Energy

Energy - a concept which we commonly use is surprisingly abstract [2]. All we know from our experience is that the total energy is conserved. The law of conservation states that there is a quantity, called energy that doesn't change with all the changes occurring around us. But, what is energy? We will try to become familiar with this important concept.

Kelvin and Rankine defined the concept of energy in order to understand the physical principles underlying the heat engines [3]. Engines were simplified as devices that raised weights by a certain height, given some amount of coal to burn [4]. In 1840s, there were very significant discoveries and publications by Joule and Mayer where they proved that heat is simply a mode of motion. The definition by Kelvin and Rankine was inspired by this.With slightly different terminology, Helmholtz proved that the ability to perform work is conserved in a wide range of processes. When we strike a matchstick to light it, the energy provided by us and the chemical reaction produces heat and light. In a moment, several transformations of energy take place. We can also ask - is there a macroscopic quantity that has changed when motion ceases “without having caused another motion”? Answer could be that objects get warmer. In his remarkable essay, the French engineer Sadi Carnot (1824) asked: Is the motive power of heat invariable in quantity, or does it vary with the agent which one uses to obtain it? After a number of subsequent developments, Helmholtz (1870 ca) concluded that energy has many forms and that the total energy should be taken as a sum of all possible forms of energy. We can appreciate it as we realize [1] that 4.18 Joules (J) is associated with all the following - (i) work done in pushing with a force 4.18 N through a distance of 1 m; (ii) can produce 1 calorie of heat; (iii) can move 2.6 x 1019 electrons through a potential difference of 1 volt; (iv) can raise 100 g by 418 cm.

From the work of Carnot and others, we were led to the concept of efficiency of engines. This led to a technological revolution where one was attempting to invent the most efficient engine.

In the earlier chapters, we have discussed mechanics and waves. Mechanics deals with point particles and rigid bodies. However, these idealizations do not allow energy to be stored in them in any form - rotational or vibrational motions. As the constituents of rigid body remain fixed in length w.r.t. each other, energy cannot be exchanged with them. Physics of systems where energy may be stored, converted from one form to another, requires us to understand the laws of thermodynamics. One of the most important concepts is that of entropy. The mystery of this concept has been removed in a series of papers by Leff [84, 85, 87, 88, 103]. We take advantage of these recent essays and follow them rather closely.

There are four laws on which thermodynamics is based. Each of the laws, zeroth law to the second law have given a new concept - temperature, energy, and entropy. The third law has established a limitation on thermodynamic functions. We shall explain the ideas and concepts in some detail. The applications of these ideas to real life are everywhere around us. The changes occurring all around from one state to another are consistently described within these laws. To relate a few common instances [100], we have noticed that the valve on a bicycle pump gets hot when we are pumping up a tyre. Why? When we pump and compress the gas, there is no heat transfer from outside. The process is adiabatic. The internal energy of the air increases, leading to an increase in temperature. This hot air heats up the valve. As a second example, again drawn from our experience, is the warm (even hot in certain regions in Northern India) dry wind that blows down from mountains into plains. It is called differently in different parts of the world - Loo (India), Kachchan (Sri Lanka), Santa Ana (Southern California), Chinook (North America), Foehn (Switzerland), Berg Wind (South Africa). As winds come down from the mountains, they move into the regions of greater atmospheric pressure. Hence, the moving air is adiabatically compressed and heated. As the descent is fast, there is no time for any significant exchange with local air. So this wind is warm and dry.

A scientific appreciation of the world around us requires classical physics. The familiar, however, looks somehow more complex than what is learned at school. That a distilled set of equations will allow us an understanding seems somewhat doubtful. During 2011–2014, in my lectures on “Classical physics” a four-month long semester course to first-year undergraduates, I tried to bring some of these observations into the classroom. The encouragement received from the students provided me enthusiasm to write these notes. I have used a large number of sources - several fascinating books and articles published in journals. Hence, this work does not claim originality. Here a compact account is presented, which is understandable in one semester. This has been experimentally verified, so to say!

The goal is to dig deeper into the mechanics of single particle to that of many particles to kinetic theory, and, to proceed from oscillations to waves to sound, eventually we discuss the elementary concepts of thermodynamics. Problem-solving is an integral part of the course; this was done by student-teams, each consisting of five to six students. Cooperation is a lesson that is learnt best, early in life.

What is classical physics?

Is it physics where the Planck's constant is zero? That does not sound very meaningful as we are given a world or a universe which is labelled by a value of the Planck's constant. It would be more meaningful to say that “Classical Physics” describes phenomena where we might do away with the Planck's constant. For instance, planetary motion may be understood without worrying about quantum mechanics. However, it is useful and important that we pursue this study with an awareness of quantum theory. Many aspects of quantum mechanics are intricately linked and even dependent on the structure of classical mechanics. The meaning of momentum operator in quantum mechanics is understood with the help of the usual notion of momentum in classical mechanics. On the other hand, there are phenomena described classically where the concept of a quantum is employed. For instance, in our dealing with turbulence of fluids or plasma the interaction between a particle or a wave with another wave is described using the quanta called plasmons - a quantum of a collective excitation.