This chapter deals with the cardiac system that underpins animal vitality that is more complex than the vegetative one discussed in the previous chapter. The central activity of this system is breathing, and the chapter outlines different types of breathing posited by Galen, the anatomy underpinning them, and his explanation of why the deprivation of breath leads to the loss of life. The chapter also focuses on the three types of pneuma theorized by Galen, discussing their proper activities and properties enabling these activities. The focus on pneuma also brings attention to yet another Galenic division of parts into solids, fluids and pneumata. This division of tissues according to their texture and speed of movement offers an important glimpse into how Galen conceives of interaction between parts. Moreover, the rapid alterations in the pneumatic tissues underpin the physiological understanding of animal vitality.

Solid mechanics, compared to mechanics of materials or strength of materials, is generally considered to be a higher level course. It is usually offered in higher semester to senior students. There are many textbooks available on solid mechanics, but they generally include a large part of theory of elasticity with in depth mathematical formulations. The usual prerequisites are one or two semester course on elementary strength of materials and a thorough mathematical background, including scalar, vector, and tensor field theory and cartesian and curvilinear index notation. The difference in levels between these books and elementary texts on strength of materials is generally formidable. However, in our experience of teaching this course for many years at premier institutes like IIT Kharagpur and Jadavpur University, despite its complexity, senior students generally cope well with the course using the readily available textbooks.

However, there is a vast student population pursuing mechanical, civil, or allied engineering disciplines across the country in colleges where AICTE curriculum is followed. Through several years of interaction with this group of students, we have found that there is no suitable textbook that suits their requirements. The book is primarily aimed at this group of students, attempting to bridge the gap between complex formulations in the theory of elasticity and elementary strength of materials in a simplified manner for better understanding. Index notations have been avoided, and the mathematical derivations are restricted to second-order differential equations, their solution methodologies, and only a few special functions, such as stress function and Laplacian operators.

The text follows more or less the AICTE guidelines and consists of twelve chapters. The first five chapters introduce the engineering aspects of solid mechanics and establish the basic theorems of elasticity, governing equations, and their solution methodologies. The next four chapters discuss thick cylinders, rotating disks, torsion of members with both circular and noncircular cross-sections, and stress concentration in some depth using the elasticity approaches. Thermoelasticity is an important issue in the design of high-speed machinery and many other engineering applications. This is dealt with in some detail in the tenth chapter. Problems on contact between curved bodies in two-dimensional and three-dimensional situations can be challenging, and they have wide applications in mechanical engineering such as in bearing and gear technology.

3.1 STATE OF STRESS AT A POINT [LO1]

When a body is subjected to external forces, its behavior depends on the magnitude and distribution of forces and properties of the body material. Depending on these factors, the body may deform elastically or plastically, or it may fracture. The body may also fail by fatigue when subjected to repetitive loading. Here we are primarily interested in elastic deformation of materials.

In order to establish the concept of stress and stress at a point, let us consider a straight bar of uniform cross-section of area A and subjected to uniaxial force F as shown in Figure 3.1. Stress at a typical section A - A′ is normally given as σ = F/A. This is true only if the force is uniformly distributed over the area A, but this is rarely true. Therefore, definition of stress must be considered by progressively reducing the area until it is small enough such that the force may be considered to be uniformly distributed.

To understand this, consider a body subjected to external forces P1, P2, P3, and P4 as shown in Figure 3.2. If we now cut the body in two pieces,

Internal forces f1, f2, f3, etc. are developed to keep the pieces in equilibrium. Now consider an infinitesimal element of area ΔA Dat the cut section and let the resultant force on the element be Δf.

learning Outcomes

After reading this chapter, the reader will be able to

• Understand the meaning of three processes of heat flow: conduction, convection, and radiation

• Know about thermal conductivity, diffusivity, and steady-state condition of a thermal conductor

• Derive Fourier's one-dimensional heat flow equation and solve it in the steady state

• Derive the mathematical expression for the temperature distribution in a lagged bar

• Derive the amount of heat flow in a cylindrical and a spherical thermal conductor

• Solve numerical problems and multiple choice questions on the process of conduction of heat

6.1 Introduction

Heat is the thermal energy transferred between different substances that are maintained at different temperatures. This energy is always transferred from the hotter object (which is maintained at a higher temperature) to the colder one (which is maintained at a lower temperature). Heat is the energy arising due to the movement of atoms and molecules that are continuously moving around, hitting each other and other objects. This motion is faster for the molecules with a largeramount of energy than the molecules with a smaller amount of energy that causes the former to have more heat. Transfer of heat continues until both objects attain the same temperature or the same speed. This transfer of heat depends upon the nature of the material property determined by a parameter known as thermal conductivity or coefficient of thermal conduction. This parameter helps us to understand the concept of transfer of thermal energy from a hotter to a colder body, to differentiate various objects in terms of the thermal property, and to determine the amount of heat conducted from the hotter to the colder region of an object. The transfer of thermal energy occurs in several situations:

• When there exists a difference in temperature between an object and its surroundings,

• When there exists a difference in temperature between two objects in contact with each other, and

• When there exists a temperature gradient within the same object.

Learning Outcomes

After reading this chapter, the reader will be able to

• Express the meaning of sphere of influence and collision frequency

• Derive the distribution function for the free paths among the molecules and demonstrate the concept of mean free path

• Calculate the expression for mean free path following Clausius and Maxwell

• Derive the expression for pressure exerted by a gas using the survival equation

• Calculate the expressions for viscosity, thermal conductivity, and diffusion coefficient of a gaseous system

• Demonstrate Brownian motion with its characteristics and calculate the mean square displacement of a particle executing Brownian motion

• State the idea of a random walk problem

• Solve numerical problems and multiple choice questions on the mean free path, viscosity, thermal conduction, diffusion, Brownian motion, and random walk

4.1 Introduction

The molecules of an ideal gas are considered as randomly moving point particles. From the concept of kinetic theory of gases (KTG), it is well established that even at room temperature, such point molecules of the ideal gas move at very large speeds. The average value of this speed can be determined assuming that the molecules obey Maxwell's speed distribution law and is given by the following expression

Learning Outcomes

After reading this chapter, the reader will be able to

• State the assumptions of kinetic theory of gases (KTG)

• Explain the concept of pressure and calculate the expression for it

• Demonstrate mathematically the gas laws using the expression for pressure derived from KTG

• Present the kinetic interpretation of temperature

• Derive the expression for specific heat at constant volume 𝐶𝑉 and constant pressure 𝐶𝑃

• Explain the concept of degree of freedom

• Solve numerical problems and multiple choice questions on KTG

2.1 Introduction

The kinetic theory of gases (KTG) is a theoretical model that describes the physical properties of a gaseous system in terms of a large number of submicroscopic particles, such as atoms, molecules, and small particles. These constituent elements are in random motion and collide constantly with each other and also with the walls of the container. Considering the molecular composition and characteristic features of such random motion of the molecules, various macroscopic properties of the gaseous system, such as pressure, temperature, viscosity, thermal conductivity, and mass diffusivity can be explained with the help of KTG. In this theory, it is postulated that the pressure exerted by a gas is due to the collision of atoms or molecules moving at different velocities on the walls of a container. It basically attempts to explain the macroscopic properties that are related to the microscopic phenomenon. The physical properties of solids and liquids, in general, are described by their shape, size, mass, volume, etc. Gases, however, have no definite shape, and size. Furthermore, their mass and volume are not directly measurable. In such cases, the KTG can be successfully applied to extract the physical properties of the gaseous system.