SCHAUM’S OUTLINE OF THEORY AND PROBLEMS OF THERMODYNAMICS FOR ENGINEERS MERLE C. POTTER, Ph,D. Professor of Mechanical Engineering Michigan State University CRAIG W,SOMERTON, Ph,D. Associate Professor of Mechanical Engineering Michigan State University SCHAUM’S OUTLINE SERIES McGRAW-HILL New York San Francisco Washington, D.C. Auckland Bogota‘ Caracas Lisbon London Madrid Mexico City Milan Montreal Neui Delhi San Juan Singapore Sydney Tokyo Toronto MERLE C. POITER has a B.S. degree in Mechanical Engineering from Michigan Technological University; his M.S. in Aerospace Engineering and Ph.D. in Engineering Mechanics were received from The University of Michigan. He is the author or coauthor of The Mechanics of Fluids, Mathematical Methods, Fundamentals of Engineering, and numerous pa- pers in fluid mechanics and energy. Currently he is Professor of Mechani- cal Engineering at Michigan State University. CRAIG W. SOMERTON studied Engineering at UCLA, where he was awarded the B.S., M.S., and Ph.D. degrees. He is currently Associate Professor of Mechanical Engineering at Michigan State University. He has published in the International Journal of Mechanical Engineering Educa- tion and is a past recipient of the SAE Ralph R. Teetor Educational Award. Appendix K is jointly copyrighted 01995by McGraw-Hill, Inc. and MathSoft, Inc. Schaum’s Outline of Theory and Problems of ENGINEERING THERMODYNAMICS Copyright 0 1993 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Except as permitted under the Copyright Act of 1976. no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. 4 5 6 7 8 9 10 I 1 12 13 14 15 16 17 18 19 20 BAWBAW 9 8 IS B N 0 - 07 - 0507 07 - 4 (Formerly published under ISBN 0-07-050616-7.) Sponsoring Editor: David Beckwith Production Supervisor: Leroy Young Editing Supervisor: Maureen Walker Library of Congress Cataloging-in-PublicationData Potter, Merle C. Schaum’s outline of theory and problems of engineering thermodynamics / Merle C. Potter, Craig W. Somerton. p. cm. -- (Schaum’s outline series) Includes index. ISBN 0-07-050616-7 1. Thermodynamics. I. Somerton, Craig W. 11. Title. 111. Series. TJ265.P68 1993 621.402’ 1--dc20 92-11555 CIP McGraw-Hill - Y A Division of TheMcGrawHiD Companies Preface This book is intended for the first course in thermodynamics required by most, if not all, engineering departments. It is designed to supplement the required text selected for the course; it provides a succinct presentation of the material so that the student can more easily determine the major objective of each section of the textbook. If proofs of theorems are not of primary importance in this first course, the present Schaum’s Outline could itself serve as the required text. The basic thermodynamic principles are liberally illustrated with numerous examples and solved problems that demonstrate how the principles are applied to actual or simulated engineering situations. Supplementary problems that provide students an opportunity to test their problem-solving skills are included at the ends of all chapters. Answers are provided for all these problems. The material presented in a first course in thermodynamics is more or less the same in most engineering schools. Under a quarter system both the first and second laws are covered, with little time left for applications. Under a semester system it is possible to cover some application areas, such as vapor and gas cycles, nonreactive mixtures, and combustion. This book allows such flexibility. In fact, there is sufficient material for a full year of study. As U.S. industry continues to avoid the use of SI units, we have written about 25 percent of the examples, solved problems, and supplementary problems in English units. Tables are presented in both systems of units. The authors wish to thank Mrs. Michelle Gruender for her careful review of the manuscript, Ms. Kelly Bartholemew for her excellent word processing, Mr. B. J. Clark for his friendly and insightful advice, and Ms. Maureen Walker for her efficient production of this book. MERLEC. POTTER CRAIGW. SOMERTON ... 111 This page intentionally left blank Contents Chapter I CONCEPTS. DEFINITIONS. AND BASIC PRINCIPLES . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Thermodynamic Systems and Control Volumes . . . . . . . . . . . . . . . . . . . 1 1.3 Macroscopic Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.4 Properties and State of a System ............................ 3 1.5 Thermodynamic Equilibrium; Processes ........................ 3 1.6 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.7 Density. Specific Volume. Specific Weight ...................... 6 1.8 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.9 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.10 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Chapter 2 PROPERTIES OF PURE SUBSTANCES ........................ 19 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 The P-c-T Surface ..................................... 19 2.3 The Liquid-Vapor Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 SteamTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 The Ideal-Gas Equation of State ............................ 23 2.6 Equations of State for a Nonideal Gas ......................... 25 Chapter 3 WORK AND HEAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Definition of Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3 Quasiequilibrium Work Due to a Moving Boundary . . . . . . . . . . . . . . . . 33 3.4 Nonequilibrium Work ................................... 37 3.5 Other Work Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.6 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Chapter 4 THE FIRST LAW OF THERMODYNAMICS ..................... 49 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 The First Law of Thermodynamics Applied to a Cycle . . . . . . . . . . . . . . . 49 4.3 The First Law Applied to a Process ........................... 49 4.4 Enthalpy ............................................ 52 4.5 LatentHeat .......................................... 53 4.6 SpecificHeats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7 The First Law Applied to Various Processes ..................... 57 4.8 General Formulation for Control Volumes ...................... 61 4.9 Applications of the Energy Equation .......................... 64 V vi CONTENTS Chapter 5 THE SECOND LAW OF THERMODYNAMICS . . . . . . . . . . . . . . . . . . . 98 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.2 Heat Engines. Heat Pumps. and Refrigerators .................... 98 5.3 Statements of the Second Law of Thermodynamics . . . . . . . . . . . . . . . . . 99 5.4 Reversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.5 The Carnot Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.6 Carnot Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Chapter 6 ENTROPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.2 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.3 Entropy for an Ideal Gas with Constant Specific Heats . . . . . . . . . . . . . . 113 6.4 Entropy for an Ideal Gas with Variable Specific Heats . . . . . . . . . . . . . . 115 6.5 Entropy for Substances Such as Steam. Solids. and Liquids . . . . . . . . . . . 116 6.6 The Inequality of Clausius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.7 Entropy Change for an Irreversible Process ..................... 119 6.8 The Second Law Applied to a Control Volume . . . . . . . . . . . . . . . . . . . 121 Chapter 7 REVERSIBLE WORK, IRREVERSIBILITY.AND AVAILABILITY . . . . . . 137 7.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.2 Reversible Work and Irreversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 7.3 Availability and Exergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7.4 Second-Law Analysis of a Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Chapter 8 POWER AND REFRIGERATION VAPOR CYCLES . . . . . . . . . . . . . . . . 149 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.2 The Rankine Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.3 Rankine Cycle Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 8.4 The Reheat Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 8.5 The Regenerative Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 8.6 The Supercritical Rankine Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 8.7 Effect of Losses on Power Cycle Efficiency . . . . . . . . . . . . . . . . . . . . . . 160 8.8 The Vapor Refrigeration Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 8.9 The Multistage Vapor Refrigeration Cycle . . . . . . . . . . . . . . . . . . . . . . 165 8.10 TheHeatPump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 8.11 The Absorption Refrigeration Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Chapter 9 POWER AND REFRIGERATION GAS CYCLES . . . . . . . . . . . . . . . . . . 186 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 9.2 Gas Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 9.3 The Air-Standard Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 9.4 The Carnot Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 9.5 TheOttoCycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 9.6 The Diesel Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 9.7 TheDualCycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 CONTENTS vii 9.8 The Stirling and Ericsson Cycles ............................. 199 9.9 The Brayton Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.10 The Regenerative Gas-Turbine Cycle ......................... 203 9.11 The Intercooling. Reheat. Regenerative Gas-Turbine Cycle . . . . . . . . . . . 205 9.12 The Turbojet Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 9.13 The Combined Brayton-Rankine Cycle ........................ 207 9.14 The Gas Refrigeration Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Chapter 10 THERMODYNAMIC RELATIONS ............................ 230 10.1 Three Differential Relationships ............................ 230 10.2 The Maxwell Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 10.3 The Clapeyron Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 10.4 Further Consequences of the Maxwell Relations . . . . . . . . . . . . . . . . . . 234 10.5 Relationships Involving Specific Heats ......................... 236 10.6 The Joule-Thornson Coefficient ............................. 238 10.7 Enthalpy. 1nternal.Energy. and Entropy Changes of Real Gases . . . . . . . . 239 Chapter 11 MIXTURES AND SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 11.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 11.2 Ideal-Gas Law for Mixtures ................................ 250 11.3 Properties of a Mixture of Ideal Gases ......................... 251 11.4 Gas-Vapor Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 11.5 Adiabatic Saturation and Wet-Bulb Temperatures . . . . . . . . . . . . . . . . . 254 11.6 The Psychrometric Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 11.7 Air-conditioning Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 Chapter 12 COMBUSTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 12.1 Combustion Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 12.2 Enthalpy of Formation. Enthalpy of Combustion. and the First LAW . . . . . . 273 12.3 Adiabatic Flame Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 Appendix A CONVERSIONS OF UNITS ................................. 287 Appendix MATERIAL PROPERTIES .................................. 288 Appendix c THERMODYNAMIC PROPERTIES OF WATER (STEAM TABLES) . . . . 295 Appendix D THERMODYNAMIC PROPERTIES OF FREON 12 . . . . . . . . . . . . . . . . 310 ... Vlll CONTENTS Appendix E THERMODYNAMIC PROPERTIES OF AMMONIA . . . . . . . . . . . . . . . 319 Appendix F IDEALGASTABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Appendix G PSYCHROMETRIC CHARTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 Appendix H COMPRESSIBILITY CHART . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Appendix I ENTHALPY DEPARTURE CHARTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 Appendix J ENTROPY DEPARTURE CHARTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Appendix K SAMPLE SCREENS FROM THE COMPANION INTERACTIVE OUTLINE ....................................... 349 INDEX ................................................................. 365 This page intentionally left blank Chapter 1 Concepts, Definitions, and Basic Principles 1.1 INTRODUCTION Thermodynamics is a science in which the storage, the transformation, and the transfer of energy are studied. Energy is stored as internal energy (associated with temperature), kinetic energy (due to motion), potential energy (due to elevation) and chemical energy (due to chemical composition); it is transformed from one of these forms to another; and it is transferred across a boundary as either heat or work. In thermodynamics we will develop mathematical equations that relate the transforma- tions and transfers of energy to material properties such as temperature, pressure, or enthalpy. Substances and their properties thus become an important secondary theme. Much of our work will be based on experimental observations that have been organized into mathematical statements, or laws; the first and second laws of thermodynamics are the most widely used. The engineer’s objective in studying thermodynamics is most often the analysis or design of a large-scale system-anything from an air-conditioner to a nuclear power plant. Such a system may be regarded as a continuum in which the activity of the constituent molecules is averaged into measurable quantities such as pressure, temperature, and velocity. This outline, then, will be restricted to macroscopic or engineering thermodynamics. If the behavior of individual molecules is important, a text in statistical thermodynamics must be consulted. 1.2 THERMODYNAMIC SYSTEMS AND CONTROL VOLUMES A thermodynamic system is a definite quantity of matter most often contained within some closed surface. The surface is usually an obvious one like that enclosing the gas in the cylinder of Fig. 1-1; however, it may be an imagined boundary like the deforming boundary of a certain amount of mass as it flows through a pump. In Fig. 1-1 the system is the compressed gas, the working fluid, and the system boundary is shown by the dotted line. All matter external to a system is collectively called its surroundings. Thermodynamics is con- cerned with the interactions of a system and its surroundings, or one system interacting with another. A system interacts with its surroundings by transferring energy across its boundary. No material crosses the boundary of a given system. If the system does not exchange energy with the surroundings, it is an isolated system. In many cases, an analysis is simplified if attention is focused on a volume in space into which, and or from which, a substance flows. Such a volume is a control volume. A pump, a turbine, an inflating balloon, are examples of control volumes. The surface that completely surrounds the control volume is called a control s u ~ a c e .An example is sketched in Fig. 1-2. We thus must choose, in a particular problem, whether a system is to be considered or whether a control volume is more useful. If there is mass flux across a boundary of the region, then a control volume is required; otherwise, a system is identified. We will present the analysis of a system first and follow that with a study using the control volume. 1.3 MACROSCOPIC DESCRIPTION In engineering thermodynamics we postulate that the material in our system or control volume is a continuum; that is, it is continuously distributed throughout the region of interest. Such a postulate allows us to describe a system or control volume using only a few measurable properties. 1 2 CONCEPTS, DEFINITIONS, AND BASIC PRINCIPLES [CHAP. 1 Fig. 1-2 Consider the definition of density given by Am p = lim - AV+O AV where Am is the mass contained in the volume AV, shown in Fig. 1-3. Physically, AV cannot be allowed to shrink to zero since, if AV became extremely small, Am would vary discontinuously, depending on the number of molecules in AV. So, the zero in the definition of p should be replaced by some quantity E, small, but large enough to eliminate molecular effects. Noting that there are about 3 X 10l6 molecuIes in a cubic millimeter of air at standard conditions, E need not be very large to contain billions and billions of molecules. For most engineering applications E is sufficiently smalI that we can let it be zero, as in (1.1). Fig. 1-3 There are, however, situations where the continuum assumption is not valid; for example, the re-entry of satellites. At an elevation of 100 km the mean free path, the average distance a molecule travels before it collides with another molecule, is about 30 mm; the macroscopic approach is already questionable. At 150 km the mean free path exceeds 3 m, which is comparable to the dimensions of the satellite! Under these conditions statistical methods based on molecular activity must be used. 3 CHAP. 11 CONCEPTS, DEFINITIONS, AND BASIC PRINCIPLES 1.4 PROPERTIES AND STATE OF A SYSTEM The matter in a system may exist in several phases: as a solid, a liquid, or a gas. A phase is a quantity of matter that has the same chemical composition throughout; that is, it is homogeneous. Phase boundaries separate the phases, in what, when taken as a whole, is called a mixture. A property is any quantity which serves to describe a system. The state of a system is its condition as described by giving values to its properties at a particular instant. The common properties are pressure, temperature, volume, velocity, and position; but others must occasionally be considered. Shape is important when surface effects are significant; color is important when radiation heat transfer is being investigated. The essential feature of a property is that it has a unique value when a system is in a particular state, and this value does not depend on the previous states that the system passed through; that is, it is not a path function. Since a property is not dependent on the path, any change depends only on the initial and final states of the system. Using the symbol 4 to represent a property, that is stated mathematically as This requires that d 4 be an exact differential; 42- represents the change in the property as the system changes from state 1 to state 2. There are quantities which we will encounter, such as work, that are path functions for which an exact differential does not exist. A relatively small number of independent properties suffice to fix all other properties and thus the state of the system. If the system is composed of a single phase, free from magnetic, electrical and surface effects, the state is fixed when any two properties are fixed; this simple system receives most attention in engineering thermodynamics. Thermodynamic properties are divided into two general types, intensive and extensive. An intensive property is one which does not depend on the mass of the system; temperature, pressure, density and velocity are examples since they are the same for the entire system, or for parts of the system. If we bring two systems together, intensive properties are not summed. An extensive property is one which depends on the mass of the system; volume, momentum, and kinetic energy, are examples. If two systems are brought together the extensive property of the new system is the sum of the extensive properties of the original two systems. If we divide an extensive property by the mass a specific property results. The specific volume is thus defined to be V U = - m We will generally use an uppercase letter to represent an extensive property [exception: m for mass] and a lowercase letter to denote the associated intensive property. 1.5 THERMODYNAMIC EQUILIBRIUM; PROCESSES When the temperature or the pressure of a system is referred to, it is assumed that all points of the system have the same, or essentially the same, temperature or pressure. When the properties are assumed constant from point to point and when there is no tendency for change with time, a condition of thermodynamic equilibrium exists. If the temperature, say, is suddenly increased at some part of the system boundary, spontaneous redistribution is assumed to occur until all parts of the system are at the same temperature. If a system would undergo a large change in its properties when subjected to some small disturbance, it is said to be in metastable equilibrium. A mixture of gasoline and air, or a large bowl on a small table, is such a system. -- ---- 4 CONCEPTS, DEFINITIONS, AND BASIC PRINCIPLES [CHAP. 1 When a system changes from one equilibrium state to another the path of successive states through which the system passes is called a process. If, in the passing from one state to the next, the deviation from equilibrium is infinitesimal, a quasiequilibrium process occurs and each state in the process may be ideahed as an equilibrium state. Many processes, such as the compression and expansion of gases in an internal combustion engine, can be approximated by quasiequiIibrium processes with no significant loss of accuracy. If a system undergoes a quasiequilibrium process (such as the slow compression of air in a cylinder) it may be sketched on appropriate coordinates by using a solid line, as shown in Fig. 1-4(a). If the system, however, goes from one equilibrium state to another through a series of nonequilibrium states (as in combustion) a nonequilibrium process occurs. In Fig. 1-4(6) the dashed curve represents such a process; between (V,,P , ) and (V2,P2) properties are not uniform throughout the system and thus the state of the system cannot be well defined. p2 1 /7 /’I PI I I I I V I V * VI v 2 Fig. 1-4 EXAMPLE 1.1 Whether a particular process may be considered quasiequilibrium or nonequilibrium depends on how the process is carried out. Let us add the weight W to the piston of Fig. 1-5. If it is added suddenly as one large weight, as in part (a),a nonequilibrium process will occur in the gas, the system. If we divide the weight into a large number of small weights and add them one at a time, as in part (b),a quasiequilibrium process will occur. Fig. 1-5 Note that the surroundings play no part in the notion of equilibrium. It is possible that the surroundings do work on the system via friction; for quasiequilibrium it is only required that the properties of the system be uniform at any instant during a process.