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cen84959_ch03.qxd 4/1/05 12:31 PM Page 154 154 | Thermodynamics REFERENCES AND SUGGESTED READINGS 1. ASHRAE Handbook of Fundamentals. SI version. Atlanta, GA: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc., 1993. 2. ASHRAE Handbook of Refrigeration. SI version. Atlanta, GA: American Society of Heating, Refrigerating, and AirConditioning Engineers, Inc., 1994. 3. A. Bejan. Advanced Engineering Thermodynamics. 2nd ed. New York: Wiley, 1997. 4. M. Kostic. Analysis of Enthalpy Approximation for Compressed Liquid Water. IMECE 2004, ASME Proceedings, ASME, New York, 2004. PROBLEMS* Pure Substances, Phase-Change Processes, Property Diagrams 3–12C How does the boiling process at supercritical pressures differ from the boiling process at subcritical pressures? 3–1C Is iced water a pure substance? Why? Property Tables 3–2C What is the difference between saturated liquid and compressed liquid? 3–13C In what kind of pot will a given volume of water boil at a higher temperature: a tall and narrow one or a short and wide one? Explain. 3–3C What is the difference between saturated vapor and superheated vapor? 3–4C Is there any difference between the intensive properties of saturated vapor at a given temperature and the vapor of a saturated mixture at the same temperature? 3–5C Is there any difference between the intensive properties of saturated liquid at a given temperature and the liquid of a saturated mixture at the same temperature? 3–6C Is it true that water boils at higher temperatures at higher pressures? Explain. 3–7C If the pressure of a substance is increased during a boiling process, will the temperature also increase or will it remain constant? Why? 3–8C Why are the temperature and pressure dependent properties in the saturated mixture region? 3–9C What is the difference between the critical point and the triple point? 3–10C Is it possible to have water vapor at !10°C? 3–11C A househusband is cooking beef stew for his family in a pan that is (a) uncovered, (b) covered with a light lid, and (c) covered with a heavy lid. For which case will the cooking time be the shortest? Why? *Problems designated by a “C” are concept questions, and students are encouraged to answer them all. Problems designated by an “E” are in English units, and the SI users can ignore them. Problems with a CD-EES icon are solved using EES, and complete solutions together with parametric studies are included on the enclosed DVD. Problems with a computer-EES icon are comprehensive in nature, and are intended to be solved with a computer, preferably using the EES software that accompanies this text. 3–14C A perfectly fitting pot and its lid often stick after cooking, and it becomes very difficult to open the lid when the pot cools down. Explain why this happens and what you would do to open the lid. 3–15C It is well known that warm air in a cooler environment rises. Now consider a warm mixture of air and gasoline on top of an open gasoline can. Do you think this gas mixture will rise in a cooler environment? 3–16C In 1775, Dr. William Cullen made ice in Scotland by evacuating the air in a water tank. Explain how that device works, and discuss how the process can be made more efficient. 3–17C Does the amount of heat absorbed as 1 kg of saturated liquid water boils at 100°C have to be equal to the amount of heat released as 1 kg of saturated water vapor condenses at 100°C? 3–18C Does the reference point selected for the properties of a substance have any effect on thermodynamic analysis? Why? 3–19C What is the physical significance of hfg? Can it be obtained from a knowledge of hf and hg? How? 3–20C Is it true that it takes more energy to vaporize 1 kg of saturated liquid water at 100°C than it would at 120°C? 3–21C What is quality? Does it have any meaning in the superheated vapor region? 3–22C Which process requires more energy: completely vaporizing 1 kg of saturated liquid water at 1 atm pressure or completely vaporizing 1 kg of saturated liquid water at 8 atm pressure? 3–23C Does hfg change with pressure? How? cen84959_ch03.qxd 4/1/05 12:31 PM Page 155 Chapter 3 3–24C Can quality be expressed as the ratio of the volume occupied by the vapor phase to the total volume? Explain. 3–25C In the absence of compressed liquid tables, how is the specific volume of a compressed liquid at a given P and T determined? 3–26 Complete this table for H2O: 3–33E Complete this table for refrigerant-134a: T, °F P, psia 80 15 10 h, Btu/lbm P, kPa 50 250 110 v, m3/kg Phase description 4.16 200 400 600 Saturated vapor 3–27 Reconsider Prob. 3–26. Using EES (or other) software, determine the missing properties of water. Repeat the solution for refrigerant-134a, refrigerant22, and ammonia. 3–34 T, °C 3–35 T, °C 3–28E Complete this table for H2O: 129.46 T, °F P, psia 300 500 400 u, Btu/lbm Phase description 782 40 120 400 Saturated liquid 3–29E Reconsider Prob. 3–28E. Using EES (or other) software, determine the missing properties of water. Repeat the solution for refrigerant-134a, refrigerant22, and ammonia. 3–30 T, °C P, kPa h, kJ/kg 200 x Phase description 0.7 950 500 800 T, °C P, kPa !8 30 320 v, 0.05 550 750 Saturated liquid 0.140 Complete this table for H2O: P, kPa u, kJ/kg Phase description 1450 Saturated vapor 2500 4000 3040 3–36 A 1.8-m3 rigid tank contains steam at 220°C. Onethird of the volume is in the liquid phase and the rest is in the vapor form. Determine (a) the pressure of the steam, (b) the quality of the saturated mixture, and (c) the density of the mixture. Steam 1.8 m3 220°C Phase description 3–37 A piston–cylinder device contains 0.85 kg of refrigerant134a at !10°C. The piston that is free to move has a mass of 12 kg and a diameter of 25 cm. The local atmospheric pressure is 88 kPa. Now, heat is transferred to refrigerant-134a 0.015 180 600 Saturated vapor Complete this table for refrigerant-134a: P, kPa 20 !12 8 Phase description FIGURE P3–36 3162.2 m3/kg T, °C v, m3/kg 0.0 Complete this table for refrigerant-134a: 3–32 P, kPa 1800 3–31 80 Complete this table for H2O: Complete this table for H2O: 140 80 1.0 400 220 190 Phase description 0.6 70 180 140 125 500 155 78 110 T, °C x | u, kJ/kg Phase description 95 Q R-134a 0.85 kg –10°C Saturated liquid 400 600 300 FIGURE P3–37 cen84959_ch03.qxd 4/1/05 12:31 PM Page 156 156 | Thermodynamics until the temperature is 15°C. Determine (a) the final pressure, (b) the change in the volume of the cylinder, and (c) the change in the enthalpy of the refrigerant-134a. 60 percent of the heat generated by the burner is transferred to the water during boiling, determine the rate of evaporation of water. 3–38E The temperature in a pressure cooker during cooking at sea level is measured to be 250°F. Determine the absolute pressure inside the cooker in psia and in atm. Would you modify your answer if the place were at a higher elevation? 3–42 Repeat Prob. 3–41 for a location at an elevation of 1500 m where the atmospheric pressure is 84.5 kPa and thus the boiling temperature of water is 95°C. 3–43 Water is boiled at 1 atm pressure in a 25-cm-internaldiameter stainless steel pan on an electric range. If it is observed that the water level in the pan drops by 10 cm in 45 min, determine the rate of heat transfer to the pan. 3–44 Repeat Prob. 3–43 for a location at 2000-m elevation where the standard atmospheric pressure is 79.5 kPa. Pressure cooker 250°F 3–45 Saturated steam coming off the turbine of a steam power plant at 30°C condenses on the outside of a 3-cmouter-diameter, 35-m-long tube at a rate of 45 kg/h. Determine the rate of heat transfer from the steam to the cooling water flowing through the pipe. FIGURE P3–38E 3–39E The atmospheric pressure at a location is usually specified at standard conditions, but it changes with the weather conditions. As the weather forecasters frequently state, the atmospheric pressure drops during stormy weather and it rises during clear and sunny days. If the pressure difference between the two extreme conditions is given to be 0.3 in of mercury, determine how much the boiling temperatures of water will vary as the weather changes from one extreme to the other. 3–40 A person cooks a meal in a 30-cm-diameter pot that is covered with a well-fitting lid and lets the food cool to the room temperature of 20°C. The total mass of the food and the pot is 8 kg. Now the person tries to open the pan by lifting the lid up. Assuming no air has leaked into the pan during cooling, determine if the lid will open or the pan will move up together with the lid. 3–46 The average atmospheric pressure in Denver (elevation " 1610 m) is 83.4 kPa. Determine the temperature at which water in an uncovered pan boils in Denver. Answer: 94.6°C. 3–47 Water in a 5-cm-deep pan is observed to boil at 98°C. At what temperature will the water in a 40-cm-deep pan boil? Assume both pans are full of water. 3–48 A cooking pan whose inner diameter is 20 cm is filled with water and covered with a 4-kg lid. If the local atmospheric pressure is 101 kPa, determine the temperature at which the water starts boiling when it is heated. Answer: 100.2°C Patm = 101 kPa m lid = 4 kg 3–41 Water is to be boiled at sea level in a 30-cm-diameter stainless steel pan placed on top of a 3–kW electric burner. If H2O Vapor FIGURE P3–48 3–49 Reconsider Prob. 3–48. Using EES (or other) software, investigate the effect of the mass of the lid on the boiling temperature of water in the pan. Let the mass vary from 1 kg to 10 kg. Plot the boiling temperature against the mass of the lid, and discuss the results. 60% 3 kW FIGURE P3–41 40% 3–50 Water is being heated in a vertical piston–cylinder device. The piston has a mass of 20 kg and a cross-sectional area of 100 cm2. If the local atmospheric pressure is 100 kPa, determine the temperature at which the water starts boiling. cen84959_ch03.qxd 4/1/05 12:31 PM Page 157 Chapter 3 3–51 A rigid tank with a volume of 2.5 m3 contains 15 kg of saturated liquid–vapor mixture of water at 75°C. Now the water is slowly heated. Determine the temperature at which the liquid in the tank is completely vaporized. Also, show the process on a T-v diagram with respect to saturation lines. Answer: 187.0°C 3–52 A rigid vessel contains 2 kg of refrigerant-134a at 800 kPa and 120°C. Determine the volume of the vessel and the total internal energy. Answers: 0.0753 m3, 655.7 kJ 3–53E A 5-ft3 rigid tank contains 5 lbm of water at 20 psia. Determine (a) the temperature, (b) the total enthalpy, and (c) the mass of each phase of water. 3–54 A 0.5-m3 vessel contains 10 kg of refrigerant-134a at !20°C. Determine (a) the pressure, (b) the total internal energy, and (c) the volume occupied by the liquid phase. Answers: (a) 132.82 kPa, (b) 904.2 kJ, (c) 0.00489 m3 3–55 A piston–cylinder device contains 0.1 m3 of liquid water and 0.9 m3 of water vapor in equilibrium at 800 kPa. Heat is transferred at constant pressure until the temperature reaches 350°C. (a) (b) (c) (d) What is the initial temperature of the water? Determine the total mass of the water. Calculate the final volume. Show the process on a P-v diagram with respect to saturation lines. | 157 3–58E Reconsider Prob. 3–57E. Using EES (or other) software, investigate the effect of initial pressure on the quality of water at the final state. Let the pressure vary from 100 psi to 300 psi. Plot the quality against initial pressure, and discuss the results. Also, show the process in Prob. 3–57E on a T-v diagram using the property plot feature of EES. 3–59 A piston–cylinder device initially contains 50 L of liquid water at 40°C and 200 kPa. Heat is transferred to the water at constant pressure until the entire liquid is vaporized. (a) (b) (c) (d) What is the mass of the water? What is the final temperature? Determine the total enthalpy change. Show the process on a T-v diagram with respect to saturation lines. Answers: (a) 49.61 kg, (b) 120.21°C, (c) 125,943 kJ 3–60 A 0.3-m3 rigid vessel initially contains saturated liquid– vapor mixture of water at 150°C. The water is now heated until it reaches the critical state. Determine the mass of the liquid water and the volume occupied by the liquid at the initial state. Answers: 96.10 kg, 0.105 m3 3–61 Determine the specific volume, internal energy, and enthalpy of compressed liquid water at 100°C and 15 MPa using the saturated liquid approximation. Compare these values to the ones obtained from the compressed liquid tables. 3–62 H 2O P = 800 kPa Reconsider Prob. 3–61. Using EES (or other) software, determine the indicated properties of compressed liquid, and compare them to those obtained using the saturated liquid approximation. 3–63E A 15-ft3 rigid tank contains a saturated mixture of refrigerant-134a at 50 psia. If the saturated liquid occupies 20 percent of the volume, determine the quality and the total mass of the refrigerant in the tank. 3–64 A piston–cylinder device contains 0.8 kg of steam at 300°C and 1 MPa. Steam is cooled at constant pressure until one-half of the mass condenses. FIGURE P3–55 3–56 Reconsider Prob. 3–55. Using EES (or other) software, investigate the effect of pressure on the total mass of water in the tank. Let the pressure vary from 0.1 MPa to 1 MPa. Plot the total mass of water against pressure, and discuss the results. Also, show the process in Prob. 3–55 on a P-v diagram using the property plot feature of EES. 3–57E Superheated water vapor at 180 psia and 500°F is allowed to cool at constant volume until the temperature drops to 250°F. At the final state, determine (a) the pressure, (b) the quality, and (c) the enthalpy. Also, show the process on a T-v diagram with respect to saturation lines. Answers: (a) 29.84 psia, (b) 0.219, (c) 426.0 Btu/lbm (a) Show the process on a T-v diagram. (b) Find the final temperature. (c) Determine the volume change. 3–65 A rigid tank contains water vapor at 250°C and an unknown pressure. When the tank is cooled to 150°C, the vapor starts condensing. Estimate the initial pressure in the tank. Answer: 0.60 MPa 3–66 Water is boiled in a pan covered with a poorly fitting lid at a specified location. Heat is supplied to the pan by a 2-kW resistance heater. The amount of water in the pan is observed to decrease by 1.19 kg in 30 minutes. If it is estimated that 75 percent of electricity consumed by the heater is transferred to the water as heat, determine the local atmospheric pressure in that location. Answer: 85.4 kPa Problems: Developing Engineering Skills ! apply the incompressible substance model. ! use the generalized compressibility chart to relate p–v–T data of gases. 115 is warranted, and appropriately using ideal gas table data or constant specific heat data to determine $u and $h. ! apply the ideal gas model for thermodynamic analysis, including determining when use of the ideal gas model Key Engineering Concepts state principle p. 69 simple compressible system p. 69 p–v–T surface p. 70 phase diagram p. 72 saturation temperature p. 73 saturation pressure p. 73 p–v diagram p. 73 T–v diagram p. 73 two-phase, liquid–vapor mixture p. 75 quality p. 75 superheated vapor p. 75 enthalpy p. 83 specific heats p. 91 ideal gas model p. 100 Exercises: Things Engineers Think About 1. Why does food cook more quickly in a pressure cooker than in water boiling in an open container? 2. If water contracted on freezing, what implications might this have for aquatic life? 3. Why do frozen water pipes tend to burst? 4. Referring to a phase diagram, explain why a film of liquid water forms under the blade of an ice skate. 5. Can water at !40"C exist as a vapor? As a liquid? 6. What would be the general appearance of constant-volume lines in the vapor and liquid regions of the phase diagram? 7. Are the pressures listed in the tables in the Appendix absolute pressures or gage pressures? 8. The specific internal energy is arbitrarily set to zero in Table A-2 for saturated liquid water at 0.01"C. If the reference value for u at this reference state were specified differently, would there be any significant effect on thermodynamic analyses using u and h? 9. For liquid water at 20"C and 1.0 MPa, what percent difference would there be if its specific enthalpy were evaluated using Eq. 3.14 instead of Eq. 3.13? 10. For a system consisting of 1 kg of a two-phase, liquid–vapor mixture in equilibrium at a known temperature T and specific volume v, can the mass, in kg, of each phase be determined? Repeat for a three-phase, solid–liquid–vapor mixture in equilibrium at T, v. 11. By inspection of Fig. 3.9, what are the values of cp for water at 500"C and pressures equal to 40 MPa, 20 MPa, 10 MPa, and 1 MPa? Is the ideal gas model appropriate at any of these states? 12. Devise a simple experiment to determine the specific heat, cp, of liquid water at atmospheric pressure and room temperature. 13. If a block of aluminum and a block of steel having equal volumes each received the same energy input by heat transfer, which block would experience the greater temperature increase? 14. Under what circumstances is the following statement correct? Equal molar amounts of two different gases at the same temperature, placed in containers of equal volume, have the same pressure. 15. Estimate the mass of air contained in a bicycle tire. 16. Specific internal energy and enthalpy data for water vapor are provided in two tables: Tables A-4 and A-23. When would Table A-23 be used? Problems: Developing Engineering Skills Using p–v–T Data 3.1 Determine the phase or phases in a system consisting of H2O at the following conditions and sketch p–v and T–v diagrams showing the location of each state. (a) p # 5 bar, T # 151.9"C. (b) p # 5 bar, T # 200"C. (c) T # 200"C, p # 2.5 MPa. (d) T # 160"C, p # 4.8 bar. (e) T # !12"C, p # 1 bar. 3.2 Plot the pressure–temperature relationship for two-phase liquid–vapor mixtures of water from the triple point temperature to the critical point temperature. Use a logarithmic scale for pressure, in bar, and a linear scale for temperature, in "C. 116 Chapter 3 Evaluating Properties 3.3 For H2O, plot the following on a p–v diagram drawn to scale on log–log coordinates: the final mass of vapor in the tank, in kg, and the final pressure, in bar. (a) the saturated liquid and saturated vapor lines from the triple point to the critical point, with pressure in MPa and specific volume in m3/kg. (b) lines of constant temperature at 100 and 300!C. 3.15 Two thousand kg of water, initially a saturated liquid at 150!C, is heated in a closed, rigid tank to a final state where the pressure is 2.5 MPa. Determine the final temperature, in !C, the volume of the tank, in m3, and sketch the process on T–v and p–v diagrams. 3.4 Plot the pressure–temperature relationship for two-phase liquid–vapor mixtures of (a) Refrigerant 134a, (b) ammonia, (c) Refrigerant 22 from a temperature of "40 to 100!C, with pressure in kPa and temperature in !C. Use a logarithmic scale for pressure and a linear scale for temperature. 3.5 Determine the quality of a two-phase liquid–vapor mixture of (a) H2O at 20!C with a specific volume of 20 m3/kg. (b) Propane at 15 bar with a specific volume of 0.02997 m3/kg. (c) Refrigerant 134a at 60!C with a specific volume of 0.001 m3/kg. (d) Ammonia at 1 MPa with a specific volume of 0.1 m3/kg. 3.6 For H2O, plot the following on a p–v diagram drawn to scale on log–log coordinates: (a) the saturated liquid and saturated vapor lines from the triple point to the critical point, with pressure in KPa and specific volume in m3/kg 150!C (b) lines of constant temperature at 300 and 560!C. 3.7 Two kg of a two-phase, liquid–vapor mixture of carbon dioxide (CO2) exists at "40!C in a 0.05 m3 tank. Determine the quality of the mixture, if the values of specific volume for saturated liquid and saturated vapor CO2 at "40!C are vf # 0.896 $ 10"3 m3/kg and vg # 3.824 $ 10"2 m3/kg, respectively. 3.8 Determine the mass, in kg, of 0.1 m3 of Refrigerant 134a at 4 bar, 100!C. 3.9 A closed vessel with a volume of 0.018 m3 contains 1.2 kg of Refrigerant 22 at 10 bar. Determine the temperature, in !C. 3.10 Calculate the mass, in kg, of 1 m3 of a two-phase liquid– vapor mixture of Refrigerant 22 at 1 bar with a quality of 75%. 3.11 A two-phase liquid–vapor mixture of a substance has a pressure of 150 bar and occupies a volume of 0.2 m3. The masses of saturated liquid and vapor present are 3.8 kg and 4.2 kg, respectively. Determine the mixture specific volume in m3/kg. 3.12 Ammonia is stored in a tank with a volume of 0.21 m3. Determine the mass, in kg, assuming saturated liquid at 20!C. What is the pressure, in kPa? 3.13 A storage tank in a refrigeration system has a volume of 0.006 m3 and contains a two-phase liquid–vapor mixture of Refrigerant 134a at 180 kPa. Plot the total mass of refrigerant, in kg, contained in the tank and the corresponding fractions of the total volume occupied by saturated liquid and saturated vapor, respectively, as functions of quality. 3.14 Water is contained in a closed, rigid, 0.2 m3 tank at an initial pressure of 5 bar and a quality of 50%. Heat transfer occurs until the tank contains only saturated vapor. Determine 3.16 Steam is contained in a closed rigid container with a volume of 1 m3. Initially, the pressure and temperature of the steam are 7 bar and 500!C, respectively. The temperature drops as a result of heat transfer to the surroundings. Determine the temperature at which condensation first occurs, in !C, and the fraction of the total mass that has condensed when the pressure reaches 0.5 bar. What is the volume, in m3, occupied by saturated liquid at the final state? 3.17 Water vapor is heated in a closed, rigid tank from saturated vapor at 160!C to a final temperature of 400!C. Determine the initial and final pressures, in bar, and sketch the process on T–v and p–v diagrams. 3.18 Ammonia undergoes an isothermal process from an initial state at T1 # 80!F and v1 # 10 ft3/lb to saturated vapor. Determine the initial and final pressures, in lbf/in.2, and sketch the process on T–v and p–v diagrams. 3.19 A two-phase liquid–vapor mixture of H2O is initially at a pressure of 30 bar. If on heating at fixed volume, the critical point is attained, determine the quality at the initial state. 3.20 Ammonia undergoes a constant-pressure process at 2.5 bar from T1 # 30!C to saturated vapor. Determine the work for the process, in kJ per kg of refrigerant. 3.21 Water vapor in a piston–cylinder assembly is heated at a constant temperature of 204!C from saturated vapor to a pressure of .7 MPa. Determine the work, in kJ per kg of water vapor, by using IT. 3.22 2 kg mass of ammonia, initially at p1 # 7 bars and T1 # 180!C, undergo a constant-pressure process to a final state where the quality is 85%. Determine the work for the process, kJ. 3.23 Water vapor initially at 10 bar and 400!C is contained within a piston–cylinder assembly. The water is cooled at constant volume until its temperature is 150!C. The water is then condensed isothermally to saturated liquid. For the water as the system, evaluate the work, in kJ/kg. 3.24 Two kilograms of Refrigerant 22 undergo a process for which the pressure–volume relation is pv1.05 # constant. The initial state of the refrigerant is fixed by p1 # 2 bar, T1 # "20!C, and the final pressure is p2 # 10 bar. Calculate the work for the process, in kJ. 3.25 Refrigerant 134a in a piston–cylinder assembly undergoes a process for which the pressure–volume relation is pv1.058 # constant. At the initial state, p1 # 200 kPa, T1 # "10!C. The final temperature is T2 # 50!C. Determine the final pressure, in kPa, and the work for the process, in kJ per kg of refrigerant. Problems: Developing Engineering Skills Using u–h Data 3.26 Using the tables for water, determine the specified property data at the indicated states. Check the results using IT. In each case, locate the state by hand on sketches of the p–v and T–v diagrams. (a) (b) (c) (d) (e) (f) (g) (h) At p ! 3 bar, T ! 240"C, find v in m3/kg and u in kJ/kg. At p ! 3 bar, v ! 0.5 m3/kg, find T in "C and u in kJ/kg. At T ! 400"C, p ! 10 bar, find v in m3/kg and h in kJ/kg. At T ! 320"C, v ! 0.03 m3/kg, find p in MPa and u in kJ/kg. At p ! 28 MPa, T ! 520"C, find v in m3/kg and h in kJ/kg. At T ! 100"C, x ! 60%, find p in bar and v in m3/kg. At T ! 10"C, v ! 100 m3/kg, find p in kPa and h in kJ/kg. At p ! 4 MPa, T ! 160"C, find v in m3/kg and u in kJ/kg. 3.27 Determine the values of the specified properties at each of the following conditions. (a) For Refrigerant 134a at T ! 60"C and v ! 0.072 m3/kg, determine p in kPa and h in kJ/kg. (b) For ammonia at p ! 8 bar and v ! 0.005 m3/kg, determine T in "C and u in kJ/kg. (c) For Refrigerant 22 at T ! #10"C and u ! 200 kJ/kg, determine p in bar and v in m3/kg. 3.28 A quantity of water is at 15 MPa and 100"C. Evaluate the specific volume, in m3/kg, and the specific enthalpy, in kJ/kg, using (a) data from Table A-5. (b) saturated liquid data from Table A-2. 3.29 Plot versus pressure the percent changes in specific volume, specific internal energy, and specific enthalpy for water at 20"C from the saturated liquid state to the state where the pressure is 300 bar. Based on the resulting plots, discuss the implications regarding approximating compressed liquid properties using saturated liquid properties at 20"C, as discussed in Sec. 3.3.6. 3.30 Evaluate the specific volume, in m3/kg, and the specific enthalpy, in kJ/kg, of ammonia at 20"C and 1.0 MPa. 3.31 Evaluate the specific volume, in m3/kg, and the specific enthalpy, in kJ/kg, of propane at 800 kPa and 0"C. 117 8 bar to 50"C. For the refrigerant, determine the work and heat transfer, per unit mass, each in kJ/kg. Changes in kinetic and potential energy are negligible. 3.35 Saturated liquid water contained in a closed, rigid tank is cooled to a final state where the temperature is 50"C and the masses of saturated vapor and liquid present are 0.03 and 1999.97 kg, respectively. Determine the heat transfer for the process, in kJ. 3.36 Refrigerant 134a undergoes a process for which the pressure–volume relation is pvn ! constant. The initial and final states of the refrigerant are fixed by p1 ! 200 kPa, T1 ! #10"C and p2 ! 1000 kPa, T2 ! 50"C, respectively. Calculate the work and heat transfer for the process, each in kJ per kg of refrigerant. 3.37 A piston–cylinder assembly contains a two-phase liquid–vapor mixture of Refrigerant 22 initially at 24"C with a quality of 95%. Expansion occurs to a state where the pressure is 1 bar. During the process the pressure and specific volume are related by pv ! constant. For the refrigerant, determine the work and heat transfer per unit mass, each in kJ/kg. 3.38 Five kilograms of water, initially a saturated vapor at 100 kPa, are cooled to saturated liquid while the pressure is maintained constant. Determine the work and heat transfer for the process, each in kJ. Show that the heat transfer equals the change in enthalpy of the water in this case. 3.39 One kilogram of saturated solid water at the triple point is heated to saturated liquid while the pressure is maintained constant. Determine the work and the heat transfer for the process, each in kJ. Show that the heat transfer equals the change in enthalpy of the water in this case. 3.40 A two-phase liquid–vapor mixture of H2O with an initial quality of 25% is contained in a piston–cylinder assembly as shown in Fig. P3.40. The mass of the piston is 40 kg, and its diameter is 10 cm. The atmospheric pressure of the surroundings is 1 bar. The initial and final positions of the piston are shown on the diagram. As the water is heated, the pressure inside the cylinder remains constant until the piston hits the stops. Heat transfer to the water continues until its pressure is patm = 100 kPa Applying the Energy Balance 3.32 A closed, rigid tank contains 2 kg of water initially at 80"C and a quality of 0.6. Heat transfer occurs until the tank contains only saturated vapor. Kinetic and potential energy effects are negligible. For the water as the system, determine the amount of energy transfer by heat, in kJ. 3.33 A two-phase liquid–vapor mixture of H2O, initially at 1.0 MPa with a quality of 90%, is contained in a rigid, wellinsulated tank. The mass of H2O is 2 kg. An electric resistance heater in the tank transfers energy to the water at a constant rate of 60 W for 1.95 h. Determine the final temperature of the water in the tank, in "C. 3.34 Refrigerant 134a vapor in a piston–cylinder assembly undergoes a constant-pressure process from saturated vapor at 4.5 cm 1 cm Q Diameter = 10 cm Mass = 40 kg Initial quality x1 = 25% ! Figure P3.40 Answer to Selected Problems 1.10 2551 1.11 9.5, 98.1 1.13 6.131 1.14 3.92, 0.125 1.16 29.62 1.18 68.67 1.21 (a) 1.33, 0.67 1.26 (a) 0.2, 2.67 1.27 58 (vacuum) 1.28 decreases 1.29 A: 2.68, B: 1.28 1.30 0.8 1.32 1.893 Mpa, 14.73 1.40 71.6 1.41 !33.33, 166.67, 1.5 1.42 no 2.2 97.8 (c) subcooled (compressed) liquid, (d) superheated vapor, (e) solid 2.3 !4800 2.4 (a) 56,520, 489,000 (b) 162.8 2.6 210 kJ 4 2.7 (b) 32.57 " 10 , 91.4 (c) 0.5 m, 53.01 2.16 0.02 4.25 25 bars 4.28 10,400 4.31 !14.08 kW 4.32 !0.14 15.98 3.8 1.36 3.9 23.4 3.10 6.189 4.36 3.11 0.025 4.40 56.1 3.14 0.188, 10.5 4.42 3.16 140, 0.8520, 0.002 (a) 3.673 kg/min (b) 615.3 kJ/min 3.18 33.86, 153.13 4.46 18 3.19 0.0296 4.53 54.7 3.24 !73.4 4.61 143.5 3.27 10.4, !32.31 4.64 (a) 47.4 kg 4.66 83.39 4.69 2.9, 1043 5.15 decrease TC 5.16 (a) $ (TH # TC)!2, (b) $ (THTC)1!2 5.17 (a) (1!!max) ! 1, (b) 1!!max 5.20 (a) $ 5.21 (a) $ (a) 0.79 (b) 0.791 5.23 952 75 3.30 !3 1.6386 " 10 274.26 kJ/kg 3 m /kg, 3.32 1751.1 3.34 2.392 kJ/kg, 20.23 3.37 52.1, 42.0 3.41 24, 239.8 3.42 !66.7, 105 3.45 49.3 3.47 # mc1dT%dt2 $ hA1T # 0 ! T2 ! W , T 1t2 $ T0 ! 1W % hA2 51 ! exp3!1hA %mc2t4 6 TC "TH ! T0# TH"T0 ! TC# T¿H"TH ! TC# TH"T¿H ! T¿C# , (b) TC TH 6 T¿C T¿H 2.19 150, 100 k, !0.125 2.17 !40 3.49 0.103 5.27 2.18 80.47 3.50 7.88 " 10!3, 148 5.29 (a) 6.7% 2.20 1.843 3.52 (a) 6.685 (b) 6.973 5.30 possible but uneconomical 2.22 300, 9.42 3.57 460 5.34 no 2.26 !1.96 3.62 425.6, 2.462 2.31 0.842 5.36 900 3.64 !297.9, 24.1, 1167.7, 0 2.33 0.064 5.39 3.33, 0.41 3.65 1.041 2.37 #350 kJ 5.40 no 3.69 (a) !252.4, (b) !245 2.44 109.8 4.3 35.3, 4.17 5.46 2.45 !1.747 4.4 tf $ 15.36 (b) 1–2: 2914, 330, 2–3: 0, 983.0, 3–4: !2140.2, !167.1, 4–1: 0, !373.0, (c) 26.5 2.46 (a) 112.6 Kpa (b) 68.89 J (c) 131.39 J 4.8 0.3717, 6.095 6.1 4.10 5.04, 0.65 4.14 0.73, 0.042 4.17 !44.6 (a) !0.667, imp (b) 0, internally reversible (c) #0.667, possible, and irreversible (a) 664.1, (b) 17, 6.2 6.2 2.49 (b) 8.28 kJ (c) 18.78 kJ (d) !36.9 kJ 3.48 2.50 15 kJ, 30% 4.18 2.56 300 kJ, 200 kJ 4.20 !25.3 kJ/kg 6.6 1.34 kW 4.22 319.6 K 6.10 (a) two-phase, liquid–vapor mixture, (b) superheated vapor, 4.23 102.5 WR ! W1 (a): $ TC # $ Qs 11 ! T0 %Ts 2 % 11 ! T0 %Tu 2 4.24 7.53, 0.108 6.12 F, T, F, F 2.57 3.1 822 (a): W $ mp(vg ! vf), Q $ m(hg ! hf)