lOMoARcPSD|13198648 [WILEY] Borgnakke Sonntag 열역학 9판 1장 연습문제 솔루션 공업열역학 (홍익대학교) StuDocu is not sponsored or endorsed by any college or university Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Borgnakke’s Fundamentals of Thermodynamics Global Edition Solution Manual Chapter 1 Introduction and Preliminaries Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 In-Text Concept Questions 1.a 1.b 1.c Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.d 1.e 1.f Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.g 1.h 1.i Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Concept-Study Guide Problems 1.1 1.2 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.3 1.4 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.5 1.6 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.7 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.8 1.9 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.10 1.11 1.13 1.14 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.15 1.16 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Properties, Units, and Force 1.17 1.18 1.19 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.20 1.21 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.22 1.23 1.24 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.25 1.26 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.27 The elevator in a hotel has a mass of 750 kg, and it carries six people with a total mass of 450 kg. One of the people weighs 80 kg standing still. How much weight does this person feel when the elevator starts moving? Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Specific Volume 1.28 1.29 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.30 1.31 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.32 1.33 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Pressure 1.34 1.35 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.36 1.37 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.38 1.39 1.40 A piston/cylinder with cross sectional area of 0.01 m2 has a piston mass of 100 kg resting on the stops, as shown in Fig. P1.40. With an outside atmospheric pressure of 100 kPa, what should the water pressure be to lift the piston? Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.41 1.42 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.43 1.44 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.45 A 2.5 m tall steel cylinder has a cross sectional area of 1.5 m2. At the bottom with a height of 0.5 m is liquid water on top of which is a 1 m high layer of gasoline. This is shown in Fig. P1.45. The gasoline surface is exposed to atmospheric air at 101 kPa. What is the highest pressure in the water? 1.46 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.47 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.48 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.49 1.50 Liquid water with density ρ is filled on top of a thin piston in a cylinder with cross-sectional area A and total height H, as shown in Fig. P1.50. Air is let in under the piston so it pushes up, spilling the water over the edge. Derive the formula for the air pressure as a function of piston elevation from the bottom, h. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Manometers and Barometers 1.51 1.52 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.53 1.54 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.55 1.56 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.57 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.58 1.59 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.60 1.61 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.62 1.63 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.64 1.65 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.66 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Energy and Temperature 1.67 1.68 1.69 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.70 1.71 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.72 1.73 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Review Problems 1.74 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.75 Two cylinders are connected by a piston as shown in Fig. P1.75. Cylinder A is used as a hydraulic lift and pumped up to 500 kPa. The piston mass is 25 kg and there is standard gravity. What is the gas pressure in cylinder B? 1.76 In the city water tower, water is pumped up to a level 25 m above ground in a pressurized tank with air at 150 kPa over the water surface. This is illustrated in Fig. P1.76. Assuming the water density is 1000 kg/m3 and standard gravity, find the pressure required to pump more water in at ground level. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 1.77 1.78 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 [WILEY] Borgnakke Sonntag 열역학 9판 2장 연습문제 솔루션 공업열역학 (홍익대학교) StuDocu is not sponsored or endorsed by any college or university Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Borgnakke’s Fundamentals of Thermodynamics Global Edition Solution Manual Chapter 2 Properties of a Pure Substance Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 In-Text Concept Questions 2.a 2.b 2.c 2.d Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.e 2.f 2.g Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.h 2.i 2.j Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.k Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Concept-Study Guide Problems 2.1 2.2 2.3 2.4 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.5 2.6 2.7 2.8 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.9 2.10 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.11 2.12 2.13 2.14 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Phase Diagrams, Triple and Critical Points o 2.15 Water at 27 C can exist in different phases, depending on the pressure. Give the approximate pressure range in Pa for water in each of the three phases: vapor, liquid, and solid. Solution: T = 27oC = 300 K Look at the P-T phase diagram in Fig. 2.4 at 300 K: From Fig. 2.4: PVL ≈ 4 × 10−3 MPa = 4 kPa , PLS = 103 MPa 0 < P < 4 kPa 4 kPa < P < 1000 MPa P > 1000 MPa Vapor Liquid Solid (Ice) 2.16 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.17 2.18 2.19 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.20 2.21 A substance is at 2070 kPa, 18oC in a rigid tank. Using only the critical properties, can the phase of the mass be determined if the substance is nitrogen, water, or propane? Solution: Find state relative to critical point properties which are from Table A.2: a. Nitrogen N2 b. Water H 2O c. Propane C3H8 3.39 MPa 126.2 K 22.12 MPa 647.3 K 4.25 MPa 369.8 K State is at 18 °C = 291 = K and P 2070 MPa < Pc for all cases: N 2 : T Tc ; Superheated vapor and P < Pc H 2 O : T Tc ; P Pc so you cannot say C3 H8 : T < Tc ; P < Pc you cannot say Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.22 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 General Tables 2.23 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.24 Determine the phase of the substance at the given state using Appendix B tables. a. Water: 93°C, 480 kPa b. Ammonia: -12°C, 130 kPa c. R-410A: -2°C, 340 kPa Solution: a) From Table B.1.1 Psat ( 93 °C ) = 78.47 kPa 480 kPa > Psat then it is compressed liquid OR from Table B.1.2 Tsat ( 480 kPa ) = 150 °C 100 °C < Tsat then it is subcooled liquid = compressed liquid b) Ammonia NH3 : 268 kPa Table B.2.1: P < Psat ( −12 °C ) = Superheated vapor c) R-410A 754 kPa Table B.4.1: P < Psat ( −2 °C ) = Superheated vapor The S-L fusion line goes slightly to the left for water. It tilts slightly to the right for most other substances. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.25 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.26 2.27 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.28 2.29 2.30 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.31 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.32 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.33 2.34 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.35 2.36 You want a pot of water to boil at 104oC. How heavy a lid should you put on the 0.16-m-diameter pot when P atm = 101.4 kPa? Solution: Table B.1.1 at 104oC: Psat = 116.67 kPa = A π π = D2 = ( 0.16 ) 0.020 m 2 4 4 2 ( (116.67 − 101.33) kPA 0.020 m 2 Fnet = ( Psat − Patm ) A = ) = 0.3068 = kN 306.8 N Fnet = m lid g = m lid F= net g 306.8 N = 31.3 kg 9.807 m/s 2 Some lids are clamped on the problem deals with one that stays on due to its weight. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.37 2.38 A rigid vessel contains saturated ammonia vapor at 21oC. Heat is transferred to the system until the temperature reaches 49oC. What is the final pressure? Solution: Since the volume does not change during this process, the specific volume also remains constant. From the ammonia table, Table B.2.1 v= 0.14922 m3 /kg 1 v= 2 Since vg at 49°C is less than 0.14922 m3 /kg , it is evident that in the final state the ammonia is superheated vapor. By interpolating between the 800- and 1000-kPa columns of Table B.2.2 at 40oC, we find that P2 = 800 kPa + (1000 − 800 ) kPa 0.14922 − 0.177945 = 946.3 kPa 0.13868 − 0.177945 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.39 2.40 Saturated liquid water at 65oC is put under pressure to decrease the volume by 1% while keeping the temperature constant. To what pressure should it be compressed? Solution: State 1: T = 65 °C , x = 0.0 ; Table B.1.1: v = 0.001020 m3 /kg Process: = T constant = 65 °C State 2: T, v = 0.99 × vf ( 65 °C ) = 0.99 × 0.001020 = 1.0098 × 10−3 m3 /kg Between 20,000 kPa & 30,000 kPa in Table B.1.4, P ≅ 23800 kPa Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.41 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.42 2.43 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.44 Saturated vapor R-410A at 15oC has its pressure decreased to increase the volume by 15%, keeping the temperature constant. To what pressure should it be expanded? Solution: Initial state: v = 0.02045 m3 /kg from table B.4.1 Final state: v = 1.15 × vg = 1.15 × 0.02045 m3 /kg = 0.0235 m3 /kg Interpolate at 15◦C between saturated vapor and superheated vapor at P = 10 kPa in Tables B.4.1 and B.4.3. 0.0235 − 0.02045 1242.4 kPa P ≅ 1255.4 + (10 − 1255.4 ) = 0.313213 − 0.02045 2.45 Saturated vapor R-410A at 38oC has its pressure increased to decrease the volume by 20% while the state is still saturated vapor. Find the new temperature and pressure. Solution: Initial state: v1 = 0.01061 m3 /kg from table B.4.1, = P1 P= 2308.5 kPa sat Final state: v 2 = 0.8 × v1 = 0.8 × 0.01061 m3 /kg = 0.00849 m3 /kg Interpolate between 500 kPa and 1000 kPa. P2 = 500 + 500 × 0.00849 − 0.06721 = 1319 kPa 0.03137 − 0.06721 P1 2308.5 = = T2 = T1 ( 311) 544.3 K 1319 P2 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.46 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.47 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.48 2.49 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.50 2.51 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.52 2.53 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.54 A pressure cooker has the lid screwed on tight. A small opening with A = 0.048 cm2 is covered with a petcock that can be lifted to let steam escape. How much mass should the petcock have to allow boiling at 121oC with an outside atmosphere of 103.4 kPa? Solution: Table B.1.1: Psat = 205.2 kPa = F mg = ΔP × A = ΔP × A/g m = ( 205.2 − 103.4 ) × 1000 × 4.8 × 10−6 9.807 = 0.0498 kg = 49.8 g Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Ideal Gas 2.55 2.56 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.57 2.58 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.59 2.60 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.61 2.62 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.63 2.64 2.65 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.66 Assume we have three states of saturated vapor R-410A at +40°C, 0°C, and −40°C. Calculate the specific volume at the set of (T, P sat ) assuming ideal gas behavior. Find the percent relative error = 100(v − v g )/v g with v g from the saturated R-410A table. Solution: R-410A. Table values from Table B.5.1 Ideal gas constant from table A.5: P sat , v g (T) R R-410A = 0.11455 kj/kg K P sat , kPa v g , m3/kg v 1D.G. = RT / P sat error % –40°C 175.0 0.14291 0.15251 6.72 0°C 798.7 0.03267 0.03917 20.0 40°C 2420.7 0.00967 0.01482 53.26 T Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.67 2.68 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.69 2.70 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.71 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Compressibility Factor 2.72 2.73 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.74 2.75 What is the percent error in specific volume if the ideal gas model is used to represent the behavior of superheated ammonia at 38oC, 550 kPa? What if the generalized compressibility chart, Fig. D.1, is used instead? Solution: 38 = °C 311.15 K , Tc = 405.5 K , Pc = 11.35 MPa from Table A.2. NH= 3 T Table B.2.2: v = 0.2646 m 3 /kg Ideal gas:= v RT = P = Tr Figure D.1: = v ( 0.48819 kJ/kg ⋅ K )( 311.15 K ) 550 KPa = 0.2762 m 3 /kg ⇒ 4.19% error 311.15 0.55 = 0.767 , = Pr = 0.048 405.5 11.35 ZRT = 0.2652 m 3 /kg P ⇒= Z 0.96 ⇒ 0.2% error Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.76 2.77 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.78 2.79 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.80 2.81 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.82 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Equations of State 2.83 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.84 2.85 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 o 2.86 Carbon dioxide at 60 C is pumped at a very high pressure, 10 MPa, into an oil well to reduce the viscosity of oil for better flow. Find its specific volume using the Soave EOS. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.87 Solve the previous problem using the carbon dioxide table, ideal gas, and van der Waals EOS by iteration. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.88 Solve Problem 2.86 using the Redlich-Kwong EOS. Carbon dioxide at 60oC is pumped at a very high pressure, 10 MPa, into an oil well to reduce the viscosity of oil for better flow. Find its specific volume using the Soave EOS. 2.89 Determine the pressure of R-410A at 37◦C, v = 0.012 cubic meter/kg using ideal gas and the vander Waal EOS. Solution: R-410A from the table A.2: Tc = 344.5 K , Pc = 4900 KPa Ideal gas:= P RT = v ( 0.11455 kJ/kg ⋅ K )( 310 K ) 0.012 m3 /kg = 2959.2 kPa For van der Waal equation of state from Table D.1 we have ( 0.11455 kJ/kg ⋅ K )( 344.5 K ) 1 RTc b= 0.125 × 0.001007 m3 /kg = = 8 Pc 4900 KPa ( a= 27b 2 Pc = 27 × ( 0.001007 ) ( 4900 ) = 0.134078 kPa m3 /kg 2 The EOS is: P= ) 2 ( 0.11455)( 310 ) 0.134078 RT a − 2= − = 2299.2 kPa v−b v 0.012 − 0.001007 0.0122 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.90 Do the previous problem using the Soave EOS. Solution: R-410A from the table A.2: Tc = 344.5 K , Pc = 4900 KPa = , Tr T= Tc 310 344.5 = 0.8999 For Soave EOS see Appendix D (very close to Redlich-Kwong) RT a = − 2 P v − b v + bv where the parameters are from Table D.1 and D.4 ω = 0.296 f= 0.48 + 1.574ω − 0.176ω2 = 0.930 ( ) 2 2 = a o 0.42748 1 + f 1 − Tr1= 0.4693 ( 0.11455)( 344.5) = RT b= 0.08664 c = 0.08664 × 0.0006978 m3 /kg Pc 4900 ( 0.11455) ( 344.5) = R 2 Tc2 a= 0.371184 = 0.371184 × 0.117967 m3 /kg Pc 4900 2 RT a − 2 v − b v + bv ( 0.11455)( 310 ) P = = 0.012 − 0.0006978 − 2 ( 0.117967 0.012 ( 0.012 + 0.0006978 ) = 2367.7 kPa Downloaded by Union 9 ([email protected]) ) 2 lOMoARcPSD|13198648 2.91 Do Problem 2.89 using the Redlich-Kwong EOS. Solution: R-410A from the table A.2: Tc = 344.5 K , Pc = 4900 KPa = , Tr T= Tc 310 344.5 = 0.8999 For Redlich-Kwong EOS we have the parameters from Table D.1 ( 0.11455 kJ/kg ⋅ K )( 344.5 K ) 6.978 10−4 m3 /kg RT b= 0.08664 c = 0.08664 × = × Pc 4900 KPa ( 0.11455) ( 344.5) = R 2 Tc2 1 0.42748 × 2.92 × 10−5 kPa m3 /kg = × 2 Pc 0.8999 ( 4900 ) 2 a= 0.42748Tr-1 2 2 The equation is: = P = RT a − 2 v − b v + bv ( 0.11455)( 310 ) 0.012 − 6.978 × 10−4 − ( 2.92 × 10−5 0.012 0.012 + 6.978 × 10−4 ) = 3142 kPa Downloaded by Union 9 ([email protected]) ( ) 2 lOMoARcPSD|13198648 Review Problems 2.92 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.93 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.94 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.95 Refrigerant-410A in a piston/cylinder arrangement is initially at 15.5oC, x = 1. It is then expanded in a process so that P = Cv −1 to a pressure of 207 kPa. Find the final temperature and specific volume. Solution: State 1: 15.5 °C , x = 1 Table B.4.1: P1 = 1121.6 kPa , v1 = 0.02016 m3 /kg Process: Pv= C= P1v1 ; ⇒ P2= C v 2= P1v1 v 2 State 2: 200 kPa, = v 2 v= 1P1 P2 kPa = ( 0.02016 m /kg ) 1121.6 207 kPa 3 0.1092 m 3 /kg v 2 < vg at 207 kPa, T2 ≅ -36.33 °C from Table B.4.2. Notice T is not constant The first part of the process may be in the sup. vapor region. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.96 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.97 2.98 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.99 2.100 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.101 2.102 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Linear Interpolation 2.103 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.104 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.105 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 2.106 2.107 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 [WILEY] Borgnakke Sonntag 열역학 9판 3장 연습문제 솔루션 공업열역학 (홍익대학교) StuDocu is not sponsored or endorsed by any college or university Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Borgnakke’s Fundamentals of Thermodynamics Global Edition Solution Manual Chapter 3 Energy Equation and First Law of Thermodynamics Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 In-Text Concept Questions 3.a 3.b Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.c 3.d 3.e Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.f 3.g 3.h Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.i Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.j Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.k 3.l 3.m Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.n 3.o Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.p 3.q 3.r Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.s 3.t Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.u 3.v Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Concept-Study Guide Problems 3.1 3.2 3.3 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.4 3.5 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.6 3.7 3.8 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.9 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.10 3.11 3.12 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.13 3.14 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.15 3.16 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.17 On a chilly 10°C fall day a house, with an indoor temperature of 20°C, loses 6 kW by heat transfer. What transfer happens on a 30°C warm summer day, assuming everything else is the same? 3.18 Liquid water is heated, so it becomes superheated vapor. Should u or h be used in the energy equation? Explain. 3.19 Liquid water is heated, so it becomes superheated vapor. Can specific heat be used to find the heat transfer? Explain Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.20 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.21 A rigid tank with pressurized air is used (a) to increase the volume of a linear spring-loaded piston/cylinder (cylindrical geometry) arrangement and (b) to blow up a spherical balloon. Assume that in both cases P = A + BV with the same A and B. What is the expression for the work term in each situation? Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.22 An ideal gas in a piston/cylinder is heated with 2 kJ during an isobaric process. Is the work positive, negative, or zero? 3.23 3.24 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Kinetic and Potential Energy 3.25 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.26 3.27 A 1200-kg car accelerates from 30 to 50 km/h in 5 s. How much work input does that require? If it continues to accelerate from 50 to 70 km/h in 5 s, is that the same? Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.28 3.29 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.30 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Force Displacement Work 3.31 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.32 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.33 3.34 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.35 3.36 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Boundary Work 3.37 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.38 The R-410A in Problem 3.13c is at 1000 kPa, 50°C with a mass of 0.1 kg. It is cooled so that the volume is reduced to half the initial volume. The piston mass and gravitation gives a float pressure of 400 kPa. Find the work in the process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.39 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.40 A 400-L tank, A (see Fig. P3.40), contains argon gas at 200 kPa and 30°C. Cylinder B, having a frictionless piston of such mass that a pressure of 150 kPa will float it, is initially empty. The valve is opened, and argon flows into B and eventually reaches a uniform state of 150 kPa and 30°C throughout. What is the work done by the argon? Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.41 A piston/cylinder assembly contains 1 kg of liquid water at 20°C and 300 kPa, as shown in Fig. P3.41. There is a linear spring mounted on the piston such that when the water is heated, the pressure reaches 3 MPa with a volume of 0.1 m3. a. Find the final temperature. b. Plot the process in a P–v diagram. c. Find the work in the process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.42 Air in a spring-loaded piston/cylinder setup has a pressure that is linear with volume, P = A + BV. With an initial state of P = 150 kPa, V = 1 L and a final state of 800 kPa, V = 2 L, as shown in Fig. P3.41. Find the work done by the air. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.43 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.44 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.45 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.46 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.47 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.48 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Heat Transfer 3.49 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.50 3.51 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.52 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.53 3.54 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.55 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.56 3.57 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.58 3.59 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Properties (u, h) from General Tables 3.60 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.61 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.62 Indicate the location of the four states in Problem 3.61 as points in both the P–v and T–v diagrams. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.63 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.64 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.65 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.66 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.67 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.68 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Problem Analysis 3.69 Consider Problem 3.81. Take the whole room as a C.V. and write both conservation of mass and conservation of energy equations. Write equations for the process (two are needed) and use them in the conservation equations. Nowspecify the four properties that determine the initial (2) and the final state (2); do you have them all? Count unknowns and match them with the equations to determine those. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.70 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.71 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.72 Look at Problem 3.142 and plot the P-v diagram for the process. Only T 2 is given, how do you determine the 2nd property of the final state? What do you need to check and does it have an influence on the work term? Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Simple Processes 3.73 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.74 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.75 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.76 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.77 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.78 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.79 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.80 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.81 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.82 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.83 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.84 A cylinder having a piston restrained by a linear spring (of spring constant 15 kN/m) contains 0.5 kg of saturated vapor water at 120◦C, as shown in Fig. P3.84. Heat is transferred to the water, causing the piston to rise. If the piston’s cross-sectional area is 0.05 m2 and the pressure varies linearly with volume until a final pressure of 500 kPa is reached, find the final temperature in the cylinder and the heat transfer for the process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.85 A piston/cylinder arrangement with a linear spring similar to Fig. P3.84 contains R-134a at 15◦C, x = 0.4 and a volume of 0.02 m3. It is heated to 60◦C, at which point the specific volume is 0.03002 m3/kg. Find the final pressure, the work, and the heat transfer in the process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.86 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.87 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.88 The piston/cylinder in Fig. P3.88 contains 0.1 kg water at 500°C, 1000 kPa. The piston has a stop at half of the original volume. The water now cools to a room temperature of 25°C. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.89 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.90 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.91 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Specific Heats: Solids and Liquids 3.92 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.93 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.94 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.95 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.96 A copper block of volume 1 L is heat treated at500°C and now cooled in a 200-L oil bath initially at 20°C, as shown in Fig. P3.96. Assuming no heat transfer with the surroundings, what is the final temperature? Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.97 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.98 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Properties (u, h, C v , C p ), Ideal Gas 3.99 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.100 Estimate the constant specific heats for R-134a from Table B.5.2 at 100 kPa and 125°C. Compare this to the specific heats in Table A.5 and explain the difference. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.101 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.102 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.103 Repeat Problem 3.102 for oxygen gas. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.104 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.105 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.106 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.107 The temperature of water at 400 kPa is raised from 150°C to 1200°C. Evaluate the change in specific internal energy using (a) the steam tables, (b) the ideal gas Table A.8, and (c) the specific heat Table A.5. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.108 Water at 20°C and 100 kPa is brought to 100 kPa and 1500°C. Find the change in the specific internal energy, using the water tables and ideal gas tables. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Specific Heats Ideal Gas 3.109 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.110 Do the previous problem for nitrogen, N 2 , gas. A rigid container has 2 kg of nitrogen gas at 100 kPa, 1200 K that is heated to 1400 K. Solve for the heat transfer using a. the heat capacity from Table A.5 and b. properties from Table A.8. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.111 Air, 3 kg, is in a piston/cylinder in Fig. P3.111 at 27°C, 300 kPa. It is now heated to 600 K. Plot the process path in a P-v diagram, and find the work and heat transfer in the process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.112 A 250-L rigid tank contains methane at 500 K, 1500 kPa. It is now cooled down to 300 K. Find the mass of methane and the heat transfer using (a) the ideal-gas and (b) methane tables. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.113 A 10-m-high cylinder, with a cross-sectional area of 0.1 m2, has a massless piston at the bottom with water at 20°C on top of it, as shown in Fig. P3.113. Air at 300 K, with a volume of 0.3 m3, under the piston is heated so that the piston moves up, spilling the water out over the side. Find the total heat transfer to the air when all the water has been pushed out. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.114 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.115 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.116 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.117 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.118 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Polytropic Process 3.119 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.120 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.121 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.122 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.123 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.124 An air pistol contains compressed air in a small cylinder, as shown in Fig. P3.124. Assume that the volume is 1 cm3, pressure is 1 MPa, and the temperature is 27◦C when armed. A bullet, with m = 15 g, acts as a piston initially held by a pin (trigger); when released, the air expands in a isothermal process (T = constant). If the air pressure is 0.12 MPa in the cylinder as the bullet leaves the gun, find Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.125 A piston/cylinder assembly in a car contains 0.2 L of air at 90 kPa and 20°C, similar to Fig. P3.125. The air is compressed in a polytropic process with n = 1.25 to a final volume six times smaller. Determine the final pressure and temperature, and the heat transfer for the process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.126 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.127 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.128 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.129 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.130 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Multistep Processes: All Substances 3.131 A piston/cylinder shown in Fig. P3.131 contains 0.5 m3 of R-410A at 2 MPa, 150◦C. The piston mass and atmosphere give a pressure of 450 kPa that will float the piston. The whole setup cools in a freezer to -20°C. Find the heat transfer and show the P-v diagram for the process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.132 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.133 Water in a piston/cylinder (Fig. P3.133) is at101 kPa, 25◦C, and mass 0.5 kg. The piston rests on some stops, and the pressure should be 1000 kPa to float the piston. We now heat the water, so the piston just reaches the end of the cylinder. Find the total heat transfer. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.134 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.135 A setup like the one in Fig. P3.131 has the R-410A initially at 1000 kPa, 50◦C of mass 0.1 kg. The balancing equilibrium pressure is 400 kPa, and it is now cooled so that the volume is reduced to half of the starting volume. Find the heat transfer for the process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.136 A piston/cylinder assembly contains 1 kg of liquid water at 20◦C and 300 kPa. Initially the piston floats, similar to the setup in Fig. P3.136, with a maximum enclosed volume of 0.002 m3 if the piston touches the stops. Now heat is added so that a final pressure of 600 kPa is reached. Find the final volume and the heat transfer in the process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.137 The piston/cylinder in Fig. P3.137 contains 0.1 kg water at 500◦C, 1000 kPa. The piston has a stop at half of the original volume. The water now cools to a room temperature of 25◦C. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.138 10 kg of water in a piston/cylinder arrangement exists as saturated liquid/vapor at100 kPa, with a quality of 50%. It is now heated so the volume triples. The mass of the piston is such that a cylinder pressure of 200 kPa will float it, as in Fig. P3.138. Find the final temperature and the heat transfer in the process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.139 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.140 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.141 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.142 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.143 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Energy Equation Rate Form 3.144 3.145 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.146 3.147 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.148 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.149 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.150 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.151 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 General Work 3.152 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.153 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.154 3.155 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.156 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.157 3.158 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Engineering Applications 3.159 3.160 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.161 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.162 3.163 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 More Complex Devices and Review Problems 3.164 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.165 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.166 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.167 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.168 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.169 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.170 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.171 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.172 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.173 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.174 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.175 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.176 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.177 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.178 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.179 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.180 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.181 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.182 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 3.183 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 [WILEY] Borgnakke Sonntag 열역학 9판 4장 연습문제 솔루션 공업열역학 (홍익대학교) StuDocu is not sponsored or endorsed by any college or university Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Borgnakke’s Fundamentals of Thermodynamics Global Edition Solution Manual Chapter 4 Energy Analysis for a Control Volume Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 In-Text Concept Questions 4.a 4.b 4.c Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.d 4.e 4.f 4.g Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.h 4.i Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.j 4.k Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Concept-Study Guide Problems 4.1 4.2 4.3 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.4 4.5 4.6 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.7 4.8 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.9 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Continuity Equation and Flow Rates 4.10 4.11 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.12 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.13 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.14 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.15 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Single-Flow, Single-Device Processes Nozzles, Diffusers 4.16 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.17 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.18 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.19 Superheated vapor ammonia enters an insulated nozzle at 20°C, 800 kPa, shown in Fig. P4.19, with a low velocity and at the steady rate of 0.01 kg/s. The ammonia exits at 300 kPa with a velocity of 450 m/s. Determine the temperature (or quality, if saturated) and the exit area of the nozzle. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.20 A diffuser, shown in Fig. P4.20, has air entering at 100 kPa, 300 K, with a velocity of 200 m/s. The inlet cross-sectional area of the diffuser is 100 mm2. At the exit, the area is 860 mm2, and the exit velocity is 20 m/s. Determine the exit pressure and temperature of the air. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.21 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.22 4.23 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Throttle Flow 4.24 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.25 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.26 4.27 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.28 4.29 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Turbines, Expanders 4.30 4.31 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.32 4.33 What is the specific work one can expect from the dam in Problem 4.23? A small turbine, shown in Fig. P4.33, is operated at part load by throttling a 0.25 kg/s steam supply at 1.4 MPa, 250°C down to 1.1 MPa before it enters the turbine and the exhaust is at 10 kPa. If the turbine produces 110 kW, find the exhaust temperature (and quality if saturated). Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.34 4.35 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.36 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Compressors, Fans 4.40 4.41 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.42 A portable fan blows 0.3 kg/s room air with a velocity of 15 m/s (see Fig. P4.15). What is the minimum power electric motor that can drive it? Hint: Are there any changes in P or T? 4.43 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.44 4.45 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.46 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.47 A compressor receives R-410a as saturated vapor R-410a at 400 kPa and brings it to 2000 kPa, 60°C. Then a cooler brings it to saturated liquid at 2000 kPa (see Fig. P4.43). Find the specific compressor work and the specific heat transfer in the cooler? Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Heaters, Coolers 4.48 4.49 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.50 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.51 4.52 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.53 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.54 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.55 4.56 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.57 4.58 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.59 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Pumps, Pipe and Channel Flows 4.60 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.61 4.62 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.63 4.64 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Multiple-Flow, Single-Device Processes Turbines, Compressors, Expanders 4.65 A steam turbine receives water at 15 MPa, 600°C at a rate of 100 kg/s, as shown in Fig. P6.65. In the middle section 20 kg/s is withdrawn at 2 MPa, 350°C and the rest exits the turbine at 75 kPa, with 95% quality. Assuming no heat transfer and no changes in kinetic energy, find the total turbine power output. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.66 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.67 A compressor receives 0.05 kg/s R-410A at 200 kPa, -20°C and 0.1 kg/s R-410A at 400 kPa, 0°C. The exit flow is at 1000 kPa, 60°C as shown in Fig. P4.67. Assume it is adiabatic, neglect kinetic energies and find the required power input. 4.68 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.69 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.70 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Heat Exchangers 4.71 A condenser (heat exchanger) brings 1 kg/s water flow at 10 kPa from 300°C to saturated liquid at 10 kPa, as shown in Fig. P4.71. The cooling is done by lake water at 20°C that returns to the lake at 30°C. For an insulated condenser, find the flow rate of cooling water. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.72 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.73 A heat exchanger, shown in Fig. P4.73, is used to cool an air flow from 800 K to 360 K, both states at 1 MPa. The coolant is a water flow at 15°C, 0.1 MPa. If the Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.74 A two fluid heat exchanger has 2 kg/s liquid ammonia at 20°C, 1003 kPa entering state 3 and exiting at state 4. It is heated by a flow of 1 kg/s nitrogen at 1500 K, state 1, leaving at 600 K, state 2 similar to Fig. P4.73. Find the total rate of heat transfer inside the heat exchanger. Sketch the temperature versus distance for the ammonia and find state 4 (T, v) of the ammonia. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.75 An energy recovery heat exchanger, shown in Fig. P4.75, is used to heat a water flow at 15°C, 0.4 MPa to saturated vapor. The energy is taken from a 2 kg/s air flow at 800 К which leaves at 360 K, both states at 1 MPa. Find the flow rate of water you can get. 4.76 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.77 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.78 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.79 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.80 An automotive radiator has glycol at 95°C enter and return at 55°C as shown in Fig. P4.80. Air flows in at 20°C and leaves at 25°C. If the radiator should transfer 25 kW what is the mass flow rate of the glycol and what is the volume flow rate of air in at 100 kPa? Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.81 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.82 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Mixing Processes 4.83 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.84 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.85 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.86 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.87 An insulated mixing chamber receives 2 kg/s R-134a at 1 MPa, 100°C in a line with low velocity. Another line with R-134a as saturated liquid 60°C flows through a valve to the mixing chamber at 1 MPa after the valve, as shown in Fig. P4.87. The exit flow is saturated vapor at 1 MPa flowing at 20 m/s. Find the flow rate for the second line. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.88 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.89 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Multiple Devices, Cycle Processes 4.90 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.91 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.92 4.93 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.94 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.95 A modern jet engine has a temperature after combustion of about 1500 К at 3200 kPa as it enters the turbine section, see state 3 Fig. P4.95. The compressor inlet is 80 kPa, 260 К state 1 and outlet state 2 is 3300 kPa, 780 K; the turbine outlet state 4 into the nozzle is 400 kPa, 900 К and nozzle exit state 5 at 80 kPa, 640 K. Neglect any heat transfer and neglect kinetic energy except out of the nozzle. Find the compressor and turbine specific work terms and the nozzle exit velocity. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.96 A proposal is made to use a geothermal supply of hot water to operate a steam turbine, as shown in Fig. P4.96. The high-pressure water at 1.5 MPa, 180°C, is throttled into a flash evaporator chamber, which forms liquid and vapor at a lower pressure of 400 kPa. The liquid is discarded while the saturated vapor feeds the turbine and exits at 10 kPa, 90% quality. If the turbine should produce 1 MW, find the required mass flow rate of hot geothermal water in kilograms per hour. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Transient Flow Processes 4.97 4.98 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.99 4.100 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.101 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.102 Steam at a pressure of 1.4 MPa and a temperature of 300°C is flowing in a pipe (Fig. P4.102). Connected to this pipe through a valve is an evacuated tank. The valve is opened and the tank fills with steam until the pressure is 1.4 MPa, and then the valve is closed. The process takes place adiabatically, and kinetic energies and potential energies are negligible. Determine the final temperature of the steam. Solution: Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.103 An insulated 2 m3 tank is to be charged with R- 134a from a line flowing the refrigerant at 2 MPa, 90°C. The tank is initially evacuated, and the valve is closed when the pressure inside the tank reaches 2 MPa. Find the mass in the tank and its final temperature. Solution: C.V. Tank and valve, transient process with no heat transfer or work. min ; Continuity Eq.4.15: m 2 − m1 = −min h in + 1Q2 − 1W2 Energy Eq.4.16: m 2 u 2 − m1u1 = Process: 1 Q2 = 0 , V = constant so 1W2 = 0 0 ⇒ m2 = min State 1: m1 = P2 P= 2 MPa , one more property State 2: = line h= 458.95 kJ/kg Energy Eq.: u= 2 in 458.95 − 446.78 State 2: (P, u) interpolate B.5.2: T2 = = 111.8 °C , 100 + 10 457.12 − 446.78 v 2 =0.01211 + ( 0.1904 )( 0.01279 − 0.01211) =0.012239 m3 /kg = m2 V= v 2 2 m3 0.012239 m3= /kg 163.4 kg Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.104 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.105 A 25 L tank, shown in Fig. P4.105, that is initially evacuated is connected by a valve to an air supply line flowing air at 20°C, 800 kPa. The valve is opened, and air flows into the tank until the pressure reaches 600 kPa. Determine the final temperature and mass inside the tank, assuming the process is adiabatic. Develop an expression for the relation between the line temperature and the final temperature using constant specific heats. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.106 A nitrogen line, 300 К and 0.5 MPa, shown in Fig. P4.106, is connected to a turbine that exhausts to a closed initially empty tank of 50 m3. The turbine operates to a tank pressure of 0.5 MPa, at which point the temperature is 250 K. Assuming the entire process is adiabatic, determine the turbine work. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.107 A tank of 2 m3 volume contains saturated ammonia at a temperature of 40°C. Initially, the tank contains 50% liquid and 50% vapor by volume. Vapor is withdrawn from the top of the tank until the temperature is 10°C. Assuming that only vapor (i.e., no liquid) leaves and that the process is adiabatic, calculate the mass of ammonia that is withdrawn. Solution: Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.108 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 Review Problems 4.109 A pipe of radius R has a fully developed laminarflow of air at P 0 , T 0 with a velocity profile as: V= V c [1 − (r/R)2], where V c is the velocity on the center-line and r is the radius, as shown in Fig. P4.109. Find the total mass flow rate and the average velocity both as functions ofV c and R. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.110 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.111 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.112 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.113 4.114 A flow of 2 kg/s of water at 500 kPa, 20°C is heated in a constant-pressure process to 1700°C. Find the best estimate for the rate of heat transfer needed. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.115 A steam engine based on a turbine is shown in Fig. P4.115. The boiler tank has a volume of 100 L and initially contains saturated liquid with a very small amount of vapor at 100 kPa. Heat is now added by the burner. The pressure regulator, which keeps the pressure constant, does not open before the boiler pressure reaches 700 kPa. The saturated vapor enters the turbine at 700 kPa and is discharged to the atmosphere as saturated vapor at 100 kPa. The burner is turned off when no more liquid is present in the boiler. Find the total turbine work and the total heat transfer to the boiler for this process. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.116 Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.117 A 2-m3 storage tank contains 95% liquid and 5% vapor by volume of liquified natural gas (LNG) at 160 K, as shown in Fig. P4.117. It may be assumed that LNG has the same properties as pure methane. Heat is transferred to the tank and saturated vapor at 160 К flows into a steady flow heater which it leaves at 300 K. The process continues until all the liquid in the storage tank is gone. Calculate the total amount of heat transfer to the tank and the total amount of heat transferred to the heater. Downloaded by Union 9 ([email protected]) lOMoARcPSD|13198648 4.118 Downloaded by Union 9 ([email protected])
