Basic Physics Of Quantum Theory, The. Basil S Davis
stationary molecules. Unless we can find such a gas somewhere in the universe — which is impossible, considering that the universe is constantly cooling down from a very hot initial state — it is impossible to reduce the temperature of any gas to absolute zero.
3.3.5Second law of thermodynamics
Suppose we have a thermally insulated container of gas with two compartments, one having gas A initially at 150° C and the other having gas B initially at 50° C and these compartments are separated by a wall that permits heat to flow through it. Since heat is due to the kinetic energies of the molecules of the gas, the average kinetic energy of the molecules of A is greater than the average kinetic energy of the molecules of B. Due to the randomness of the collisions of the gas molecules with the molecules of the wall that separates them, the molecules of A will gradually impart some kinetic energy to the molecules of the wall, which in turn will pass on the kinetic energy to the molecules of B. The result is that the molecules of A will gradually slow down, and the molecules of B will gradually speed up. This transfer of kinetic energy will continue until both compartments have the same average kinetic energy. Thus both the gases will have the same temperature, and heat has flowed from the hotter body A to the cooler body B. It is impossible for the reverse to happen. And thus the Second Law of Thermodynamics follows from the fact that any piece of matter is made of a very large number of particles in random motion.
Because heat cannot flow from a cold body to a hot body by itself, the Second Law of Thermodynamics provides a unique arrow of time. Suppose an ice cube were placed in a glass of warm water. A video recording will show the ice melting as it receives heat from the water. If the video were played backwards it would show a tiny piece of ice gradually becoming bigger until it acquired the shape of a cube floating on the warm water. It is evident that this sort of time reversal cannot occur in nature. The flow of time is like the flow of heat. It cannot be reversed. As we saw earlier in this chapter, when we have a large number of microscopic particles, no matter how orderly they are arranged in the beginning, once the system is set in motion, the random collisions will create a disorder from which the original order can never be retrieved. This has some very important consequences.
One consequence is the diminishing of available energy. An array of molecules all moving together can apply a concerted force which can therefore do a lot of work on an object and impart a corresponding energy to the object. But if the molecules are moving haphazardly, the force they can exert together is considerably less, and so the amount of energy that can be provided is less. Thus, in an irreversible process the amount of available energy decreases. So the Second Law can also be stated as: natural processes always take place in such a way that the amount of available energy decreases.
Another consequence is the collapse of orderliness. An array of molecules all moving with the same velocity parallel to each other is a highly orderly system. But as the system is left to itself, the degree of orderliness will gradually diminish until there is total randomness. So the Second Law can also be stated thus: natural processes will always take place in such a way that there is a loss of order. Disorderliness is also called entropy. So another formulation of the Second Law: Natural processes occur in such a way that the entropy increases. Yet another consequence is the loss of information. We could create different arrays of molecules which are all orderly, but not identical with each other. Let us say we have two boxes with the same number of molecules all moving parallel to each other. In one box we divide the molecules into two parallel arrays with a gap between them. In the second box we have the same number of molecules, all parallel to each other, but without a gap. We could label the first box 0 and the second box 1. The distinction between the two boxes allows us to store information. The simplest information is binary — yes or no. We could agree that 0 means yes and 1 means no, or vice versa. Now, suppose we allow both the boxes to stand for a while. After some time all the molecules in both boxes will be moving at random, and the gap between the molecules in the first box will vanish. And so the distinction between the two boxes has disappeared. We can no longer tell which is 0 and which is 1. The information is lost. So the Second Law can be stated thus: Natural processes tend to destroy information.
The Second Law explains our consciousness of the flow of time. Momentary experiences are instantly converted to memories which are constantly being stored in our brains. We remember the past but not the future because the past has left an imprint in our memories, somewhat like the sedimentary layers under the soil studied by archaeologists. As we acquire more knowledge, more information is stored in our brains. At first sight this appears to go against the Second Law, but it is not hard to see that the Second Law is not violated. The increase of information stored in the brain is accompanied by the loss of biological information which had been stored in the food that we digested and converted to energy. So overall, as human knowledge increases, it does so at the expense of the information that exists outside of our bodies. The storing of information in computer memories also requires energy which is ultimately obtained by the loss of information in the fuels that produce the energy. The constant supply of energy maintains the increase of information and order within our bodies, but even this process is not unending. The Second Law is also responsible for biological aging and the gradual erosion of our memories with time. The body is programmed to generate order and to decrease entropy through the intake of food and oxygen. But eventually the body will give up the fight against the tendency to greater disorder and higher entropy. Biological death is a consequence of the Second Law.
The most important thing to learn about the Second Law is that it is a statistically based law. Its validity rests on the very large number of atoms or molecules that make up a normal mass of matter. Maxwell — one of the pioneers of Statistical Mechanics — boldly declared: “The true logic of this world is in the calculus of probabilities.”3 Maxwell showed that Newton’s Laws do not forbid heat from flowing from a cooler body to a warmer body, but he pointed out that the probability of this occurring is microscopically small.4 So a law so fundamental as the Second Law of Thermodynamics is rooted in probability. This seemed an outright affront to the determinism that was engendered by Newton’s Laws, and many philosophers and physicists resisted this statistical explanation of a basic physical law. But eventually all objections were overcome with the establishment of the atomic or molecular structure of matter.
Maxwell’s dictum about the true logic of this world ultimately won the day in the triumph of quantum theory, of which he himself knew nothing. Maxwell died at the age of 48 in 1879, twenty one years before the birth of quantum theory. In quantum theory, it is probabilities that dictate the outcome of any process. The only real prediction we can make is the probability of observing one or another outcome. Maxwell’s prophetic insight into microscopic phenomena made it easier for scientists to embrace the counterintuitive notions of quantum theory.
3.4Summary
All matter is composed of indivisible particles called atoms. Atoms tend to combine with other atoms to form molecules. (Some molecules such as Helium and Argon consist of a single atom). The most important visible proof of the existence of such microscopic molecules is Brownian motion, the erratic dancing motion of pollen grains suspended in water. The laws of the combination of elements according to proportions of weight also reveal the atomic structure of matter.
The atomic structure of matter is especially discernible in the experience of heat and temperature. Heat is the energy possessed by the molecules of an object. The temperature of an object is proportional to the average kinetic energy of the molecules. Because there are a very large number of molecules in any normal quantity of a material, it is impossible to study the motions of all the molecules with precision. So we study their statistical behavior. This branch of physics is called statistical mechanics.
The study of the relationship between heat and mechanical energy is called thermodynamics. There are four important laws of thermodynamics:
a) the zeroth law which deals with objects in thermal equilibrium with one another,
b) the first law which states that heat can be converted to work and vice versa and there is no loss or gain of energy in this process,
c)