Social scientists need to employ a comparative approach if they want to explain cultural variation from a cross-cultural perspective (Smith et al. 2012). The fundamental analytical problem is that the modern era simply does not encapsulate enough of the variation for how humans have lived or in fact do live. Although a few economists have attempted to include premodern economies into formal modeling of economic systems (Dow and Reed 2022), the collection of evidence on premodern economies and its interpretation primarily is the job that anthropologists and historians must undertake. This volume undertakes the challenge of developing a comparative understanding of premodern economies. We feel that economists often misrepresent modern economies by oversimplifying processes by not considering many earlier economic relationships of labor and exchange that continue into the present day. We envision economies as historically developed, adding new processes related to scale and changing objectives over time. As a first step, we should clarify what we mean when we discuss premodern economies.

1.1 Introduction

“Thermodynamics” is the branch of science that deals with the macroscopic properties of matter. In this branch of physics, concepts about heat and work and their inter-conversion, energy and energy conversion, and working principle of heat engines with their efficiency are mainly discussed. The name “thermodynamics” was originated from two Greek words: “therme” means “heat” and “dynamics” means “power” or “energy”. Thus, matter related to heat and energy is primarily paid attention in this subject. Further, it is believed that the term “thermodynamics” arises from the fact that the macroscopic thermodynamic variables used to describe a thermodynamic system depend on the temperature of the system.

Thermodynamics is the branch of physics in which the system under investigation consists of a large number of atoms and molecules contributing to the macroscopic matter of the system. The average physical properties of such a thermodynamic system are determined by applying suitable conservation equations such as conservation of mass, conservation of energy, and the laws of thermodynamics in equilibrium. The equilibrium state of a macroscopic system is achieved when the average physical properties of the system do not change with time and the system is not driven by any external driving force during the course of investigation. The interrelationships among the various physical properties are established with the help of associated thermodynamic relations derived from the laws of thermodynamics. These average (macroscopic) properties of thermodynamic systems are determined from the macroscopic parameters such as volume 𝑉 , pressure 𝑃 , and temperature 𝑇 , which do not depend on the detailed positions and ocities of the atoms and molecules of the macroscopic matter in the system. These macroscopic quantities are called thermodynamic coordinates, variables or parameters. Further, these macroscopic properties depend on each other. Therefore, from the measurements of a subset of these properties, the rest of them can be calculated using the associated thermodynamic relations.

DISTRIBUTIONS ARE GENERALIZATIONS of mathematical functions from a purely technical standpoint. But perhaps it is most pertinent to begin by asking a more utilitarian question. Why should we study distributions? Specifically, why should we study probability distributions? One of the motivations stems from a practical limitation of experimental measurements that is underlined by the uncertainty principle postulated by Werner Heisenberg (see Figure 2.1). The very fabric of reality and the structure of scientific laws that govern our ability to understand physical phenomena demand a probabilistic (statistical) approach. Our inability to make infinite-precision measurements of data necessitates the consideration of averages over many measurements, and under similar conditions, as a more reliable strategy to affix experimental values to unknowns with reasonable accuracy.

5A Saha ionization equation

At a high enough temperature and/or density, the atoms in a gas suffer collisions due to their high thermal energy, and some of the atoms get ionized, making an ionized gas. In this process, a number of electrons that are normally bound to the atom in orbits around the atomic nucleus become free and thus form an independent electron gas cloud coexisting with the surrounding gas of atomic ions and neutral atoms. These ionized atoms and electrons generate an electric field that causes motion of the charges, and a current is generated in the gaseous medium. This current produces a localized magnetic field. The state of matter thus created is called plasma. In thermal equilibrium, the ionization state of such a gaseous system is related to the ionization potential, temperature, and pressure of the system. Thus, the Saha ionization equation. expresses how the state of ionization of any particular element in a star changes with varying temperatures and pressures. This equation takes into account the combined ideas of quantum mechanics and statistical mechanics for its derivation and is used to explain the spectral classification of stars. This equation was developed by the Indian astrophysicist Prof. Meghnad Saha in 1920. 5A.1 Derivation of Saha ionization equation According to Prof. M. N. Saha, the temperatures in the interior of stars are extremely high, and the elements present there are mostly in the atomic state. Saha argued that under the prevailing conditions inside the stars, atoms move very rapidly and undergo frequent collisions. In the process of such collisions, valence electrons are stripped off from their orbits. This is referred to as thermal ionization and is accompanied by electron recapture to form neutral atoms. The degree of such thermal ionization depends on the temperature of the star. Using the Saha ionization equation, a general relation between the degree of thermal ionization and the temperature can be obtained from the statistical description of plasma in thermodynamic equilibrium.

The advent of the internet and sensor technology has enabled humankind to collect, store, and share data in bulk. In turn, access to a variety of data has amplified a different kind of problem, which is to devise an appropriate strategy to derive meaning from data. Indeed, extracting information from data has acquired the highest priority among tasks performed by engineers and scientists alike. State-ofthe-art machine learning algorithms are used to process and analyze data in order to leverage maximum gains in developing new technology and creating a new body of knowledge.

Further, the data-rich tech-universe has inherent complexity in addition to the vastness in terms of numbers. This complexity arises from the fact that often this data is embedded in a higher-dimensional space. For example, the data acquired by a camera hosted on a robot is in the form of multiple grayscale images (frames); each data-frame is constituted of a sequence of numbers that represents the intensity of grayness of each pixel. If each image has a resolution 100 × 100 (pixel count), then this image data is embedded in a 10000 dimensional space. Additionally, if the camera records 100 frames per second for one minute, then we have 6000 data points in a 10000 dimensional space. This is just an illustrative example of how a high-dimensional large data set may be generated. Quite evidently, not all the 10000 dimensions host most of the information. One of the most important techniques that we will learn in this chapter will allow us to extract a lower dimensional representation of the data set that will retain sufficient information for the robot to navigate and perform its tasks.

Analog electronic circuits are generally offered as a core subject during the third or fourth semester of the second year in a four-year course in the electronics and communication, instrumentation and control, and computer engineering branches. It is an important subject and may be slightly toned down in the electrical, civil, chemical, and information technology branches of engineering. Design of discrete and linear integrated circuits (ICs), digital electronic modules, and electronic instrumentation are some of the obvious areas where knowledge of microelectronic circuits becomes essential. Therefore, it becomes important for students at this level of study to be proficient in electronic circuit analysis and their usage in relevant areas.

There are many fine books on electronic (devices and) circuits. Many of them have combined “devices” and “circuits”; a good practice, but sometimes resulting in the book becoming bulky. The idea here is to provide a text that deals with the fundamentals of analog electronic circuits for those who already have a basic knowledge of electronic devices, like semiconductor diodes, bipolar junction transistors (BJTs), and metal oxide semiconductor transistors (MOSFETs), either as full subject or as an introductory subject. Serious effort has been made in preparing the text so that it is not only as study material for examinations but also emphasizes fundamental concepts without being overly voluminous.

3A Temperature in Thermodynamics

For an infinitesimal reversible process, a combination of first and second laws of thermodynamics results

where 𝑌 𝑑𝑋 denotes the generalized expression for work done by the system, 𝑑𝑆 is the change in entropy, and 𝑑𝑈 is the change in internal energy of the system. Equation (16) leads to the definition of temperature 𝑇 as

Thus, equation (17) indicates that the temperature at any point depends on the slope of the 𝑆 − 𝑈 curve. If the slope of this curve (point 𝐴 in Figure 3A.1) is positive, the temperature will be positive. On the other hand, the temperature will be negative for the negative slope of the curve (point 𝐶 in Figure 3A.1).

Appendix B

The book Heat and Thermodynamics: Theory, Problems, and Solutions is an informal, readable introduction to the basic ideas of thermal physics. It is aimed at making the reader comfortable with this text as a first course in Heat and Thermodynamics. The basic principles and phenomenological aspects required for the development of the subject are discussed at length. In particular, the extremum principles of entropy and free energies are presented elaborately to make the content of the book comprehensive. The book provides a succinct presentation of the material so that the student can more easily determine the major objective of each section of a particular chapter. In fact, thermal physics is not the subject in physics that starts with its epigrammatic equations—Newton’s, Maxwell’s, or Schrodinger’s, which provide accessibility and direction. Instead, it (thermodynamics) can be regarded as a subject formed by the set of rules and constraints governing interconversion and dissipation of energy in macroscopic systems. Further, the syllabus of statistical mechanics for graduate students has changed significantly with the introduction of National Education Policy 2020.

Thermal physics has established the principles and procedures needed to understand and explain the properties of systems consisting of macroscopically large numbers of particles, typically of the order of 1023 or so. Examples of such collections of systems include the molecules in a closed vessel, the air in a balloon, the water in a lake, the electrons in a piece of metal, and the photons (electromagnetic wave packets) emitted by the Sun. By developing the macroscopic classical thermodynamic descriptions, the book Heat and Thermodynamics: Theory, Problems, and Solutions provides insights into basic concepts and relationships at an advanced undergraduate level. This book is updated throughout, providing a highly detailed, profoundly thorough, and comprehensive introduction to the subject. The laws of probability are used to predict the bulk properties like stiffness, heat capacity, and the physics of phase transition, and magnetization of such systems.

8.1 INTRODUCTION [LO1]

In simple words, the application of a torque on a prismatic member causes twisting or torsion. This causes shear stress if a torque alone is applied. However, this is rarely true in practical cases. A circular bar, used to transmit torque between a prime mover and a machine, is a typical example of a torsion member. However, in many applications, a torque along with a bending moment and axial loading are applied, and there we need to combine these effects and find the principal stresses. A typical example of such combined stresses is a propeller shaft. Torsional problems are important in many applications both in industry and in our daily life. Therefore, we consider torsion alone in this chapter in some detail.

Torsional problems for circular members are generally solved assuming that plane sections normal to the axis of the bar remain plane even after twisting. This assumption was first made by Coulomb intuitively in 1784, and he came up with a correct usable equation for members with circular sections. However, this assumption does not apply to bars with a noncircular cross-section. Navier attempted to solve torsional problems with noncircular sections using Coulomb's assumption and came up with an erroneous solution. The correct solution was provided by St. Venant in 1853 using a warping function. Much later, in 1903, Prandtl came up with a membrane analogy method that could solve problems with any complicated cross-section. First, we shall consider torsional problems with circular cross-sections.

8.2 TORSION OF MEMBERS WITH CIRCULAR CROSS-SECTION [LO2]

The torsion analysis of members with a circular cross-section starts with simplified assumptions made by Coulomb. In order to establish a relation between the applied torque and shear stress developed and the angle of twist in such cases, the following assumptions are made:

• 1. Material is homogeneous and isotropic.

• 2. Plane sections perpendicular to the axis of a circular member remain plane after twisting. No warping or distortion of the parallel planes occurs.

Transistor Biasing

When transistors are used as switches, they operate either in cut off or in saturation mode. Whereas, when transistors are used to amplify small signals, a quiescent operating point is selected somewhere in the middle of the conduction range. The region of the location of a quiescent point depends on the kind of amplifier. For example, an amplifier may be used for maximum voltage and/or current gain, or high input resistance, or power gain. In some applications, an amplifier ought to consume minimum power, especially when it is used with a battery-operated device. After selecting the quiescent operating point, it is also required that it remains stable. If there is some change in the operating temperature or variation in supply voltage, the operating point may change its location. Variations due to the manufacturing tolerance in component values and in transistor parameters also affect the quiescent point. Irrespective of the reason, it is required that the quiescent point should remain located within specified limits.

Three amplifier configurations are commonly used while employing either BJT or FET amplification. The configuration depends on the terminals, out of the three, that is common to the input and the output of the amplifier. These configurations are studied on the basis of their characteristics, such as voltage gain, current gain, input and output resistance, and bandwidth, i.e., the frequency range within which the amplifier operates without any significant reduction in the output waveform. The operating frequency range becomes limited as the voltage gain drops at low and high operating frequencies. Hence, the study of frequency response becomes important.