Chapter 1 Fundamentals

Transcription

1 Chater Fundamentals. Overview of Thermodynamics Industrial Revolution brought in large scale automation of many tedious tasks which were earlier being erformed through manual or animal labour. Inventors discovered many machines which could be oerated with steam ower or run with combustion gases generated from the burning of fossil fuels. The ossibility of converting energy from one form to another- articularly from heat to useful work was understood; thus was born the science of Thermodynamics. While the overall balance of energy in any rocess gave rise to the I Law of Thermodynamics, limitations on the erformance indices of machines dealing with heat & work gave rise to the II law of Thermodynamics. Although Thermodynamics develoed as a by-roduct of industrial revolution, in course of time, its alication extended to the study of many hysical and chemical rocesses. In articular, the changes that occur in the roerties of substances during energy exchanges were characterized in detail. Also, the feasibility of any rocess under given conditions could be systematically studied. An amazing asect of this subject is that its concets could be alied to reactions occurring between tiny molecules or to gross changes which occur over the whole universe. The three basic laws of Thermodynamics rovide very owerful tools to analyze the oeration of virtually every machine or rocess on which our modern civilization is based. The only notable excetions for classical thermodynamic analyses, one may say, are the rocesses that involve mass-to-energy conversion as in the case of nuclear article interactions.. Basic Definitions In any thermodynamic analysis, the very first task taken u is that of identifying the object or the satial domain which forms the focus of the study. Two tyes of analyses are commonly erformed- those corresonding to that of a System and that of a Control olume. Some text books refer to the system as a Closed System and the control volume as an Oen System. A System is defined as a fixed mass of matter on which attention is focussed. The choice of the system is indicated with the hel of a dash line, drawn very close to the boundary of the system on the interior side. The rest of the universe which lies outside the system is called the Surroundings. Let us consider the situation corresonding to the conversion of heat to work by a system, as shown in Fig... Here, Q is the heat transferred from the surroundings to the system. Also, W is the work done by the system on surroundings. The difference between Q and W (say, equal to E) is the change in the energy stored within the system. Deartment of Mechanical Eng Indian Institute of Technology Madras

2 Surroundings Q System W Fig.. Definition of System Examles of system are: electric bulb, hotovoltaic solar cell, nuclear ower lant, domestic refrigerator, electrical heater, gas enclosed in a cylinder-iston device which exands on heating, an iron rod which is heated in a furnace. Note that in the electrical devices mentioned here, the electrical energy inut or outut is considered as work. More discussion about Work is rovided in the next chater. Also, every rocess need not always have heat or work exchange- in some rocesses either Q or W (or both) could be zero. A Control olume (or C for short) is a fixed volume on which attention is focussed. Aart from energy interactions in the form of heat or work, it can also admit in-flow or out-flow of mass through an inlet or an exit, resectively. Similar to the case of system, the rest of the universe outside the control volume is also called as Surroundings. The energy and mass interactions of a tyical control volume are shown in Fig... In the figure, Q and W reresent the energy interactions and, m i and m e reresent the in-flow and out-flow mass exchanges between the C and the surroundings. Surroundings W m i Control olume Q m e Fig.. Definition of C Deartment of Mechanical Eng Indian Institute of Technology Madras

3 Examles of control volume are: water um, air- conditioner, aircraft engine. It is evident from the above discussions that a system analysis ermits only energy exchanges. It is ossible that the volume of the system undergoes change during the rocess under consideration. For instance, the volume of gas enclosed in a cylinder- iston arrangement may change because of heat addition and this rocess can be modeled through the system analysis. In a control volume analysis, on the other hand, the volume of C remains fixed although the mass enclosed inside C could change. As in the case of the aircraft engine, the whole C could be moving in some alications. A water tank which is being filled with water flowing from a ta could be analyzed as a C- even when the drain of the tank is closed. Note that in this case Q and W are zero and m e = 0. Thus, a control volume analysis can be alied when at least one of the two- namely the inlet or the outlet- is oen and mass exchange occurs between the C and the surroundings. There are some cases which can not be categorized either as a system or as a control volume. For instance, a balloon which is inflated with the air blown into it, is neither a system nor a C. In such roblems, it is better to fix a quantity of air (say, the air which finally occuies the balloon) and aly system analysis to this air. Aart from the definitions of system, control volume and surroundings, there are a few other definitions which are fundamental to any thermodynamic analysis. These definitions are given below. Proerty : Any measurable, macroscoic characteristic of a substance. Examles are : mass, volume, density, ressure, temerature, velocity, elevation, secific heat. Some quantities which may not be directly measurable but can be exressed in terms of measurable quantities are also treated as roerties. For instance, kinetic energy is a roerty which can be exressed in terms of the mass and velocity. Potential energy in a gravitational field can be exressed in terms of the mass and elevation from a datum. Internal energy can be exressed in terms of the mass, secific heat and temerature. Proerties can classified as intensive roerties and extensive roerties. An intensive roerty is indeendent of the size of the system (eg. density, ressure, temerature) while an extensive roerty deends on the size of the system (eg. mass, kinetic energy, volume). State : State reresents the collection of all roerties of a system. Consider for examle, a system undergoing some rocess. Initially, the system roerties may be: ressure, volume, temerature T, velocity and elevation z. All these roerties could be taken together to define the initial state. Similarly, if the final roerties at the end of the rocess are given by: ressure, volume, temerature T, velocity and elevation z. These roerties could Deartment of Mechanical Eng 3 Indian Institute of Technology Madras

4 be taken together to define the final state. In the case of some simle systems, two roerties are often sufficient to define the state. For examle, the state of a gas of given mass undergoing an exansion or comression rocess (with no motion or change in elevation), can be defined in terms of the ressure and volume. It is then ossible to denote the initial and final states of the system as the oints (, ) and (, ) in - diagram. Process : A rocess is the sequence of states followed by a system. If a system changes from the initial state (, ) to the final state (, ), the curve connecting all the intermediate values of (,) for the system, reresents the rocess undergone by the system in a - diagram. State Process - State Fig..3 State and Process State deendent and ath (rocess) deendent quantities : When a system undergoes a rocess, there are many associated changes. For instance, the ressure, volume and temerature of the system may change. Some heat and work interactions may occur between the system and the surroundings. There is a need to quantify such changes- from the beginning to the end of the rocess, or some times even during the course of the rocess itself. Let us consider a gas exansion rocess from state (initial) to state (final). Let the changes in ressure and volume during a small art of the rocess be: -d/ to +d/ and from -d/ to +d/ (Fig..4 a). For the exansion rocess under consideration, the volume will exand (d>0) while the ressure will decrease (d<0). The overall change in ressure or volume can be obtained as: Deartment of Mechanical Eng 4 Indian Institute of Technology Madras

5 d. d. It is evident from the above exressions that that the overall changes in ressure or volume deend only on the corresonding initial and final values of ressure or volume. They do not deend on the articular rocess- for examle, both rocess x and rocess y shown in Fig..4 b will have same and. On the other hand, a quantity such as the work done will deend on the rocess. We will show in the next chater that the work done during a small change in volume and ressure is given by.d where is the average ressure and d is the change in volume, as shown in Fig..4 a. Work done during gas exansion is the shaded area shown in the figure. For the whole rocess -, the work done by the gas is given as : W. d For a rocess -, the gas exansion work is the area under the curve in the - diagram. It deends not only on the end state (initial and final) roerties but also on the rocess between the states and. For this reason, differentials like d, d etc. are called exact differential and a differential quantity such as.d is called an inexact differential. Similar to work, the heat interaction Q during a rocess also deends on the ath (i.e. tye of rocess). It is customary to denote exact differentials as d, d, dt etc. while the inexact differentials will be denoted using the symbol del for instance: Q, W etc. Process x Process y (a) (b) Fig..4 State deendent and ath deendent quantities Deartment of Mechanical Eng 5 Indian Institute of Technology Madras

6 Pressure measurement : We need to measure the absolute ressure in some alications and the relative ressure difference between two different locations in some cases. For examle, for meteorological uroses, the absolute value of atmosheric ressure is measured on a daily basis and it is reorted in the news aers each day. The device used for this urose is the barometer which derives its name from Greek language (bar- ressure; meter- to measure). It consists of an inverted tube which is filled with mercury and ket immersed in a bath of mercury as shown in Fig..5 a. This device gives the local atmosheric ressure as : atm = Hg.g.h where g is the acceleration due to gravity, h is the height of mercury column read from the barometer and Hg is the density of mercury. The standard atmosheric ressure ( atm) is defined as corresonding to a mercury column height of 760 mm and using values of g = m/s and density of mercury = 3600 kg/m 3, we get the standard atmosheric ressure as aroximately equal to 0300 Pa or 0.3 kpa or 0.03 MPa. Here Pascal (denoted by the symbol Pa) is defined as equal to Newton er square meter. In other words, Pa = N/m. Another convenient unit which is commonly used for ressure is the bar. One bar is equal to 0 5 bar. Thus, atm =.03 bar. A U-tube manometer is used to measure the ressure difference between two locations. Or, it could also be used to measure the ressure at a location, relative to that of the atmosheric ressure. The ressure at a oint relative to that of atmoshere is known as the gauge ressure or vacuum ressure. For examle, if the ressure at a oint A is secified as 0 mm Hg gauge, it means that the absolute value of ressure at A corresonds to a mercury column height of ( = 770 mm), assuming that the local atmosheric ressure is equal to the standard value of 760 mm Hg. Similarly, if the ressure at a is secified as 0 mm Hg vacuum, it imlies that the absolute ressure at A corresonds to a mercury column height of 740 mm Hg. In general, a manometer may use any fluid (not necessarily mercury alone). The ressure difference between the two meniscii of the manometer is exressed as :. g. h where is the density of the manometric fluid, g is the acceleration due to gravity and h is the height difference between the two meniscii. Aart from the manometer, there are several tyes of ressure gauges. For instance, a device known as Bourdon gauge is commonly used to measure the ressure at some location in a ie which transorts a fluid. The Bourdon gauge consists of a soft metallic tube of ellitical cross-section, which deforms deending on the value Deartment of Mechanical Eng 6 Indian Institute of Technology Madras

7 of local fluid ressure. The deformation of the tube is eventually calibrated in terms of the movement of a needle which denotes the corresonding gauge ressure ( atm ) in the fluid. Deartment of Mechanical Eng 7 Indian Institute of Technology Madras