggs are more disordered than intact eggs, and entropy increases, which is how time flows. Another explanation is that the difference between entropy increase and time reversibility comes from the initial condition, not the equation. The equation of molecular motion is time reversible, but the initial condition is not.

The most important difference here is between the symmetry of the equation and the symmetry of its solution. The equation of the colliding molecule has time reversal symmetry. From the time reversibility of the equation, it can be inferred at most that there must be another solution, that is, the time reversibility of the first solution. If Xiao Ming throws the ball to Xiao Hua, the reverse of time is that Xiao Hua throws the ball to Xiao Ming. Similarly, since the mechanical equation allows a vase to fall to the ground and break into a thousand pieces, they must also allow a solution, that is, a thousand pieces of glass to mysteriously gather together to assemble a complete vase.

But we have never seen a broken vase recover by itself. This is also a problem about boundary conditions (initial conditions). The initial conditions of the vase breaking experiment are easy to realize and the experimental equipment is easy to obtain. In contrast, vase assembly experiments require extremely precise control of countless individual molecules without any interference.

The mathematical calculation of entropy masks the details on these very small scales. It makes the vibration disappear without increasing; it converts friction into heat, but not heat into friction. The difference between the second law of thermodynamics and microscopic reversibility comes from the coarse granulation hypothesis. These assumptions implicitly specify a time arrow: large-scale disturbances are allowed to disappear below perceptible levels over time, but small-scale disturbances are not allowed to follow time reversals.

If entropy keeps increasing, how does the chicken create an orderly egg? A common explanation is that life systems somehow borrow "order" from their environment and compensate for "disorder" by making the environment more disordered than it used to be. This extra order is equivalent to "negative entropy", which chickens can use to hatch their eggs without violating the second law.

This article comes from the official account of Wechat: Lao Hu Shuo Science (ID:LaohuSci). Author: I am Lao Hu.

Welcome to subscribe "Shulou Technology Information " to get latest news, interesting things and hot topics in the IT industry, and controls the hottest and latest Internet news, technology news and IT industry trends.