$4 Some Concepts and Definitions 2.14 The level ofthe water in an enclosed water tank i 40 m above te ground ‘The pressure in the air space above the water is 120 kPa. The average density of the water is 1000 kgim?. What is the pressure t arenes Bi he pressure of the water at 2.15 A gas is contained in two cylinders 4 and B, connected by a piston of wo! different diameters, as shown in Fig. 2.8, The mass of the piston is 10 ky and the gas pressure inside cylinder 4 is 200 kPa, Caleu pee i kPa, Calculate the pressure Fig. 28 Sheteh for Problem 2.5, 3 Properties of a Pure Substance In the previous chapter we considered three familiar properties of a substance, namely, specific volume, pressure, and temperature, We now {urn our attention to pure substances and consider some of the phases in which a pure substance may exist, he number of independent properties 4 pure substance may have, and methods of presenting thermodynamic properties. 3.1 The Pure Substance ‘A pure substance it one that hasa homogeneous and invariable chem- ical composition. It may exist in more than one phase, but the chemical composition is the same in all phases. Thus, liquid water, a mixture of liguid water and water vapor (steam), or a mixture of ice and liquid water are all pure substances, for every phase has the sarne chemical imposition. On the other hand, « mixture of liquid air and gaseous air is not a pure substance, since the composition of the liquid phase is different from that of the vapor phase. Sometimes a mixture of gases, such as air, ie considered & pure sub- stance as long as there is no change of phase. Strictly speaking. this is not true, but rather, as we shall see later, we should say that a mixture of sases such as ait exhibits some of the characteristics of a pure substance as long as there is no change of phase. In this text the emphasis will be on those substances which may be called simple compressible substances. By this we understand that 3596 Properties of a Pure Substance surface effects, magnetic effects, and electrical effects are not significant when dealing with these substances. On the other hand changes in ‘volume, such as those associated with the expansion of a gas in acylinder, are most important. However, reference wll be made to other substances in which surface, magnetic, or electrical effects are important. We will refer to a system consisting of a simple compressible substance as 2 simple compressible system. 3.2 Vapor-Liquid-Sotid Phase Equilibrium ina Pure Substance Consider as a system 1 kg of water contained in the piston-cylinder arrangement of Fig. 3.16, Suppose that the piston and weight maintain a e ’ . Fix.2.1- Constant. pressure change rom quit apor phase fora puresubstance. pressure of 0.1 MPa in the cylinder, and that the initial temperature is 20°C. As heat is transferred to the water the temperature increases appreciably, the specific volume increases slightly, and the pressure remains constant, When the temperature reaches 99.6°C, additional heat transfer results in a change of phase, as indicated in Fig. 3.10. That is, some of the liquid! becomes vapor, and during this process both the temperature and pressure remain constant, but the specific volume iereases considerably. When the last drop of liquid has vaporized, forte eraafer of es reno in an ineese in both vemperatre and specific volume of the vapor, 4g. 3.1c ‘The term saturation temperature designates the temperature at which vaporization takes place at a given pressure, and this pressure is called the seturation pressure for the given temperature. Thus for water at 99.6°C the saturation pressure is 0.1 MPa, and for water at 0.1 MPa the saturation temperature is 99.6°C. For a pure substance there is a definite relation between saturation pressure and saturation tempera- © saturation temperature and pres- \Vapor-Liquid:-Soid Phase Equil jum ina Pure Substance ture, a typical curve being shown in pressure curve, Ifasubstance existss li 3.2. This is called the vapor- id atthe g £ WV “sure, itis called saturated liquid. 1f the temperature of the liquid is Jower than the saturation tempera ture for the existing pressure, itis called either a subcooled liquid (im- plying that che temperature is lower than the saturation temperature for the given pressure) ora compressed Tiquid (implying that the pressure ig greater chan the saturation pressure for the given temperature). Either term may be used, but the latter term will be used in this text ‘When a substance exists as part liquid and part vapor at the saturation, temperature, its quality is defined as the ratio of the mass of vapor to the ‘par Tass. Thus, in Fig. 3.14, if the mass of the vapor is 0.2 kg and the ‘mass of the liquid is 0.8 ky, the quality is 0.2 or 20 per cent. The quality may be considered 2s an intensive property, and it has the symbol x. Quality has meaning only when the substance isin a saturated state, ie., at saturation pressure and temperature. Ifa substance exists as vapor at the saturation temperature, itis called saturated vapor. (Sometimes the term dry saturated vapor is used to emphasize that the quality is 100 per cent.) When the vapor is at a temperature greater than the saturation temperature, itis said to exist as superheated vapor. ‘The pressure and temperature of superheated vapor are independent properties, since the temperature may increase while the pressure remains constant. Actually. the substances we call gases are highly superheated vapors. Consider Fig. 3.1 again, and Jet us plot on the temperature-voh diagram of Fig, 3.3 the constant-pressure line that represents the states through which the water passes as itis heated from the initial state of | 0.1 MPa and 20°C. Let state 4 represent the initial state, B the saturated: Jiquid state (9.6°C), and line AB the process in which che liquid is heated from the initial temperature to the sat Point Cis the saturated vapor state, and line BC isthe constant-tempera ture process in which the change of phase from liquid to vapor occurs. Line CD represents the process in which the steam is superheated at constant pressure, Temperature and volume both increase during this process. Now let the process take place at a constant pressure of 1 MPa, | Teper Fig.22.Vavorpreure cur of pure stbstance 3738 Properties of a Pure Substance Fig.3.3 Temperature volume dlgram for water showing ould and vapor phases (nat to scale beginning from an initial temperature of 20°C. Point E represents the | initial stete, the specific volume being slightly less than at 0.1 MPa and 20°C, Vaporization now begins at point F, where the temperature is | 179.9°C, Point G is the saturated-vapor state, and line GHT the constant- Pressure process in which the steam is superheated. Ina similar manner, a constant pressure of 10 MPa is represented by line JJKL, the saturation temperature being $11.1°C. ‘At a pressure of 22.09 MPa, represented by line MNO, we find, however, that there is no constant-temperature vaporization process. Rather, point N is a point of inflection with a zero slope. This point is called the critical point, and at the criticat point the saturated-liquid and saturated-vapor states are identical. The temperature, pressure, and specific volume at the critical point are called the critical temperature, 0, That is, as the pressure approaches zero, the 20 1a 1 Ccomrestiy,pu/ RT 2440 Pressur, Pe Fe 3.7 compressibility roeProperties of a Pure Substance PaxT behavior closely approaches that predicted by the ideal g equation of state. Note also that at temperatures of 300 K and abo {ie., room temperature and above) the compressibility factor is nei unity up to pressures of about 10 MPa. This means that the ide 88 equation of state can be used for nitrogen (and, as it happens, als air) over this range with considerable accuracy. Now suppose we reduce the temperature from 300 K while keeping the pressure constant at 4 MPa. The density will increase and note a sharp decrease below unity in the value of the compressbil factor. Values of Z <1 mean that the actual density is greater than}. ~ ‘would be predicted by ideal gas behavior. The physical explanation off this is as follows: As the temperature is reduced from 300K while pressure remains constant at 4 MPa, the molecules are brought closer together. In this range of intermolecular distances, and at this pres sure and temperature, there is an attractive force between che mole! cules. The lower the temperature the greater is this intermolecular attractive force. This attractive force between the molecules meant ‘The Vapor Phase of a Simple Compressible Substance --T behavior for a particular gas over the entire superheated vapor ‘more complicated equations of state have been developed. Several -complexity of these equations we refer to one of the best known, narnely, the Beattie Bridgeman equation of state. Thisequation is, Sho a) en 8 B= Be(1—/8), €= aT, and Ay, a, By, b, and c fege consants for different gues. The values of these consian for Berous substances are gvenin Table 3.3. “Table 3.3 Constants of the Beattie-Bridgeman Equation of State that the density is greater than would be predicted by the ideal gai (Pressure in kilopascals; specific volume in mmol; temperature in behavior, which assumes no intermolecular forces. Note also from the compressibility chart that above 30 MPa, the compressibility factor is always greater than unity. In this range the intermolecular distances are very small, and there it a repulsive force between the molecules. This tends to make the density less than would otherwise be expected. “The precise nature of intermolecular forces is a rather complex ‘matter. These forces are a function of the temperature as well as the density, The preceding discussion shouldbe considered as a qualitative analysis to assist in gaining some understanding of the ideal gas equa ‘ion of state and how the P-t-T behavior of actual gases deviate from) this equation. From a practigal point of view in the solution of problems, wo things should be mowed Fi. at very tow pressure, ideal ga behavior canbe) assumed with good accuracy, regardless of the temperature: Second, at temperatures that are double the critical temperature or above (the ental temperature of gitrogen is 15 K) Kea! gas behavior can be assumed with good acclfacy to pressures of around 10 MPa. When the temperature is less than twice the critical temperature, and the pressure above a very low value, say ambient pressure, we are in the superheated vapor region, and the deviation from ideal gas behavior may be considerable. In this region it is preferable to use tables of thermodynamic properties or charts for a particular substance. These tables are considered in the following section. The concept of the gen- eralized compressibility chart is introduced in Chapter 10. very high densities, for pressuresl) Kelvin; R = 8.31434 N m/mol K). = 4 * a E Fium 2.1886 0.05984 0.01400 ‘Argon 130.7802 0.02528 0.03831 b Hydrogen 200117 0.00506 0.02096 004359 O.d504 Nivogen 156.2515 0.02617 DSM —0.00691 420 Onygen 510887 0.02562 Oo4s24 —D.004208 480 er 181.8441 0.01981 04511 —D001101 434 Gorse a.lor7s —Og7285. 66.00 Carbon dioxide 507 2836 ‘The matter of equations of state will be discussed further in Chapter 10. The observation to be mace here in panicutar is that an equation of sate that accurately describes the relation between pressure, temper ature, and specific volume is rather cumbersome and the solution requires considerable time, When using a large digital computer, it is often mast conveniem to determine the thermodynamic properties in a given state from sitch equations. However, in hand calculations itis much more convenient to tabulate values of pressure, temperature, specific volume, and other thermodynamic properties for various substances. The Appendix includes summary tables and graphs of the thermodynamic properties of water, ammonia, Freon-l2, oxygen, nitrogen, mercury, and Freon-13. The tables of the properties of water are usvally referred to as che “steam tables” and are extracted from “Steam Tables” by Keenan, Keyes, Hill and Moore. The method for a48 Properties of a Pure Substance Tables of Thermodynamic Properties 49 compiling the PT" data for such a table isto find an equation of statyevsion of a very extensively used volume by Keenan and Keyes, which that accurately is the experimental data ancl then (solve the equati wa published in 1986, The Appendix incudes a summary oF the 1969 of state for thevalues listed in the tuble. edition of “Steun) Tables,” and reference to these tablesis macle through- / ‘out this text U7 Pampled1 In Table A.L.L, the first column after the temperature gives the cor- ‘What is the mass of air contained in a room 6 m X 10m X4 mil tresponding saturation pressure in kilopascals oF megapascals. The pressure is 100 kPa and the temperature is 25°C? Assume air t0 be 2 next two columns give specific volume in cubic metres per kilogram. idea! gas. ‘The fist of these gyres the specific volume of the savurated liquid, 2; By using Eq. 3.4, and the value of R from Table AB the second column gives the specific volume of saturated vapor, u,. The difference between these two. vj—2, represents the increase in specific APY 100 kN/m* x 240m" ygy.g yy volume when the tate changes from staurated figuid w saturated vapor, "= RT ~ UBT RN mikg KX 298.15 K isdesignated wy. ‘The specific volume of a substance having a given quality can be Example 3.2 found by utilizing the definition of quality. Quality has already been A tank hasa volume of 0.5 mand contains 10 kg of an ideal gos hag defined as the ratio of the mass of vapor to total mass of liquid plus ing a molecular weight of 24,‘The temperature & 25°C, What is ry Yapor when a substance i ina saturation state. Let us consider a mass of assure? kg having a quality x ‘The specific volume is the sum of the volume Pethe gas con of the liquid and the volume of the vapor. ‘The volume of the liquid is u {1=#)yp and the volume of the vapor is 2%», ‘Therefore the specific 831434 kN m/kmol K volume vis ‘24 kg/kmol = su,t (I-20, 38) 346 43 KN n/kg K ant is determined first: Since +m vy. Eq.3.8 can also be written in the following forms We now solve for P. teen eo pw BRT _, 10 ky 0.346 43 KN mikg K x 298.15 K Vv 0.5 mt = 4-1 a)% 8.10) 2008.8 kPa ‘As an example, let us calculate the specific volume of saturated steam. 3,5. Tables of Thermodynamic Properties at 200°C having a quality of 70%. Using Eq. 3.8, “Tables of thermodynamic properties of many substances are availabl. 0.3 (0.001 157) + 0.7 (0.127 36) and in general all chese have the same form. In this section we shal refé = wn ioe Ream bles The seam bles ae sled both ws vehi 0.0895 meg presenting thermodyggmic tables and because steam is used extet Iq Table A.1.2, the first column after the pressure lists the saturation sively in power planis*and industrial processes. Once the steam tabi temperature for each pressure. ‘The next columns list specific volume in ave understood, other thermodynamic tables can be readily used. |g manner similar to Table A.1.L. When necessary, vj can readily be Several different versions of steam tables have been published. Twi found by subtracting vfrom v». new tables have recently been published in the United States. In 186 Table 3 of the steam tables, whichis surnmarized in Table A.1.3 in the The American Society of Mechanical Engineers published a volum Appendix, gives the properties of superheated vapor, In the superheat entitled “Thermodynamic and ‘Transport Propestes of Steam.” com) regon, pressine ancl temperature are independent properties, and monly referred to as the 1967 ASME steam tables. “Steam Tables) sherefore, for each pressure a large number of temperatures is given, by Keenan, Keyes, Hill, and Moore was published in #969. ‘This (sand for each temperature four thermadynimic properties are listed,50 Properti of a Pure Substance Thermodynamic Surfaces 51 eat onsen a ivan mount hat malta foes taper) gu Fig.28 tiustationotcomeresseatiuid state, the first one being specific volume. Thus, the specific volume of stea ata pressure of 0.5 MPa and 200°C is 0.4249 mY%kg, ‘Table 4 of the steam tables, summarized in Table A.1.4 in the Appe dix, gives the properties of the compressed liquid. To demonstrate use of this table, consider a piston and a cylinder (as shown in Fig. 34 that contains 1 kg of saturated liquid water at 100°C. Its properties ay given in Table A. 1.1, and we note that the pressure is 0.1013 MPa and th specific volume is 0.001 044 m#/kg. Suppose the pressure is increa 10 10 MPa while the temperature is held constant at 100°C by th necessary transfer of heat, Q. Since water is slightly compressible, wt would expect a slight decrease in specific volume during this proces, ‘Table A.L gives this specific volume as 0.001 089 kg, Note hat is only a slight decrease, and only a small error would be made if of assumed that the volume of a compressed liquid was equal to the speci volume of the saturated liquid at the same temperature, In many ca this is the most convenient procedure, particularly in those cases whe compressed liquid data are not available. Furthermore, since specific volume does change rapidly with tem auure, care should be exercised in interpolation over the wide ter ature ranges in Table A.1.4. (In some cases it may be more accurate use the saturated liquid data from Table A.L.1, and interpolate diffe ences between Table A.1.1, the saturated liquid data, and Table A.1 the compressed liquid gata.) 3.6 Thermodynamic Surfaces ‘Table 6 of the steaM tables, which is summarized in Table A.1.5 4. The matter discussed in this chapter can be well summarized by a the Appendix, gives the properties of saturated solid and saturate consideration of a pressure-specific volume-temperature surface. Two vapor that are in equilibrium. ‘The first column gives the temperaturfssuch surfaces are shown in Figs, 3.9 and 3.10, Figure 3.9showsa substance and the second collumn gives the corresponding saturation pressury such as water in which the specific volume increases during freezing, and ‘As would be expected, all these pressures are less than the triple-poiy Fig. 3.10 shows @ substance in which the specific volume decreases during, pressure. The next two columns give the specific volume of the saturate freezing, Solid and saturated vapor (note that the tabulated value is v % 10%) In these diagrams the pressure, specific volume, and temperature are Temperature Volume Fa.29 Pressure vue temperature suracefors substance tht expands on freezing52 Properties of @ Pure Substance eo “This, of course, follows from the fact that in the two-phase region, lines of constant pressure are also lines of constant temperature, though the pecfc volume may change. The triple point actually appears as the ple ine on the P-eT surface, since the pressure and temperature of ‘he triple point are fixed, but the specific volume may vary, depending “on the proportion of each phase. Itis also of interest to note the pressure-temperature and pressure~ =yolume projections of these surfaces. We have already considered the _pressuresemperature diagram for a substance such as water. Its on this, Giagram that we observe the triple point. Various lines of constant Stemperature are shown on the pressure-volume diagram, and the Corresponding constant-temperature sections are lettered identically ‘on the P-1-T surface. The critical isotherm has a point of inflection atthe ‘tical point. ‘One notices that with a substance such as water, which expands on ‘reeting, the freezing temperature decreases with an increase in pres- sure. With a substance that contracts on freezing, the freezing tempera Te F ture increases as the pressure increases. Thus, asthe pressure of vapor is Fincreased along the constanttemperature line abcdef in Fig. 3.9, a sub- ea stance that expands on freezing first becomes solid and then liquid. For at 7 ithe substance that contracts on freezing, the corresponding constant- et a ‘temperature line, Fig. 3.10, indicates that as the pressure on the vapor is mi |B cased, it first becomes liquid and then solid. mi ‘Example 33 ST ua on ‘A vessel having a volume of 0.4 m? contains 2.0 kg of a liquid water Tani — “and water vapor mixture in equilibrium at a pressure of 6 bar Fie.210 Pressure wlume-emperature surface fore substance that contracts on treezng (0.6 MPS). plotted on mutually perpendicular coordinates, and each poss ‘equilibrium state is thus represented by a point on the surface. follows directly from the fact that 2 pure substance has only two in pendertintnave proggrs, Al points slong 2 qusiquibiun pr lie on the P-u-T surfiee, since such a process always passes throuj equilibrium states. "The cegions of the surface that represent a single phase, namely, solid, quid, and vapor phases, are indicated, these surfaces curved. The two-phase regions, namely, the solid-liquid, solid-va ‘and liquid-vapor regions, are ruled surfaces. By this we understand they ate made up of straight lines parallel to the specific volume 2x From the steam tables (Appendix Table A.1.2) Y= 0.8157-0.001 101 =0.31464 Properties of a Pure Substance The quality can now be calculated, using Eq, 3.10 0.20 = 08157 —(1 ~9) 03146 “01157 tne= BUST 03678 x= 0.6822 ‘Therefore the mass of liquid is 32 2.0 (0.3678) = 0.7356 kg f ‘The mass of vapor is 2.0 (0.6399) = 9646 bg ' “The volume of liquid is : a Mug ~ 0.7856 (0.001 101) = 0.0008 m* : “The volume of the vapor i } Pray = Meanty ~ 1.2644 (0.8157) = 0.8992 m? t Example 3.4 less ‘A rigid vessel contains saturated ammonia vapor at 20°C. Heat | trated to the system ul the temperature reaches 40°C, What the final pressure? Since the volume does not change during thig process, the specit volume also remains constant, From the ammonia tables. Table A.2. | 34 9 = 0.1494 ming } bss Since at 40°C is less than 0.1494 mi/kg, itis evident that in & final state the ammonia fs superheated vapor: By interpolating ere} the 900 and 1000 kPa columns of Table A.2.2, we find shat P, = 938 kPa Problems PROBLEMS 3.1 A spherical balloon has) radius of 5m. The atmospheric pressure 16 Tobit tamper 808 ar If the balloon is filled with helium at 100 kPa, 20°C, what is the =a this balloon dls ae Fig. 311 SketchtorProblem 32, 0.2 mf, and the si is intially t 200 kPa, 500°C. The a result of heat transfer to the surroundings. (@) What is the temperature of the air inside whe the stops? {@) If che cooling is continued wn‘ the temperature reaches 20°C, what is the pressure inside che eylinder a this state? ‘A racium pump is used to pump a vacwim over a bath of liquid heliom, ‘The volume tate of flow into the vacuum pump is 1.5 m¥/s, The pressure at the vacuum pump inlet is 15 Pa and the temperature is ~25°C, What ‘ase of helium enters the pump per minute? ‘A metat sphere of 150 mm inside diameter is weighed on a precision beam balance when evacuated and agair when filled to 875 kPa with an wh Known gas. The difference in weight i 0.0025 kg. The room temperature is 25°C, What is the gas, assuming ic wo be a pure substance? air is then cooled as the piston reaches A rigid vesel 4 is connected to a spherical elastic balloon B as shown Fig. 3.12. both conta aiv a the ambient temperature 25°C. The volume ‘of vessel / is 0.1 mand the initial pressure is 300 kPa."The initial diameter ‘of the balloon is 0.5 m and the presure inside is 100 kPa. The valve con. necting 4 and B is now opened, and remains open. It may be assumed that the pressure inside the balloon is directly proportional to its diameter, and also that the final temperature of the air is uniform throughout at156 Properties of a Pure Substance 36 37 38 39 3.10 Problems 57 pressure in the system andl the Final volime qf 3.1) ota pressure specific volume diag water showing the following lines (a) Sauraved qui. (0) Sauraed vapor (6) The following constant temperate lines Gnchiding the compressed: liquid region) 150°C. 250°C, 350°C, 400°C; 500°C, {d) The Following lines of constant qsality: 10%, 50%, 90%, on log hag paper (8 % 8 cycles) tor ® © 4.12 Plot a presmmrespecfic volume diagram on log log paper (2X 3 eyeles) Lor Freon-1?, showing the following lines ; (a) Sseurated liquid wa (© Saturated vapor, (9 The Following constanttempersuure fines: ~10°C, 50°C, 110°C, Fig 312, Sketch forProblem3.5 Le : {d) The Fellowing constant-quilty fines: 108, 50%, 80%, 5.18 A dosed tank contains vapor and liquid H,O in equilibrium at 250°C. The distanice from the bottom of the tank :o the liquid Jevel is 10m. What is the pressure reading at the bottom of te ank as compared! to the pressure © eading at the top of the tank? 5.14 A spacecraft storage vessel of 0.1 m? capacity contains 100 kg of saturated ‘oxygen at 99 K. Determine the percentages of liquid and vapor in the F vessel on a mas basis and also a votre bass, | 3.15 A rigid vessel contains saturated water at 100 kPa, Find the percentage of liquid (on a volume basis) at ehis state such that the water will pass through the critical point when heated. “3.16 A vessel fitted with a sight glass contains Freon-12 at 26°C. Liquid is wit drawo from the bottom at 2 slow rate, and the temperature remains con- stant duing the process, If the area of the vessel is 0.05 m? and the level drops 150 min, determine the mass of Freon-L2 withdrawn, Is it reasonable to assume that a che given states the substance beha san ideal gs: (a) Nitrogen at 30°C, 3 MPa, 18) Carbon dioxide at 80°C, 3 MPa. 46) Water at 1300°C, 3 Pa, 42) Water at 50°C, 10 kPa 4@) Water at 30°C, 10 kPa Determine whether water a each of the following sates is compres liquid, a superheated vapor, or 4 mixture of saturated liquid and va 120°C, 150 kPa; 0.55 MPa, 04 m'/kg; 160°C, Ot mg: 200 KPa, 110 300°C, 001 még: 5 KPa, 10°C Plot the following vapor-pressure uunves (saturation pressure vs stu tion temperneare) {@) Water on Cartesian coordinates, ~40%C to 20°. (©) Water on Cartesian coordinates, 0 to 28 MPa {@) Water, FreonI2, and ammonia on semiog paper (pressure onl sco, 10 Kato 10 MPa, “SCI SO Cateulate the following specie volumes {@) Ammonia, 30°C, 80% quali. (@) Freon-12, 50°, 18% quay. (Water, 8 MPa, 98% quali. {@) Nitrogen, 0 1. 40% qualty Determine the quality Gif saturated) oF temperature if superheated) 4 the Following substances in the given states {@) Ammonia, 20°C, 0.1 m?/kg; 800 kPa, 0.2 m*/k. I @) Freon-12, 400 kPa, 0.04 mi/hy: 400 kPa, 0.045 1h k (6) Water, 20°C, 1 mfg: 8 MPa, 0.01 m? (©) Nitrogen, 0.5 MPa, 0.08 mfg; 8D K, O.U8 rm? Fi-39.StetehlorPolen 316Properties of a Pure Substance 3.17 For a certain experiment, Freo! tube at 30°C. Icis desired to know the pressure a this condition, but then is no means for measuring it, since the tube is sealed. However, if she tube is eooled to 10°C, small droplets of liquid are observed on the glass wale What is the presture inside at 30°C? 3.18 A tank contains Preon-12 at 35°C, The volume of the tank ix 0.1 m, and ly the volume of the ligu vapor. Additional Freon-l2 is foreed foto the tank unl the mass of Freoa] 12 in the tank reaches 80 kg. What is the final volume of liquid in the ‘ank, assuming that the temperature is maintained at 35°C? How mua) mass enters the tank? 3.19 A rigid vessel of 0.015 m? volume contains 10 kg of water (liquid plu vapor) at 30°C. The vessel is then slowly heated. Will the liquid level inside ‘eventually rise to the top or drop to the bottom of the vessel? What if te vessel contains | kg instead of 10 kg? 3.20 A refrigeration unit of 0.05 m? volume is evacuated and then slowly charged with Freon-12. During this process, the temperature of the Freon-I? remaing constant at the ambient temperature of 25°C. (@) What will be the mass of Freon-12 in the system when the pressure reaches 250 kP.? (6) What will be che mass of Freon-12 in the system when the system Filled with saturated vapor? (0. What fraction of the Freon-12 will exist as a liquid when 5 kg of Freon-12 have been placed in the system? 3.21 Tank d (Fig. 3.14) has a volume of 0.1 ra? and contains Freon-12 at 25%} 10% liquid and 90% vapor by volume, while rank B isevacuated. The vabe| js then opened, and the tanks eventually come to the same pressure, whi} is found to be 200 kPa. During this process, heat is ansferred such tha the Freon remains at 25°C, What is the volume of tank B? Base siento rim. 3.82 A container of liquid nitrogen at 229 kPa pressure has a cross-sectional area of 0.04 m* (Fig. 3.15). As the result of heat wansfer to the liquid nitrogen, some of the nitrogen evaporates and in one hour, the level drops 20 mm, The vapor that leaves the insulated container passes through + 12 vapor is contained in a sealed gla in the tank is equal to the volume of dxf 8.28 Water is contained in a cylinder fitted with a fret Problems 59 Fig.3.18 Sete orPrclem 322. heater and leaves at 200 KPa, 275 K. Calculate the volume rate of flow out fof the heater, assuming ideal gas behavior, and compare this with the result obtained when using the nitrogen tables, Table 4.5, est piston, as shown in Fig. 3.16. The mass of water is 1 kg and the area of the piston is 0.5 m* ‘Ac the initial state the wacer is at 110°C, with a quality of 90%, and che spring just touches the piston, but exerts no force on it, Now, ferred to the water, and the piston bexins o rise, During this process, the resisting force of the spring i proportional to the distance moved. with a force of 10 N/mm, Calculate the pressure in the cylinder when the tem WHO EX Fe. 3.16- Sheth fr Problen328,@0 Properties of a Pure Substance 324 A oiler feed pump delivers 50 kgs of water st $00%C, 20 NPa, What the volume rate of fow in ms? What would be the percent vor i Properties of saturated iid water a 30°C were wed in heat 5.25 Consider compressed liquid water at 40°C. What pressure i requied dzcrease the specie volume by 1% from saturated iu aie? 3.26 One bg of HO exists a the ple point. The value of the liquid ph il the vole of the Sle, he okt the ap pase sequal w 10" times the volurn of thei phage. What the ma ‘of H,0 in each phase? ania 827 A 0.) m tank containing saturated vapor water a 200 kPa it cole “20°C. What percentage, on 3 volume bn of the water isle at 3.28 Compare the specific volume of nitrogen at 6 MPa, 150 K as given if the mirogen tables, AS. wth the value clube fhom the Beate ridgeman equation and with the value caleutated from the ide gas equation of x 5.29 Write a computer program to sive the falling problem, For any spa fed substance, desire to cae the precure according a Beade-drdgnhn enn ste ors sen eo ee ure and specie wltme, ad to compare the esl wih the ea ‘equation of six. * Hei he ea 330 Write a computer program to sole the following problem. For any fe substance es denited to solve the Beauie-Brdgeman equon sete for specie volume any given ctor seu) of pressure nnd temper tutes and compare the esl wih he del ga cquton of ace 4 Work and Heat In this chapter we shall consider work and heat. Itis essential for the student of thermodynamics to understand clearly the definitions of both work and heat, because the correct analysis of many thermodynamic problems depends upon distinguishing between them. 4.1. Definition of Work Work is ustally defined as a force F acting through a displacement x, the displacement being in the direction of the lorce. Thatis, ay “This is very uselial relationship because it enables us to find the work required 10 raise a weight, wo stretch a wire, or w move a charged particle through magnetic held, However, wwhen eating thermodynamics from i macroscopic point of view. it is advantageous t0 tie in the definition of work with the concepts of systems. properties, anid processes. We therefore define work as Follows: work is clone by a system if the sole effect on the sur roundings (everything external to the system) could be the raising of a ‘weight, Notice that the raising of a weight is in effect a force acting, through a distance. Notice, also, that our definition does not state that weight was actually raised, or that a force actually acted through a fiven elistanace but that the sole effect external to the system could be the raising of a weight, Work done Up 2 system is considered positive and62 Work and Heat work done on a system is considered negative. ‘The symbol W designate} the work done by a system. In general, we will speak of work as a form of energy. No attempt wil be made to give a rigorous definition of energy. Rather. since the conf cept is familiar, the term energy will be used as appropriate, and variou forms of energy will be identified. Work is the form of energy thal fulfils the definition given above. Let us illustrate this definition of work with a few examples. Conside as a system the battery and motor of Fig, 4.la and let the motor drived TT ro7To { ‘eg | we PSH] | hale me Prit it | | | sean u FE. 4.1 Example of workone a the boundary ofa syste, fan, Does work cross the boundaty of the system? To answer this ques} ‘ion using the definition of work given above, let the fan be replaced with a pulley and weight arrangement shown in Fig.4.1b. As the motor turns} the weight is raised, and the sole effect external to the system is the rai ing of a weight. Thus, for our original system of Fig. 4.la, we conclude that work is crossing the boundary of the system since the sole effea| ‘external to the system could be the raising of a weight Let the boundaries of the system be changed now to include only the battery shown in Fig. 42. Again we ask the question, does work cross theft boundary of the system? In answering this question, we will bewnswering a more general question; namely, does the flow of electrical energy across the boundary of gpystem constitute work? “The only limiting facior in having the sole external effect the raising of a weight is the inefficiency of the motor. However, as ve design a more efficient motor, with lower bearing and electrial losses, we recogni that we can approach a certain limit, which does meet the requirement of having the only external effect the raising ofa weight. Therefore, we can conclude that when there isa flow of electricity across the boundary of system, as in Fig 4. itis work with which we are concerned ‘Work Done in a Quasiequilibrium Process, aaa) (bound, Lia Fg. 42.Erample of werk crossing the boundary of a system because of a flow of an electric ‘urn! acts he syaten Douay. - — Il Tr T 1 | U fasten} weit 4.2. Units tor Work Asalready noted, we consider work done byasystem, such as that done by a gas expanding aguinst 1 piston as positive, and work done on # system, such as that done by a piston compressing a gas, as neyative, ‘Thus, positive work means that energy leaves the system and negative | work means that energy is added to the system. Our definition of work involves the raising of a weight, that is, the | product of a unit force (one newton) acting through a unit distance (one etre), This unit for work in SI units is called the joule (J) 1J=1Nm Power is the lime vate of doing work, and is designated by the symbol = Mar ‘The unit for power is a rate of work of one joule per second, which is a watt (W), Iw=lJs 4.3, Work Done at the Moving Boundary of a Simple Compressible System in a Quasiequilibrium Process We have already noted that there are a variety of ways in which work ‘ean be done on o by a system. These include work done by # rotating shaft electrical work, and the work done by the movernent of the system boundary, such as the work done in moving the piston in a cylinder. In this section we will consider in some detail the work done at the moving boundary of a simple compressible system during a quasiequilibrium process.64 Workand Heat Work Done ina Quasiequilibrium Process Consider as a system the gas contained in a cylinder and piston, as i Fig 43. Let one of the small weights be removed from the piston, causing the piston to move upward a distanc| dL, We can consider this a quas equilibrium process and calculate the} amount of work W done by the system during this process. The total force oa the piston is Pf, where P is the Shown. At the conclusion of the process the piston iy in position 2. and shown at point 2on the P- diagram. m process, and sed through the states shown by ecting states 1 and 2 on the P-V diagram. The assumption, E siequilibrium process is essential here becitise each point on pressure of the gasand fs the area of represents a definite state, and these states will correspond co the the piston, Therefore, the work 857 if civil state of the system only if the deviation frony equilibrium is inkin- E itesinal. The work done on the air daring this compression process bbe found by integrating Eqat 2 w= [ow=f' par 3) cy ke Fig. 42 Example of work done atthe ‘moving Boundary oto sytem Ih 8 ‘Guneequitoriam process aw = Pott) But sf dl. ~ dV, the change in volume of the gas Therefore, p The syinbol Wis wo be interpreted as the work done cluring the process aw = Pd (4.2)fh from state | 0 state 2. Its clear from examining the P-V diagram that ely. ‘The work done at the moving boundary during a given quasiequilibrium| process can be found by integrating Fq.4.2. However, this integration fiew ‘can be performed only if we know the relationship between P and ¥) ‘ during this process. This relationship might be expressed in the form of ‘an equation, or it might be shown in the form of a graph. Let us consider a graphical solution firs, using as an example a com- pression process such as that which occurs during the compression of ait ina cylinder, Fig, 44. At the beginning of the process the piston is a is represented by the area under the cu * example the volume decieased. und the area o-I-2 ba represents work F done on the system. If the process had proceeded trom state 2 to state 1 B along the same path, the same area would represent work cone by the “gystem, "Further consideration of « P-V diagram, Figel.5, leads to another important conclusion. It is possible to go from state | (0 state 2 along Fig-44 Use o pressure volume diagram to show work dae atthe moving Boundary of» yetomla (SGussequiibau peesas = 65Work and Heat many different quasiequilibrium paths, such as 4. B.or C. underneath each curve represents the work for each process itis evident that the amount of work involved in esch case is a funtion noc only of| the end states of the process, but in addition is dependent on the path that is Followed in going from one statete another. For this reason work, is called a path function, or in mathemstical parlance. BW is am inex, different ‘This leads to a brief consideration of point and path timnetions or, to use another term, exact and inexact differentials. Thermodynanie properties are point functions, a name that zuises from the fact that for a given point on a diagram (such as Pig.t.5) or surface (such as Fix. 3), the state is fixed, and thus there is 2 definite value of each property corresponding tu this point. The differently of point functions are exact differentials, and the integration issimply fearon “Thus, we can speak of the volume in sate 2 and the volume in state, il the change in volume depends orly on the initial and final state. . been indicated, the work done in a quasiequilibrium process between two given states depends on the path followed. The dilfere inexact differentials, and the symbol 8 will be used in this texto desig hate inexact differentials (in contrast te d for exact differentials). Thus, for work we would write faw=, It would be more precise 1@ use the notation GH/:.) which would indicate the work done during the change from state | 102 along path 4. However, implied in the notation ,H isthat the process between states [ sand 2 has been specified. 11 should be noted, we never speak about work in the system in state | or state 2,sand thus we would never write W.-W, ° Example 4.1 Consider as a system the yw contaired in the cylinder shown in 46, which is fited with a piston on which «i number of small weights are placed. The initial pressure is 200 kPa and the initial volume of the gas i 0.04 me Is of path funetions are fe Work Done in @ Quasiequilibrium Process 67 (@)Let a Bunsen burner be placed under the finder, and let the volume of the gas in- crease (0 0.1 m# while the pressue remains Constant. Caleulate the work done by the system during this process, Wy Fig.AG Shetet forEvamoie dl. since presses constant, weconchde from E943, Men Pffar= PU.—P) Wy 0.04) 0 Pa X (0.1 12.0 ky (© Consider the same system and initial conditions, but at the same time that the Bunsen burner is under the cylinder and the piston is | rising, let weights be removed from the piston at sucha rate that, during the process, the relation between pressure and volume is given by the expression PY constant = P,V, =P Let the final volume again be Om We first determine the final pressure. PM 0.04 pA = 200 x 55 so kPa Agin we wse EA tcakult the wok ate [ira Weecan substitute P = constant/ = P,¥,/V/ into this equation. Wry we nf raw't " 2x jn 20 200 kPa 0.04 mt x In Bg = 73 We 4] {0 Consider the same system, but during the hear transfer lee the weights be removed at such a rate thatthe expression PF'3= constant describes the relation between presstire and volame during the process. ‘Again the final volume is 0]. Calculate the workSystems Involving Work ata Moving Boundary 69 68 Work and Heat ‘Some Other Systems Involving Work ata Moving, y Let us first solve this problem for the general case of PV* = constant: PY" = constant = PWV" = PY" pom A a ate [rer ~consan = onson| 2 Vit PY 1 Te/A2Preceure wume dingram showing otk dona inthe vorias uorsseesof Example 4.1 E process. There are other types of systems that involve work at a moving boundary, and in this section we shall briefly consider two such systems, ‘stretched wire and a surface film. ‘Consider as a system stretched wire that is under a given tension 7” E When the length of the wire changes by the amount dL, the work done B ty the system is a Piha =P T=13 ow =- Fat (4.4) 6.41 : z ia negative. This can be integrated to give | (© Consider the system and initial state given inthe firs three examples, | but let the piston be held by a pin so that the volume remains constant. J jjIn addition, let heat be transferred from the system until the pressure ‘drops to 100 kPa. Calculate the work. Since 6H! = PdV for a quasiequilibrium process, the work is zer0 because in this case there is no change in volume. || The process for each of Four examples is shown on the P-V diagram of |} Fig. 4.7, Process 1-2aisa constant-pressure process, and area I~2a-f-e-l represents the work. Similarly, line 1-2) represents the process in whi [PV = constant, Hine 1-2e &e process in which PV" = constant, and line ||-2d represents the constant-volume process. ‘The student. should ‘compare the relative areas under each curve with the numerical results |obrained above. men [ae cas) ‘The integration can be performed either graphically or analytically if the relation between F and L is known. The stretched wire is a simple F example of the type of problem in solid body mechanics that involves the ‘aleulation of work. Example 4.2 ‘A metallic wire of initial length Ly is stretched. Assuming elastic | behavior, cetermine the work done in terms of the modulus of elas and the strain. = Leto stress, ¢= strain, and E iodulus of elasticity. 4.4 Some Other Systems Involving Work at a Moving Boundary In the preceding section we considered the work done at the moving boundary of a simple compressible system during a quasiequilibrium pWork and Heat ‘Systems That Involve Other Modes of Work 7 ‘Therefore systems jrwohing electrical modes of werk. We shall consider a quiasi- ae : 1 process Lor theve systems. and present expressions for the work done during such a process. From the definition of strain, In order to visualize how work cw be accomplished by magnetic ‘effect, let us briefly describe magnetic cooling, or adiabatic demagnet: de tion, which isa process used to produce temperatures well below 1 K. F Atemperature of 1.0K can be produced by pumping a vacuum over bath of liquid helium (helium has the lowest normal boiling point of any substance, namely 4.2K at one atmosphere pressure). An apparatas in netic cooling is accomplished is shown schematically in Fig. 49. The paramagnetic salt is che magnetic substance in which Therefore, BW =-F dL =—StBelgde want ede 289 Terme —~l Now consider a system that consists of a liquid film having a surface f tension 7. A schematic arrangement of such a film is shown in Fig, 48, F ice ane suits hn Bow presse F eee Sehange 6 Paramognei ge 5) oa Fig.4.8Screratic rangement showing wk doneona srace im Mograt where a film is maintained on a wire frame, one side of which can be moved. When the 2rea of the film is changed, for example by sliding the movable wire along the frame, work is done on or by the film, When the area changes by an amount df, the work done by the system is swat “6 vacuum (4.18) HP the shaft, and can be associated with the shearing forces in the rotating = shaft. In Fig, 4.115 the system includes shaft and weight as well zs the given process. Thus we could write and the derivative of a related extensive propert It should also be noted that there are many other forms of work which f canbe identified in processes that are not quasiequilibrium processes. An | example of these is the work done by shearing forces in a process involv- | ing friction in a viscous fluid or the work done by a rotating shaft that J crosses the system boundary. | ‘The identification of work is an important aspect of many thermo- vooum — stem | ound a . > Fig 410 Example ota process imvlving»chengectvolumetor which the works xr + = Fig. A11 expe shoming how loco ofthe system which shows a gas separated from the vacuum by a membrane. Let the membrane rupture and the gas fill the entire volume, Neglecting, any work associated with the rupturing of the membrane, we can ask if there is work involved in the process. If we take as our system the gas and the vacuum space, we readily conclude that there is no work involved. since no work can be identified at the system boundary. If we take the gasasa system we do have a change of volume, and we might be tempted to calculate the work from the integral ‘gas and the container, In this case there is no work crossing the sys: tem boundary as the weight moves downward, As we will see in the nest chapter, we can identify 2 change of potential energy within the system, but this should not be confused with work crossing the system boundary. 4.7. Definition of Heat ‘The thermodynamic definition of heat is somewhat different from the everyday understanding of the word. Therefore, itis essential to under- stand clearly the definition of heat given here, because itis involved in so many thermod ynamic problems. However, ¢ work cannot be calculated from this relation. Rather, since there is no resistance at the system boundary as the volume increases we conclude | that for this system there is no work involved in this process ‘Another example can be cited with the aid of Fig. 4.11. In Fig. 4.114 Definition of Heat 75Comparison of Heat and Work 76 Work and Heat If a block of hot copper is placed in a beaker of cold water, we know. from experience that the block of copper cools down and the water | ‘warms up until the copper and water reach the same temperature. What | ‘causes this decrease in the temperature of the copper and the increase in | the temperature of the water? We say that itis the result of the transfer of energy from the copper block to the water. Iti outof such a transfer: of encrgy that we arrive ata definition of heat Heat is defined as the form of energy that is transferred across the | and is recognized as an inexact differential, Uhatis, the amount of heat transferred when a system undergoes a change of state from state 1 to © state 2 depends on the path thac the system follows during the change of “sate. Since heat isan inexact differential, the dilferental is written 8Q. On imegeating. we write fpa= boundary of a system at a given temperature to another system (or the J id state surroundings) at & lower temperature by virwe of the temperature | which heat is uaunsferreel to a system is designated by the difference between the two systems. That is, heat is transferred from the system at the higher to the system atthe lower temperature, and the heat | wwansfer occurs solely because of the temperature difference between the | two systems. Another aspect of this definition of heats thata body never contains heat, Rather heat can be identified only as it crosés the jie boundary. Tas, heat a nt phenomenon. If we considerthe hot | ‘lod of copper as ‘one system and the cold water in thebeakerasanother | system, we recognize that originally neither system contains any heat | (they do contain energy, of course). When the copper is placed in the water and the (wo are in thermal communication, heat is transferred | from the copper to the water, until equilibrium of temperature is established, At that point we no longer have heat transfer, since there is | no temperature difference. Neither of the systems contain heat at the’ conclusion of the process. It also follows that heat is identified at the J boundary of the system, for heat is defined as energy heing transferred | across the system boundany. o-G Itis also convenient wo spenk of the heat transfer per unit mass of the F system, q, which is defined as : 2 4 4.8. Comparison of Heat and Work At this point itis evidenc that there are 1 and work, and these are summarized here. eransient ph similarities between heat Heat and wor _ Syst ossess boundary when a ‘stem undergoes & change of stare. | 2. Both heat and work are boundary phenomena. Both are observed {the boundaries of the system, and both represent energy ing fe boundary ofthe system. 3. Both heat and work are path functions and inexact differentials. 4.8 Units of Heat As discussed above, heat, like work, isa form of energy transfer to or | from a system. Therefore, the units for heat, and to be more general for | any other form of energy as well, are the same as the units for work, ‘which in the International System has been defined as the joule, Further, heat transferred (0 a system is considered to be positive, and | heat transferred from a system, negative. Thus, positive heat represents. energy transfered to a system, and negative heat represents energy’ twansferred from a system. The symbol Qis usec to represent heat. ‘A process in which there is no heat transfer (Q =O) is called an adiabatic process From i mathematical perspective, heat, like work, i a path function should also be noted that in our sign convention, + Q represents heat | ansferved io the system, and thus is energy added to the system, and | +W vepresents work done by the system and thus represents energy b leaving the system. ‘A final illustration may be helpful to indicate the diflerence between F heat and work. Figure 4.12 shows a gas contained in a rigid vessel. Resis:ance coils are wound avound the outside of the vessel. When F current flows through the resistance coils, the temperature of the gas | increases. Which crosses the boundary of the system, heat or work? n78 Workand Heat Stim Boa cas 7 In Fi energy crosses the boundary of the system be the walls is higher than the temperature of the gis. Therefore, we recognize that heat crosses the boundary of the system, In Fig. 4.128 the system includes the vessel and the resistance heater. Flectrcity crosses the boundary of the system, and as indicated earlier, this is work. PROBLEMS al 42 43 i 412. Anexarpla showing the cterence between nest ard work, 4.124 we consider only the gas as the system. In this case the ise the temperature of Five kilograms of saturated vapor water at 1 MPais contained ina cylinder fied with suvvable piston, This ayatem ia now hosted at constant pressure until dhe temperature of the steam is $00°C. Calculate the work done by the steam during the process One-tenth kilogram of oxygen is contained in a cylinder fitted with piston. The initial conditions are 150 kPa, 20°C. Weights are then added to the piston, and the O, is slowly compressed isothermally unit the final pressure is 500 kPa, Calculate the work done during this process. Consider the system shown in Fig. 4.13. The initial volume inside the cyl der is 0.1 m, At thie state the pressure inside is 100 kPa, which just bal lances the atmospheric pressure outside plus the piston weight: the spring 4 is touching but exerts no force on the piston at chs state. The gas is now. heated until the volume is doubled. The final pressure of the gas is 300 kPa, fof the piston from the initial postion, Ne Fig. 4.19. Seen er Prolem a 3 Problems: (a) Show the process on @ P-V diagram, @) Considering the gas insde as the system, calculate the work done by the system, What percentage of this work is done against the spring? “The eylinder-piston arrangement shown in Fig. 4.14 contains carbon di- ‘ride at 300 bP2, 200°C, at which point the volume is 0.2 m*. Weights are then removed at such a rate that the gas expandls according to the relation PP constant “until the final temperature is 100°C. Determine the work done during this proves. ¥ 0, Fig.4.4 Sketchtor Problem 44 [A balloon which is initially fla is inflated by filing it with air from a tank of compressed air. The final volurne of the balloon is 5 m*. The barometer reads 95 kPa. Consider the tank, the balloon, and che connecting pipe as a system, Determine the work for this process. ‘The cylinder shown in Fig 4.15 contains 1 kg of saturated water at 30°C. The piston hae a cross ectional area of 0.065 mt, a mass of 40 kg, And is resting on the stops as shown, The volume at this point is 0.1m ‘Atmospheric. pressure outside is 94 KPa, and the local gravitational acceleration is 9.75 mst. Heat is now transferred to the system until the ‘ovlinder contains saturated vapor. (a) What isthe temperature of the water when the piston first rises from the stops? (0) Calculate the work done by the water during the overall process. Pan Fig.A1 Shetchor Problem 4680 Work and Heat a7 4a 19 410 “The gas space above the waver in a closed tank contains nitrogen at 25°C, 100 KPa. ‘The tank has a total voluine of 4 m? and contains 500 kg of water at 25°C, An additional 500 ky of water is naw slowly forced ints the tank. Assuming that the temperature remains constant, calculate the final pressure of the Nz. and the work done on the Ns during the proc A spherical balloon hasa diameter of 0.8 m, and contains air ata pressure of 150 kPa. The diameter ofthe balloon increases to 0.4 m due to heating, and during this process the pressure is proportional to the diameter. Ca ‘alae the work done by the air during this process. ‘A spherical balloon having a radius of 10 m is to be filled with helium | from a bank of high pressure gas cylinders that contain helium at 15 MPA. 25°C. The balloon is initially lat, and the atmospheric pressure is 101 kPa] (a) How much work is done against the atmosphere as the balloon i inflated? Assume no stretching of the material {rom which the balloon is made and that the pressure in the balloon is essentially equal tothe atmos: pheric pressure, (©) What is the required volume of the high pressure cylinders, if the final pressure in the cylinders is the same as that in the balloon? 4 Ammonia is compressed in 2 eylinder by a piston. The inital temperature, is 80°C, the initial pressure is 500 KPa, and the final pressure is 1400 KPa! ‘The following data are available for this process: Pressure, kPa Volume, 500 135 650 08, 800 0.96 350 084 1100 on 1350. 0.60 1400 0.50 (4, Determine the work for the process considering the ammonia ae the system. (0) What isthe final temperature of the ammonia? Ina rocket, abotde of helium gasis used to maintain a constant pressure! 4.1 Mv on uid oxygen sw the engine pump, The pressure (4) Calculate the work done by the helium during this process. (8) Determine the required volume of the helium bowe saat Tea oe Q) 00 toe ‘Twwottie SOT MPa at 0.1 MPS ours “one ‘tian "eps se such or Paton “4.12 Sawuraed water vapor at 200°C: is eon Problems iv a cjlinder fitted with a piston. The initial volume of the steam is 0.01 mt. The steam then expands in-a quasiequilibrium isothermal process uncil the Final pressure is 200 kPa and in s0 doing does work against the piston. ine the work done during this proces. ich error would be made by assuming the steam to behave as an ideal gas? and contains argon at 260 kPa, 30°C. Cyl der B containsa frictionless piston of a ase such thata pressure of 150 kPa inside the cMinder required to raise the piston, The valve connecting the two is now opened. allowing argon to flow into the cylinder. Ever tually, the argon is at a uniform state of 80°C, 150 kPa throughout. Calculate the work done by the argon during the process. stops on the olinder-walls such that the contained volume is 0.08 m*. The mass of the piston is such that 300 kPa pressure is required to raise the piston against atmospheric pressure, When the piston has moved to i point where the contained volume is 0.075 m?, the piston encounters linear spring that requires 360 kN to deflect it 1 mi. Initially the cylinder contains 4 hg of saturated («wo-phase) water at 35°C, The final pres- sure is 7 MPs, Determine the final state of the HO and the work done during the process Meee i @ Fig 4.18. Shetchfor Problem 4.14 a82 Work and Heat 4 Problems (415 A vertical eyinder fired with a piston contains 008 mB Fennel? at 96° piled in tension in a ten land a quality of 90%. The piston has mass of 90 ly, cose sectional rea sil teting machine. How much work is required to produce a strain of ‘of 0,006 mi, and is held in place by a pin, as shown in Fig. 4.19. The fof 0.1%? The modulus of clastkity of steel is 200 GN/an. ambient pressure is 100 kPa. 4.18 A sealed vessel having the shape of a rectangular prism with the area of the base of and height Ly and of negligible mass is initally floating on a liquid of density p, Fig. 421, Derive an expression in terms of the give ‘mosphere posara Pa ea Inia positon Freon-12 Fe4.19. Sketch for Problem 4.15, ‘The pin is now removed, all time, the system cornes to equilibrium, with the final temperature being 25, (a) Determine the final pressure and volume of the Freon-12. Fig. 4.21 Sketch for Problem 4.18, () Calculate the work done by the Freon-12 during this process and ff variable forthe work requted to move the vessel tthe boom ofa very xpleia whet this work is dane againet: | large tank in which depth ofthe liqui 4.18 The epinder indicated in Fig. 4208 fied with piston which restrained f° 4.19 Repeat Problem 4.18 assuming thatthe sealed tank has a mass m. by spring co arranged that for zero volume in the cylinder the pring ® 4 99 ax 20°C ethanol has a surface tension of 22.5 mN/m. Suppose that 2 fim of eshanol is maintained on the wire frame as shown in Fig. 4.22. one ‘i side of which can be moved. The original dimensions ofthe wire frame ‘cylandes fe 0.12 mi when the piston encounters be aigyg: The cylindet cag {res show Determine the work done (consider the fla tobe the system), tains 4 kg of water iialy t 350 KPa, 1% quality and the water isthe Corte hd cooley ‘neated unlit exists 2s eaturated vapor. Show the process on a P-V dlagran fe Zi GH: 0 ig.422- Sketch or Poti 4.20, F420. StatchforProsiem 4.16. 21 A storage battery is well insulated (thermally) while iis being charged. The which includes the sautration region and determine: charging voltage is 12.3 V (volt) and thecurrent is 24.0 A (amperes). Con- (a) The final pressure. Fe sidering the storage bauery as the system, what are the heat transfer and () The work ‘work in a 15-minute period?8 Workand Heat 422 A room is heated with steam radiators ona winter day. Examine thefollow- EB ingsystems regarding heat transfer (including sig: ; ‘a) The radiata 6) The room, ties + The First Law eee f Thermodynamics ") The combustion chamber and combustion gus side of the hese trans: fev area. () The furnace asa whole i chine) 424 Write a computer program to sov the following problem. Determine the 4 boundary movement work for a specified gas undergoing an isothermal | provess at temperature T from % 10 vs using the Beattie Bridger : tion of state, and compare the result with that found assuming ideal gas behavior q 42% Write 2 computer program (0 solve the following problem. Determine 4 the boundary movement work for a specified substance undergoing 3 process, given a st of data (values of pressure and corresponding volume he 4 foodies 4 ‘uring the process). FB _Having completed our consideration of basic definitions and concepts | we are ready to proceed to a discussion of the first law of thermo dynamics. Often this law is called the law of the conservation of energy, | and as we shall see later, this is essentially true, Our procedure will be to _ State this law frst for a system undergoing a cycle, and then for a change Of state of a system. Finally the first law of thermodynamics will be Applied to a control volume. The law of the conservation of matter will also be considered in this chapter, luding the hot and cold air ducts and 5:1 The First Law of Thermodynamics for a System Undergoing a Cycle The first law of thermodynamics Wy eyele at system Kes thar during the oyclc integral of the heat is proportional to the cycle fhe work To illusirite this law, consider as a system the gus in the container E shown in Fig. 5.1. Le this system go through a cycle that is comprised of | 19 processes. In the frst process work is done on the system by the D paddle that turns as the weight is lowered. Let the system then be ned to its initial state by transferring heat from the system util the Gyele has been completed. Historically, work was measured in mechani stance, as for example foot-pounds force or jules, while measure. © ients of heat were made in thermal units, such'as the British ‘Thermal Sit or the calorie, Measurements of work and heat were made during I units of force times