Thermal Physics Lecture Notes PDF

FEDERAL UNIVERSITY OF TECHNOLOGY, AKURE SCHOOL OF PHYSICAL SCIENCES DEPARTMENT OF PHYSICS P. M. B. 704, AKURE, NIGERIA MODULE TITLE: THERMAL PHYSICS MODULE CODE: PHY 205 1 Module Contents: Introduction to Thermodynamics The found...

FEDERAL UNIVERSITY OF TECHNOLOGY, AKURE SCHOOL OF PHYSICAL SCIENCES DEPARTMENT OF PHYSICS P. M. B. 704, AKURE, NIGERIA MODULE TITLE: THERMAL PHYSICS MODULE CODE: PHY 205 1 Module Contents: Introduction to Thermodynamics The foundation of Classical Thermodynamics Zeroth Law of Thermodynamics and Temperature The First Law of Thermodynamics Work, Heat and Internal Energy Carnot Cycles and Second Law of Thermodynamics Entropy and Irreversibility Thermodynamic Potentials and the Maxwell Relations Applications: Qualitative Discussion References 1. Robert P. Baumann, Modern Thermodynamics with Statistical Mechanics, Macmillan, New York, 1992. 2. Ralph Baierlein, Thermal Physics, Cambridge University Press, New York, 1999. 3. Herbert B. Callen, Thermodynamics, John Wiley & Sons, New York, 1960. 4. Stephen J. Blindell, Concepts in Thermal Physics 5. Federick Reif, Fundamentals of Statistical and Thermal Physics 6. Ashley H. Carter, Classical and Statistical Thermodynamics, Prentice Hall, 2000. 2  INTRODUCTION TO THERMODYNAMICS Thermodynamics Thermodynamics is the branch of physical science that deals with the relations between heat and other forms of energy such as mechanical, electrical, or chemical energy. It explains the relationship between all energy forms. The main idea of thermodynamics is the association of heat with work done by or on a system. There are several important terms in thermodynamics. Thermodynamics is the science of heat energy transfer from hotter bodies to cooler bodies, and its effect on the physical properties of substances (such as change in state or shape). It is based upon observations of common experience which have been formulated into thermodynamic laws. These laws govern the principles of energy conservation. The applications of the thermodynamic laws and principles are found in all field of energy technology, notably in steam and nuclear power plants, internal combustion engines, gas turbines, air conditioning, refrigeration, gas dynamics, jet propulsion, compressors, chemical process plants and direct energy conversion devices. In this section, we will be describing two forms of thermodynamics according to the properties of the system that are considered in the observation. They are microscopic and macroscopic thermodynamics. Thermodynamic Behaviour of Matter The thermodynamic behavior of matter can be considered or studied in terms of two viewpoints, i.e., the macroscopic and microscopic point of view. Macroscopic Thermodynamics Macroscopic thermodynamics refers to the relationships between the large-scale bulk properties of a system, such that the events occurring at the molecular level are not being taken into account. The typically considered bulk properties include volume, temperature, pressure, specific heat, elastic moduli and so on. These are parameters that are easily measurable. Therefore, the macroscopic thermodynamics approach concerns the gross or average effects of many molecules’ infractions as a bulk. Any system that is large enough to be observable using our senses are known as a macroscopic system. In the macroscopic approach, a certain quantity of matter is considered, without the events occurring at the molecular level being taken into account. Therefore, macroscopic thermodynamics is only concerned about the average effects of the actions of many molecules, and these effects can be perceived by human senses. For example, considering a macroscopic quantity such as pressure, which is defined as the average rate of change of momentum due to all the molecular collisions made on a unit area. The effects of pressure can be felt on a body when a certain amount of pressure is exerted on it, which may result into deformation that can be perceived by the human eyes. Another example is when heat is applied to a body of certain mass, each of the molecules will feel the effect and react accordingly to the changes (i.e., react to the heat change in the system). However, 3 macroscopic thermodynamics is concerned about the collective effect and not the individual effects of the molecules. In general, the macroscopic point of view is not concerned with the action of individual molecules, and the force on a given unit area can be measured by using a pressure gauge, thermometer etc. These macroscopic observations are completely independent of the assumptions regarding the nature of matter. All the results of classical or macroscopic thermodynamics can however, be derived from the microscopic or statistical study of matter. Examples: A gas enclosed in a cylinder, a liquid in a vessel & a solid of definite dimension. The state of a macroscopic system is represented by macroscopic parameters like pressure, volume, temperature, entropy, electrical resistivity and so on. When the macroscopic parameters of an isolated system do not change with time, the system is said to be in equilibrium. Microscopic Thermodynamics Microscopic thermodynamics refers to the relationships between the small-scale properties of a system, without considering the bulk properties of the large-scale system. This phenomenon includes the behavior of every molecule by using statistical methods. The properties considered in the microscopic thermodynamics include the properties of atoms that are on a very small scale; for example, intermolecular forces, chemical bonding, atomicity, etc. A system of atomic dimension or of a size unobservable with our senses is known as microscopic system. In a microscopic system there are a large number of minute particles positioned randomly and moving with random momentum. Thus, position and momentum of individual particles are known as microscopic parameters. Since a large number of particles constitute the assembly, or an ensemble, they possess unpredictable parameters. The theory of probability is used to predict the behaviour of constituent microstates of the system. From the microscopic point of view, matter is composed of countless number of molecules. If it is a gas, each molecule at a given instant has a certain position, velocity and energy, and for each molecule these properties change very frequently as a result of collisions. The total behavior of the gas is described by summing up the behavior of each molecule. Such a study is done by microscopic or statistical thermodynamics. Difference between Macroscopic and Microscopic in Thermodynamics The key difference between macroscopic and microscopic in thermodynamics is that macroscopic thermodynamics refers to the relationships between large scale bulk properties of a system, whereas microscopic thermodynamics refers to the relationships between small scale properties of a system. Moreover, macroscopic thermodynamics include volume, elastic moduli, temperature, pressure, and specific heat, whereas microscopic thermodynamics include properties of atoms such as intermolecular forces, chemical bonding, atomicity, etc. The following image summarizes the difference between macroscopic and microscopic in thermodynamics, in tabular form. 4 Summary – Macroscopic vs Microscopic in Thermodynamics Thermodynamics is the branch of physical science that deals with the relations between heat and other forms of energy such as mechanical, electrical, or chemical energy. There are two forms of thermodynamics according to the properties of the system that are considered in the observation: microscopic and macroscopic thermodynamics. The key difference between macroscopic and microscopic in thermodynamics is that macroscopic thermodynamics refers to the relationships between large scale bulk properties of a system, whereas microscopic thermodynamics refers to the relationships between small scale properties of a system. We can understand thermodynamics from two viewpoints (or approaches). One is microscopic and another is macroscopic. Let us discuss each of them in detail. However, in Mechanical Engineering we only consider macroscopic approach. Macroscopic (or Classical) view In macroscopic approach we fix our attention to certain quantity of matter without considering the activities (or events) happening at molecular level. In this approach we determine the properties (e.g. Pressure, Volume, Temperature) which get affected by the systems interaction with the surrounding. 5 There are some macroscopic properties which can be sensed by the human and some cannot. Even the macroscopic properties which cannot be sensed by human can be related to the properties which can be sensed by the humans. These relations can be established either by experiments or by theory at some macroscopic level. Microscopic (or Statistical) view In microscopic view we try to determine behavior of a system by the events happening at molecular level. We can easily find that macroscopic behavior is always related to microscopic behavior because a matter is always comprised of molecules. One can see that macroscopic behavior is an average of microscopic behavior of large number of molecules over a considerable period of time. For example: Pressure is a macroscopic property, it can be sensed but it too has a microscopic explanation. Pressure can also be explained as the change of momentum due to molecular collision. Difference in Macroscopic and Microscopic views of Thermodynamics Table given below will help in understanding the differences in a better way. Sr. Macroscopic Approach Microscopic approach No. This approach is certain quantity of Events happening at molecular level is taken 01 matter without the events happening at into account molecular level Macroscopic approach deals with the A statistical approach is required for properties which can be sensed by 02 microscopic approach since number of humans. Or which can be obtained from molecules is very large mathematical relations. It is an averaged value of the activities These are real values and hence difficult to 03 happening at molecular level measure In order to describe a system from In order to describe a system from microscopic macroscopic we need very less number of 04 approach we need a very large number of properties like pressure, volume, variables. temperature etc. 6 The Foundation of Classical Thermodynamics: Macroscopic Descriptions of Systems Topics - Thermodynamic Systems: Surroundings, State (thermodynamic) Variables, Boundaries - States and Functions: Equilibrium state and Steady state - Thermodynamic Properties/State Variables: - Classification of state variables - Extensive and intensive variables - Conjugate pairs of thermodynamic variables - Thermodynamic Processes and cycle - Homogenous and Heterogeneous Systems - Thermodynamic Equilibrium OBJECTIVES: At the end of this lecture you should be able to 1. Define the following terminologies: Thermodynamics, thermodynamic system, phase, closed system, open system and isolated system, rigid and diathermal walls, adiabatic and adiabatic changes, equilibrium state, state variables, intensive and extensive variables 2. Distinguish between: closed and isolated systems, adiabatic and diathermal walls, intensive and extensive variables 3. Explain the concept of conjugate pairs of thermodynamic variables. Introduction In the next few lectures we shall be dealing with introductory macroscopic thermodynamics (A detailed course of thermodynamics under Thermal Physics). As described earlier, Macroscopic Thermodynamics is defined as a science concerned with the relationships between the large-scale bulk (macroscopic) properties of a system, which are measurable, such as volume, elastic moduli, temperature, pressure and specific heat. For this reason macroscopic thermodynamics belongs to classical physics. It is important to note that thermodynamics by itself cannot give us fine microscopic details, but can only tell us about the bulk properties of the system. The branch of physics that relates the macroscopic properties of matter to the underlying microscopic processes (behaviour of the constituent atoms or molecules) is called statistical mechanics. In this module we shall familiarize ourselves with terminologies that are often used when dealing with the subject of thermodynamics. It is therefore very important that these terminologies become part and parcel of your vocabulary. Thermodynamic System A thermodynamic system is defined as a quantity or body of matter, or a region in space confined by a boundary or wall, with defined permeabilities which separates it from its surroundings. The surrounding may include other thermodynamic systems, or physical systems that are not thermodynamic systems. 7 The surrounding can be defined as all the region that is outside or external to the system. This means that everything external to the confined system is called the surroundings or the environment. Universe Fig. 2: A thermodynamic system showing boundary and surroundings The interactions in a thermodynamic system As shown in the figure below, the system is separated from the surroundings by the system boundary. The boundary may be either fixed or moving. A system and its surroundings together comprise or makes a universe. 8 Outside the system is known as the surrounding. The system and the surrounding are separated by a boundary or wall, as depicted in Fig. 2. The system and the surrounding in general, may exchange energy and matter, depending on the nature of the wall. Thus, a thermodynamic system is that portion of the universe which we select for investigation, e.g., a gas in a cylinder is a simple system, whereas a mixture of water and alcohol is a more complicated system as it contains two different substances or components. There are three classes of thermodynamic systems, namely; (1) Closed system, (2) Open system, and (3) Isolated system.  Closed System The closed system is a system of fixed mass, such that there is no mass transfer across its system boundary. There may be energy transfer into or out of the system. A typical illustration of a closed thermodynamic system For example: A certain quantity of fluid in a cylinder bounded by a piston constitutes a closed system. 9 The illustration below shows a typical example of a closed system where only heat transfer takes place. In this case, a metallic block is being heated and there is heat radiation from the block into the surroundings. However, due to the nature of the system, there cannot be a mass transfer across the system.  Open System The open system is one in which matter or mass crosses the boundary of the system (i.e., there may be mass in and out as matter crosses the boundary), and there may be energy transfer into or out of the system. Most of the engineering devices are generally open systems. 10  A typical illustration of an open system For example, an air compressor in which air enters at low pressure and leaves at high pressure, and there are energy transfers across the system boundary. An air compressor showing the flow of energy and matter The internal compartment of the system is the control volume, and the control surface serves as the boundary. In this system, matter and energy crosses the control surface. For thermodynamic analysis of an open system such as an air compressor, the following principle of operation describes the thermodynamic processes involved. Principle of Operation of an Air Compressor This device can be used in refrigerators to provide air at high pressure. Low pressure air (i.e., air at low pressure) is supplied into the system (i.e., Mass in) and then the motor does work (Energy in) on the compartment filled with air. As the work is done by the motor, it puts more pressure into the system to push out the air (i.e., Mass out) at very high pressure. Also, we will have a reaction within the system such that heat will be created in it and in order for thermodynamics to take place such that heat transfer must 11 be achieved, then heat must be expelled from the system (i.e., Energy out) into the surrounding (i.e., to achieve equilibrium: heat from hotter body to cooler body). Another example is the boiler or water heater as shown below:  Isolated System This is the system whereby there is no interaction between the system and the surroundings. It has fixed mass and energy. There is no mass or energy transfer. A typical illustration of an isolated thermodynamic system A completely sealed thermodynamic system or a physical system so far removed from other systems that it does not interact with them. Neither matter nor heat can transfer to or from the system. An example of an isolated system can be seen in an insulated thermoflask as shown below. Here, the mass and heat within the thermoflask will remain the same, because there is no interaction with the surroundings. 12 Practical Example of various thermodynamic systems: Adiabatic Boundary, Adiabatic Changes and Diathermal The system can be influenced either thermally, or by doing work on it. For example, heating is a thermal process, and compression is a work-like process. If the boundary inhibits the system from changing it volume or shape so that no mechanical work is performed on it, the wall is said to be rigid. Walls that prevent thermal interactions are called adiabatic, and a system enclosed by an adiabatic wall is called an isolated system. An isolated system cannot exchange heat with its surroundings, though work may be done on it. Such changes it will undergo are called adiabatic changes. Walls that allow some interactions between the system and the surrounding are called diathermal, and two systems separated by a diathermal wall are said to be in contact. In other words two systems are in thermal contact if heating one of them results in macroscopic changes in the other. For example, you are aware that if we place two 13 metal containers of water in physical contact, and heat one container, the water in both containers becomes hotter. We say that the two containers are in thermal contact. States and Functions Equilibrium state This is one state in which all the bulk physical properties of a system are uniform throughout the system and do not change with time. An equilibrium state is one whose macroscopic properties—temperature, volume, etc.—are invariant in time. We also require that such a state not be under the influence of any driving forces, such as temperature or pressure gradients. An equilibrium state is said to be at thermal equilibrium. Steady State In contrast, a steady state is one whose macroscopic properties are invariant in time, but under the influence of a driving force. Example 1 (Equilibrium state, steady state): A tank of water placed in an insulated container is at equilibrium, having a fixed temperature, volume, and so on. If we remove the insulated container and apply a continuous heat source to the water, we heat up the water and introduce a temperature gradient between the water and the tank. When as much heat per unit time is introduced by the heat source as is dissipated through the tank, the water reaches steady state. Finally, if we open up the tank and let water evaporate, then it is neither at equilibrium nor at steady state. The definition of an equilibrium state comes with an explicit length scale (“macroscopic”). If we look closely enough at a tank of water, the atoms making up the tank are vibrating, and necessarily the volume of the tank suffers minute fluctuations. We choose to ignore this detail and work only with macroscopic averages. Put more roughly, macroscopic thermodynamics doesn’t believe in atoms. An equilibrium state also has an implicit time scale. It is well-known that graphite is a more stable allotrope of carbon than diamond, and hence that diamond should decompose into graphite. Operationally, however, for all intents and purposes, a diamond at ambient conditions is at thermal equilibrium. State and Path Functions A state function is a physical quantity with a fixed value for each equilibrium state of a system. A path function is a physical quantity that does not. Mathematically, state functions are functions, whereas path functions are relations. Example 2 (State and path functions): Pressure, volume, internal energy, and density are examples of state functions. The total heat put into or total work done on a system are examples of path functions. State functions, in contrast to path functions, are independent of the process by which the system arrives at a given equilibrium state. Equivalently, for a given equilibrium state, state functions are well defined. Path functions depend on the history by which the state is achieved. 14 Exercise 1 (State and path functions) 1. Identify as true or false: (a) A system can be both at steady state and at equilibrium. (b) If a physical quantity is not a state function, it must be a path function. 2. What is the flaw in this argument? A system has a definite value of the total heat put into the system for every equilibrium state, even though this value is generally not known. By definition, this means that the total heat put into the system is a state function. Thermodynamic Properties or State Variables Thermodynamic properties are the certain characteristics that describes the system’s physical condition. These are the coordinations or elements or characteristics to describe the state of the system (physical condition). The thermodynamic system properties are the state variables describing the state of a system (e.g. Volume, temperature, pressure etc.). It is important to realize that we require two variables to specify the equilibrium state of a simple system. These measurable variables are called state variables (or thermodynamic properties or thermodynamic variables or thermodynamic coordinates). For example, for a gas, specifying the equilibrium values of a pair of independent variables P and V, and mass, fixes all the macroscopic (bulk) properties of the gas. Change of state can take place when one or more properties of a system changes during an operation. Solid Path of the change of state Liquid Gas or Vapour Heat Volume reduces The path of the change of state is the succession of states passed through during a change of state. Classification of State Variables The classification or types of state variables or thermodynamic properties can be explicitly defined as follows: Types of Thermodynamic Properties (1) Intensive Properties: These are independent of the mass in the system. Example of this are pressure, temperature etc. That is, even if the mass changes, it doesn’t affect their values. 15  (2) Extensive Properties: These are the properties that are mass related, that is, they depend on the mass. For Example: Volume, energy, etc. If the mass of the system increases, the values of the extensive properties also increases. It should be noted that we can have specific extensive properties, i.e. extensive properties per unit mass. 𝑉𝑜𝑙𝑢𝑚𝑒 For instance, Volume per unit mass or Energy per unit mass:. 𝑢𝑛𝑖𝑡 𝑚𝑎𝑠𝑠 This specific extensive properties are referred to as intensive properties. That is, it is a way of converting to intensive properties. For example, specific volume, specific energy, density etc. Thermodynamic Processes and Cycles Thermodynamic Processes The thermodynamic process is the path of the change of state of a system. When the path of the change of state is completely specified, the change of state is called a process. For example, a constant pressure process. The path A – B in the PV diagram below is referred to as a process. Reversible, quasistatic, and irreversible processes A process connects two equilibrium states. In a reversible process, the system is at thermal equilibrium internally and with its surroundings at every point during the process. Any process that is not reversible is irreversible. In a quasistatic process, the system is internally at thermal equilibrium. A quasistatic process occurs slowly enough that internal equilibrium is maintained. An obvious question arises: if reversible processes are constantly at equilibrium, how can an initial state evolve into a final state? We resolve this paradox by introducing infinitesimal changes. We assume that infinitesimal changes are small enough not to perturb the system from equilibrium, but that the sum of infinitely many such infinitesimal changes yields a finite change. This allows for evolution of a state in infinite time. Reversible processes are never physically possible, being idealized abstractions of real physical processes. In general, however, we are concerned with state functions in thermodynamics, and are free to choose any path connecting two states. The most useful path is almost invariably reversible. 16 Example 3 (Quasistatic process) A quasistatic process is not necessarily reversible. This situation is possible if the system exhibits hysteresis, in which the state of the system depends on its state at previous times (i.e. the system has memory). The classic example of a system exhibiting hysteresis is an iron nail. By applying a magnetic field to a regular iron nail, we can cause the magnetic domains in the nail to align, and hence make the nail a magnet. If we then lower the magnetic field slowly, we find that even at zero field the nail remains magnetized. We thus have two states of the nail—unmagnetized and magnetized—that both correspond to zero field. The actual state of the nail depends on its memory, which characterizes hysteretic behavior. Thermodynamic Cycle A thermodynamic cycle is defined as a series of state changes such that the final state is identical with the initial state. From the PV diagram below, the path 1 – 2 – 1 is referred to as a cycle. The concept of a thermodynamic cycle is based on depicting thermodynamic processes which involve the transfer heat and work. This is achieved by altering temperature, pressure, as well as other state variables; the cycle ultimately returning to its initial state. The fundamental basis of these cycles is the first law of thermodynamics which states that ‘energy cannot be created nor destroyed but only converted from one form to another’. As shown in the Figure below, thermodynamic cycles are split into two primary classes – refrigeration cycles (also known as heat pump cycles) and power cycles such as the combustion engine cycle. 17  The map of all thermodynamic cycles Cycles which transfer heat from low temperature to high temperature are classified as heat pump cycles, whereas cycles that convert heat input into mechanical work are designated as power cycles. And so, not inappropriately, thermodynamic power cycles provide the foundation for the operation of a heat engine. Power cycles are then further divided into groups depending on the type of heat engine. For cycles modelling internal combustion engines the groups are the Otto, Diesel, and Brayton cycles and for external combustion engines, they are the Rankine, Organic Rankine, and Kalina cycles. Homogenous and Heterogeneous Systems Phase: This is the physical structure or chemical composition of a quantity of matter. Every quantity of matter or substance can exist in any one of the three phases, i.e. solid, liquid and gas. Homogenous System: This is a system consisting of a single phase. Heterogeneous System: This is a system consisting of more than one phase. Thermodynamic Equilibrium Thermodynamic equilibrium is a phenomenon where there are no net macroscopic flows of matter (mass) or energy, either within a system or between systems. Therefore, the system behaves as if it is isolated from its surroundings, because no macroscopic change occurs (i.e., there is change in any microscopic property). Also, in a system that is in its own state of internal equilibrium, no microscopic change occurs. It should be noted that, this majorly refers to isolated systems where they are always in equilibrium state. For a system to attain a state of thermodynamic equilibrium, the following 3 types of equilibrium states must be achieved or satisfied: 18  (a) Thermal Equilibrium: The temperature of the system does not change with time and has same value at all points of the system. (b) Mechanical Equilibrium: When there are no unbalanced forces within the system or between the system and the surroundings. For instance, the pressure in the system is the same at all points and does not change with time. (c) Chemical Equilibrium: When no chemical reaction takes place in the system and the chemical composition which is the same throughout the system does not vary with time. Summary System and surroundings: The system is defined by a real or imaginary boundary enclosing a volume of interest. The surroundings is the volume outside the system. When we treat the surroundings as a constant-temperature source or sink, we call it a thermal reservoir. Several adjectives are in common use to describe various systems: System Characteristics Closed No mass transfer Open Energy and mass transfer Isolated No energy or mass transfer Insulated No heat transfer However, it should be noted that the isolated and insulated system are inter-related and that is why there are only three main thermodynamic systems. An unopened can of soda is a closed system that consists of a fixed amount of mass. No mass can cross the boundary of a closed system. Energy, however, can enter or exit a closed system. A human body is an open system in the sense that both energy and mass can cross its boundary. The entire universe is an isolated system in which the total mass and total energy remain the same because neither mass nor energy can cross its boundary. We will expound on thermodynamic systems in a later chapter. 19 The state variables may be classified into two groups: the intensive variables and the extensive variables. Intensive variables are those that are discrete (local) in nature, i.e., are size independent. Examples include pressure, electric field, force, and density. Extensive variables are proportional to the mass of the system if the intensive variables are kept constant, that is, they correspond to some measure of the system as a whole. Examples include volume, internal energy and length. If the extensive variables are expressed per unit mass of the system they are then known as specific variables. system Intensive Variable Extensive variable Gas/fluid Pressure (P) Volume (V) Film Surface tension () Area (A) cell E.m.f (E) Charge (Z) 20 Questions 1. Two identical-looking physical systems are in the same macroscopic state. Must they be in the same microscopic state? Explain. 2. Two identical-looking physical systems are in the same microscopic state. Must they be in the same macroscopic state? Explain. 3. Draw the diagram of an air-compressor showing all the necessary thermodynamic interactions. 21