UNIT 6 THERMODYNAMICS Structure 6.1 Introduction i Objectives 6.2 Overview Thc Zeroth Law of Thermodynam~cs I Thc First Law of Thermodynamics Second Law of Thermodynamics Reversible and Irreversible Processes 6.3 The Carnot Cycle Real Heat Eng~nes Refr~gerators 6.4 Entropy and Its Significance Entropy and the Second Law of Thermodynamics Physical Concept of Entropy Combined Forms of the First and Second Law of Thermodynamics 6.5 Summary 6.6 Terminal Questions 6.7 Solutions and Answers 6.1 INTRODUCTION How would you like to introduce this subject to your students? You may like to start by explaining that matter (solid, liquid or gas) is composed of a very large number of interacting atoms or molecules that can be regarded as systems of particles. Many processes involving the exchange of energy between matter and its surroundings can be studied without considering the atomic or molecular structure of matter. The study of such processes is the subject of thermodynamics which was developed during the eighteenth and nineteenth centuries as a rather formal and elegant empirical theory. Thermodynamics demands greater understanding of concepts on the part of learners. The contents of this unit have been selected keeping in view the problem areas that need to be given greater focus by us in our classroom deliberations. In this context we assume that you are already familiar with the various basic terms and definitions used in the study of thermodynamics. You would know, for example, about (i) the thermodynamic system, (ii) classification of systems, i.e., open and closed systems, (iii) thermodynamic state of a system, (iv) thermodynamic variables, and (v) thermodynafiic equilibrium. , In this unit we will briefly review the teaching-learning of the three laws of thermodynamics, and the sign conventions used in the development of various thermodynamical relations. We will also discuss different statements of the second law of thermodynamics, and the concept of reversible and irreversible processes, Carnot cycle, real heat engines and refrigerators. Finally, we will discuss the concept of entropy and its significance, and try to link entropy and the second law of thermodynamics. Objectives After studying this unit, you should be able to: help your students learn better the laws of thermodynamics and their applications to various processes; acquire skills in explaining the different statements of second law of thermodynamics and their equivalence; Thermodynamics, Vibrations,Waves and explain with confidence the various steps involved in the derivation of expression Optics for the efficiency of Carnot cycle and extend its concept to real heat engines and refrigerators; assess the learning difficulties of your students vis-a-vis the concepts of thermodynamics and devise strategies to help them overcome these difficulties. 6.2 OVERVIEW You may like to explain to your students in the very beginning that like classical mechanics, thermodynamics is also based on empirical laws -there is no way to prove them - and is therefore pheromenological. Nevertheless, it is very exact and powerful. Each of these laws introduces a new concept (viz. temperature, internal energy, entropy) which gives a definite meaning to physically measurable quantities and provides useful correlation between observable properties of matter. As mentioned in the introduction, we assume that you are already familiar with the various terms and definitions frequently used in the development and formulation of thermodynamics. These are i) A thermodynamic system, ii) Concept of surroundings and boundary of a system, iii) State of a system and thermodynamic variables, iv) Thermodynamic equilibrium, and v) Thermodynamic process and its various forms. We will use these concepts and various terms in the ensuing sections. You must have been using the term temperature quite freely, but you need to emphasise that its basis lies in a law of thermodynamics. Let us study this law which is known as Zeroth law. 6.2.1 The Zeroth Law of Thermodynamics You know the statement of the Zeroth law of thermodynamics: Iftwo systems are separately in equilibrium with a third system then they must be in thermal equilibrium with one another. You may have explained how this statement forms the basis of the concept of temperature: All the three systems can be said to possess a property that ensures their being in thermal equilibrium with each other. This property is called temperature. Thus temperature of a system may be defined as the property that determines whether or not the system is in thermal equilibrium with the neighbouring systems. Your students may like to know why it is called the Zeroth law. Why do we call it the Zeroth Law? The phenomenon that the two systems in contact tend towards a common temperature is so common that historically its importance had been overlooked. When physicists finally did appreciate its significance and its fundamental nature, it was decided to have it elevated to the status of a "law of thermodynamics". By that time the first and second laws of thermodynamics had already been developea. So in order to place it ahead of these laws, it was termed as 'Zeroth law'. Equation pv = nrT is quite well known to you. Can such relations exist for other thermodynamic systems? In fact from the Zeroth law, it can be established mathematically that a relation exists between temperature and other thermodynamic variables associated with the system. Such a relation, as you know is called an equation of state. The general equation of state for any system is represented by Thermodynamics where f is a single valued function of pressurep, volume/V and the absolute temperature T. Charles7 and Boyle's laws give such relations for gaseous systems. 6.2.2 The First Law of Thermodynamics You know that the first law of thermodynamics is the statement of the principle of conservation of energy and applies to every process in nature. According to the first law of thermodynamics "when some quantity of heat (6Q) is supplied to a system capable of doing external work, then the quantity of heat absorbed by the system (6Q) is equal to the sum of the increase in the internal energy of the system (dU) due to rise in temperature, and the external work done by the system (6W) in expansion", i.e. This equation represents the differential form of the first law of thermodynamics. The first law of thermodynamics thus establishes an exact relationship between heat and work. You have to point out that the statement of this law involves the assumption that the internal energy is a function of the system only, i.e., dUdoes not depend on the path whereas 6Q and 6 Ware dependent on the path of the system followed in going from the initial to the final state. Mathematically, the differentials of such quantities are said to be inexact. It is to emphasize this difference between exact and inexact differentials that we have used different symbols - d for exact and 6 for inexact differentials. You may like to consider giving simple examples of exadin-exact differentials. For a given function df = (3x2 + 3y) dx + (ex + 2y) dy, you could find c for which df is an exact differential. Suppose you want to integrate df from point (0,O) to (2, 1) along two different paths, one, along a straight line connecting the two points, and two, first along the x-axis from (0, 0) to (0, 1) and then along the y-axis from (0, 1) to (2, 1). You could show that the integrals differ unless c takes the value which made df exact, and which you have already found. Significance From the first law of thermodynamics, we learn that it is impossible to get work continuously from any machine without giving an equivalent amount of energy back to the machine. Just as the zeroth law of thermodynamics introduces the concept of temperature, the first law of thermodynamics introduces the concept of internal energy. Thus according to this law, the internal energy (and hence temperature) of a system can be increased by supplying heat to it or by doing work on the system or both. Sign conventions The system of using plus/minus sign in dealing with the three quantities 6Q, dUand 6 W involved in the first law of thermodynamics is found to be difficult by our students. You may like to explain it as follows: (i) When heat is supplied to a system, 6Q is taken as positive. When it is drawn from the system, 6Q is taken as negative. (ii) When the temperature of the gas increases, its internal energy dU increases, and is taken as positive. When temperature of a gas decreases, its internal energy dU decreases, and is taken as negative. , (iii) When a gas expands, work done by the gas GW is taken as positive. When the gas is compressed, work is done on the gas, and hence G W is taken as negative. Thermodynamics, Vibrations, Waves and Optics In summary, the audit of energy or work done is done with respect to the system. 6.2.3 Second Law of Thermodynamics The first law of thermodynamics gives us a statement concerning conservation of energy in thermal processes. However, it gives no information about the way a thermodynamic system evolves or the direction of flow of heat. Further, the first law does not give us any idea about the conditions under which conversion of heat takes place into work or vice versa. The second law takes into account both these conditions and can be stated in any of the following ways: Kelvin-Planck statement "It is impossible to construct a device, which operating in a cycle has the sole effect of extracting heat from a single reservoir and performing an equivalent amount of work".