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.

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The Cambridge Companion to Periyar has been jointly edited by two researchers belonging to two different generations. When the first editor began his writing career in the mid-1980s, Periyar's was not a name that could be taken in genteel, academic circles. By the time the second editor began his doctoral work at a British university in 2011, the topic was a study in political theory, comparing Periyar with a major international thinker (Frantz Fanon). In the intervening generation, much had changed in the fortunes of academic writing on Periyar. After decades of being ignored or consigned to the margins by Indian sociologists and historians, we can say that Periyar has arrived in global scholarship. This volume exemplifies this turn.

Paralleling Periyar's rising influence during these intervening decades, there has been vigorous academic interest in studying the Dravidian movement. Newer and newer editions of Periyar's writings—covering the spectrum from multivolume sets to popular paperbacks—are being published every year. Any visitor to the annual Chennai Book Fair would be amazed by the piles of books by and on Periyar. The transformation of the Periyar Library and Research Centre housed in the Chennai headquarters of the Dravidar Kazhagam (DK) from a sweltering hall roofed by an asbestos sheet in 1981, when the first editor first consulted it, to a comfortable air-conditioned hall with expanded print resources indexes the growing academic interest in Periyar. Social media is also abuzz with young readers discussing animatedly the ideas of Periyar.

A little over a hundred years after the non-Brahmin manifesto put forth by the South Indian Liberal Federation, better known as the Justice Party, in 1916 that advocated for adequate representation for non-Brahmin groups, Tamil Nadu's legislative assembly is India's most diverse in terms of caste representation (Verniers et al., 2021).

This legislative assembly's diverseness has been often attributed to the capacious Dravidian– Tamil1 identity and its ethos, which continue to inform the politics of the Dravidian parties that have governed the state since 1967. The capaciousness of the ethos that defines the Dravidian– Tamil identity, which has allowed for horizontal solidarities across caste groups that otherwise share a hierarchical relationship, stems from the socio-economic and cultural aspirations of these groups. These horizontal solidarities and aspirations continue to derive both their legitimacy and sustainability from the ever incremental and yet radical, anti-caste episteme and activism of Periyar. This chapter is an attempt to engage with him and the way his ideas may be located or traversed both within and outside the literature of other academics, intellectuals, and scholars not just of the subcontinent but across the world. His anti-caste episteme and the vocabulary of his activism are informed by a demand for adequate representation of non-Brahmins—grounded either in their demographic weight or in a historically embedded sense of tension with Brahminical hegemony.

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.

9.1 Introduction to Classification

We rely on machine learning (ML) to make critical decisions or predictions in the modern world. It is very important to understand how computers by using ML make these predictions. Usually, the predictions made by ML models are classified into two types, i.e., classification and regression. The ML models use various techniques to predict the outcome of an event by analyzing already available data. As machines learn from data, the type of training or input data plays a crucial role in deciding the machine's capability to make accurate decisions and predictions. Usually, this data is available in two forms, i.e., labeled and unlabeled. In label data, we know the value of the output attribute for the sample input attributes, while in unlabeled data, we do not have the output attribute value.

For analyzing labeled data, supervised learning is used. Classification and regression are the two types of supervised learning techniques used to predict the outcome of an unknown instance by analyzing the available labeled input instances. Classification is applied when the outcome is finite or discrete, while the regression model is applied when the outcome is infinite or continuous. For example, a classification model is used to predict whether a customer will buy a product or not. Here the outcome is finite, i.e., buying the product or not buying. In this case, the regression model predicts the number of products that the customer may buy. Here the outcome is infinite, i.e., all possible numbers, since the term quantity refers to a set of continuous numbers.

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).

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.

11.1 INTRODUCTION [LO1]

Stresses developed at the contact between two loaded elastic bodies are generally localized and most machine parts or structures are designed based on the stresses in the main body. However, there are many important machine members where the localized stresses developed at the contact between curved surfaces with initially limited contact area play an important role in their design. Ball or roller bearings, gears, cams, and valve tappets of internal combustion engines are some of the examples of machine parts where contact stresses must be taken into account in order to predict their failure probability.

The localized contact stresses that develop between two curved bodies as they are loaded with small deformations are often referred to as Hertzian stresses, following the work of H. Hertz (1881), who first solved these contact problems elegantly more than a century ago. Since then the topic has received a good deal of attention by the researchers due to its importance in engineering practice and science. Much work has been done on the stress distribution at the Hertzian contact surfaces and sub-surfaces. Ball bearings and gear teeth often fail by pitting. Hertzian stress analysis can precisely locate the depth at which maximum shear stress occurs where cracks may initiate and propagate leading to failure. Thus, a remedy to such failures may be prescribed in terms of limiting stresses. In many rolling contact problems, failure occurs with the initiation of a tiny crack that eventually grows due to repeated contacts. Analysis of crack initiation and growth is often based on Hertzian stress analysis. In this chapter, we shall consider the basics and application of contact stress analysis, beginning with some basic elasticity theory necessary for such analyses.

2.1 MATHEMATICAL PRELIMINARIES [LO1]

In any scientific or engineering field of study, knowledge of some mathematical techniques and methods are essential. Solid mechanics is no exception. To develop proper formulation methods and solution techniques for elasticity problems, it is necessary to have an appropriate mathematical background. In this chapter, we shall discuss Cartesian tensors, which have a special significance in the discussion of stress, strain, and displacement fields, and their manipulation. Other mathematical details will be discussed as and when they are required in solving different problems.

Tensors may be defined in a number of ways. One simple definition is that a tensor is a physical quantity that is governed by certain transformation laws when the coordinate system is changed. A tensor is invariant under any change of coordinate system, but its components along the coordinate axes change with the changed coordinate system. Tensors of order zero are called scalars. Common examples of scalars are temperature, density, Young's modulus, or Poisson's ratio. They have a single magnitude at each point in space, and they are invariant with coordinate transformations. A typical example of scalars is often taken as temperature T at a point in space with coordinates (x, y, z) represented as T(x, y, z). Temperature at the same point does not change if we choose a different coordinate system (x′, y′, z′) represented as T′(x′, y′, z′) and we may say

T=T′. (2.1.1)

Tensors of first order are vectors, and we know that a vector has a magnitude and a direction. A typical example of a vector is a velocity vector V. It is sometimes taken as a convention to represent a vector by a bold letter. Consider the velocity vector V in (x, y, z) coordinate system.

Ideologue, reformer, feminist, firebrand secessionist: these are some of the many things E. V. Ramasamy Periyar has been called. If there is one strand of Periyar's thought that runs through all these titles and the politics that informed them, it would be his clarion call for self-respect. Not one to stop at dismantling the hegemonic power structures that he saw around him in India, Periyar was committed to the cause of reform in and for the Tamil diaspora as well. His views on nationhood thus ‘constantly violated the certitude about boundaries, identities, agents of change, and went beyond the territoriality of the nation’ (Pandian, 1993, p. 2282). Periyar emphasized that foreign settlement could enable the regeneration of Tamil society abroad, unfettered by India's oppressive traditions. Moreover, he saw the diaspora as an important source of financial support for the Dravidian movement. To this end, Self-Respect literature often asserted that Tamil people everywhere were bound by obligations of mutual assistance and reciprocity (Alagirisamy, 2016). Periyar visited British Malaya and Singapore twice in his lifetime: once in 1929–1930 and again in 1954–1955. Both visits were pivotal in aiding the development of a settled Tamil political consciousness in Singapore.

Scholars of the Indian Ocean world continue to trace the comings and goings of sojourners and settlers, privileging the ocean itself as a key agent of change (Moorthy and Jamal, 2010; Amrith, 2013; Menon et al., 2022). Yet, settlement also brought with it a sea-change in the lived presents and anticipated futures of migrant communities that aspired to citizenship.

The popular focus on Periyar and Dravidian—as a person leading his loyal people—may invite placing nationalism's assertion, rather than critique, at the heart of political thought in twentieth-century Tamil-speaking South India. ‘Nationalism’ names the intuition that ‘France [is] for the French, England for the English … and so forth’ (Shaw, 2013) or, more generally, ‘nationalism is a theory of political legitimacy … requir[ing] that ethnic boundaries should not cut across political ones’, insisting on ‘congruence of state and nation’, and refusing ‘ethnic divergence between rulers and ruled’ (Gellner, 1983, pp. 1, 134). Much turns on ‘ethnic’. Considerations include whether ‘ethnic’ is ‘racial’ or ‘historically constituted’ (Lenin and Stalin, 1970, pp. 66–68) and nationalism's ‘inherent contradictoriness’, both because its ‘rational and progressive’ promises of modernity are often premised on ‘traditional and conservative’ gestures to the past and because its anti-colonial articulation usually adopts the very imperial ‘representational structure … nationalist thought seeks to repudiate’ (Chatterjee, 1986, pp. 22, 38). So, when the August 1944 creation of the Dravidar Kazhagam (DK) was heralded with ‘Long live Periyar, Dravida Nadu for the Dravidian, let the Dravidar Kazhagam flourish’1—entrenching an ‘ethnic’ idiom for Tamil-speaking South India's politics—an invitation for ‘a chapter on Periyar and nationalism’ encourages the interrogation of a twinned presumption of coherence: not simply of ‘Dravidian’ as a people loyal, but of ‘Periyar’ as a person leading.