ADVANCED THERMODYNAMICS ENGINEERING phần 9 pdf

c) Is there any entropy generated during the process? If so, how much for unit mass? d) Comment on the areas under process 1-2 in the P-v and T-s diagrams. Problem C69 10 kg of Ar is contained in the piston–cylinder section A of a system at the state (1.0135 bar, 100ºC). The gas is in contact through a rigidly fixed diathermal wall with a piston–cylinder section B of the system that contains a wet mixture of water with a quality x = 0.5 that is constrained by a weight. As the gas in section A is compressed the temperature in A remains at 100ºC using QE process due to contact with section B. Assume that the quality in section B increases to 90%. Both systems are well in- sulated except at the diathermal wall. Determine: a) the initial pressure in Chamber B, b) the heat transfer Q 12, B in kJ to Chamber B during compression of Ar in Chamber A, c) the work for sections A and B in kJ, d) the change in the entropies of Ar and H 2 O (both liquid and vapor), and e) the volume V 2 in Chamber A f) Is the process for the composite system (A+B combined together) isothermal and isentropic? Problem C70 A piston–cylinder assembly contains Ar(g) at 60 bar and 1543 K (state 1). a) Determine the work done if the gas undergoes isothermal expansion to 1 bar (state 2). What is the heat transfer? Does this work process violate the Sec- ond Law? b) Determine the work done if the gas undergoes quasistatic adiabatic expan- sion to 1 bar (state 3). Can we continue the expansion to v 3 → ∞ by remov- ing the insulation and adding heat? Problem C71 A rigid container of volume V is divided into two rigid subsystems A and B by a rigid partition covered with insulation. Both subsystems are at the same initial pressure P o . Subsystem B contains 4 kg of air at 350 K, while subsystem A contains 0.4 kg of air at 290 K. The insulation is suddenly removed and A and B are allowed to reach ther- mal equilibrium. a) What is the behavior of the overall entropy with respect to the temperature in subsystem A. What is the equilibrium temperature? b) As heat is transferred, the entropy of subsystem A increases while that of subsytem B decreases. The entropy in the combined system A and B is held constant by removing heat from subsystem A. Plot the behavior of the over- all internal energy with respect to the temperature in subsystem A. What is the equilibrium temperature? c) Both subsystems are allowed to move mechanically in order to maintain the same pressure as the initial pressure P o . The entropy is held constant by al- lowing for heat transfer. Plot the behavior of the overall enthalpy with re- spect to the temperature in subsystem A. What is the equilibrium tempera- ture? Problem C72 A piston–cylinder–weight assembly is divided into two insulated subsystems A and B separated by a copper plate. The plate is initially locked and covered with insulation. The subsystem A contains 0.4 kg of N 2 while subsystem B contains 0.2 kg of N 2 . a) The insulation is removed, but the plate is kept locked in locked positions. Both subsys- tems are at the same initial pressure P 1A = P 1B = 1.5 bar with temperatures T 1A = 350 K, and T 1B = 290 K. Both A and B reach thermal equilibrium slowly. Assuming that internal equilibrium exists within each subsystem, plot (S = S A + S B ) with respect to T B for specified values of U, V, and m. What is the value of T B at equilibrium? b) The plate insulation is maintained, but the lock is removed. Assume P 1B = 2.48 bar and P 1A = 1.29 bar and equal temperatures T A,1 = T B,1 = 335 K. Assume quasiequilibrium expansion in subsystem B and plot S with respect to P A for specified values of U, V, and m b) The insulation is removed, but heat transfer to outside ambience is allowed with the restraint that the entropy of the combined system A+B is constant. Plot U with respect to T B . What is the value of T B at equilibrium? Problem C73 An adiabatic rigid tank is divided into two sections A (one part by volume) and B (two parts by volume) by an insulated movable piston. Section B contains air at 400 K and 1 bar, while section A contains air at 300 K and 3 bar. Assume ideal gas behavior. The insulation is suddenly removed. Determine: a) The final system temperatures. b) The final volumes in sections A and B. c) The final pressures in sections A and B. d) The entropy generated per unit volume. Problem C74 Steam enters a turbine at 40 bar and 400ºC, at a velocity of 200 m s –1 and exits at 36.2ºC as saturated vapor, at a velocity of 100 m/s. If the turbine work output is 600 kJ kg –1 , determine: a) The heat loss. b) The entropy generation assuming that the control surface temperature T b is the average temperature of the steam considering both inlet and exit. c) The entropy generation if the control surface temperature T b = T o = 298 K, which is the ambient temperature Problem C75 Determine entropy generated during the process of adding ice to tap water. A 5 kg glass jar (c = 0.84 kJ kg –1 K –1 ) contains 15 kg of liquid water (c = 4.184 kJ kg –1 K –1 ) at 24ºC. Two kg of ice (c = 2 kJ kg –1 K –1 ) at –25ºC wrapped in a thin insulating foil of negligible mass is added to water. The ambient temperature T o = 25ºC. The insulation is suddenly removed. What is the equilibrium temperature assuming that no ice is left (the heat of fusion is 335 kJ kg –1 ), and what is the entropy generated? Problem C76 Consider the isentropic compression process in an automobile engine. The compres- sion ratio r v = (V 1 /V 2 ) = 8 and T 1 = 300 K. Assuming constant specific heats, deter- mine the final temperature and T 2 and the work done if the fluid is air and Ar respec- tively. Explain your answers. B A Figure Problem C.72 Problem C77 The fuel element of a pool–type nuclear reactor is composed of a core which is a ver- tical plate of thickness 2L and a cladding material of thickness t on both sides of the plate. It generates uniform energy ′′′q , and there is heat loss h H (T s – T ∞ ) from the plate surface, where T s denotes the surface temperature of the cladding material. The temperature profiles are as follows: In the core, (T – T ∞ )/( ′′′q L core 2 /2k core ) = 1 – (x/L) 2 – B, where B= 2(k core /k clad ) + 2 (L clad /L core ) (k core /k clad ) (1 + k clad /(h H L clad )). For the cladding material (T – T ∞ )/( ′′′q L core 2 /2k clad ) = –(x/L) 2 + c, where C = (L clad /L core )(1 + k clad /(h H L clad )) and L clad = L core + t. Here L denotes length, k the thermal conductivity, h H the convective heat transfer co- efficient, and t thickness. a) Obtain expressions for the entropy generated per unit volume for the core and clad. b) Simplify the expression for the entropy generated per unit volume at the center of core? c) Determine the entropy generated per unit surface area for the core and clad. Problem C78 The energy form of the fundamental equation for photon gas is U = (3/4) 4/3 (c/(4 σ)) 1/3 S 4/3 V –1/3 where c denotes speed of light, σ Stefan Boltzmann constant, and V volume. a) Obtain an expression for T(S,V). b) Obtain an expression for (P/T) in terms of S and V. c) Using the results for parts (a) and (b) determine P(T,V). Problem C79 A heat engine cycle involves a closed system containing an unknown fluid (that is not an ideal gas). The cycle involves heat addition at constant volume from state 1, which is saturated liquid, to state 2, adiabatic reversible expansion from state 2 to state 3 which is a saturated vapor, and isobaric and isothermal heat rejection from state 3 to state 1 (that involves condensation from saturated vapor to saturated liquid). The cy- cle data are contained in the table below. The heat addition takes place from a thermal energy reservoir at 113ºC to the system. Heat rejection occurs from the system to the ambient at 5ºC. Determine the heat added and rejected, the cycle efficiency, the asso- ciated Carnot efficiency, and the entropy generated during the cyclical process State P, bar T, ºC v, m 3 kg –1 h, kJ kg –1 1 50 5 0.003 720 2 310 113 0.003 965 3 50 5 0.004 860 Problem C80 An ideal gas available at state (P 1 ,T 1 ) is to be isentropically expanded to a pressure P 2 . Given the choice that you can either use a turbine or a piston–cylinder assembly, which one do you recommend? Are the isentropic efficiencies the same for both de- vices if the final states are the same? Problem C81 Show that the reversible work for an isothermal process undergoing expansion from a pressure of P 1 to P 2 in a closed system is same as the work in an open system (neglect kinetic and potential energies in the open system) for the same pressure change with an ideal gas as the medium of fluid. Is this statement valid for an adiabatic reversible process for the same pressure changes in both the open and closed systems and with the same initial/inlet conditions? Justify. Problem C82 Show that the expression dU = T dS - P dV + µdN (A) reduces to the expression du = Tds – Pdv. Problem C83 Assume that we have 2 kmol of N 2 at 400 K and 1 bar in a rigid tank, and S 1 = 200.1×2 = 400.2 kJ/K. We add 0.1 kmols of N 2 and transfer heat from the system such that S 2 = S 1 . a) Determine U at states 1 and 2. b) Determine the temperature at state 2. b) Determine the chemical potential µ(= ∂U/∂N) S,V Problem C84 Consider a counter-flow heat exchanger in which two streams H and C of specific heats c pH and c pC flow counter to each other. The inlet is denoted as i and the exit as e. If T H,i and T H,e are the inlet and exit temperatures of stream H, and T C,i is the inlet of stream C., then obtain an expression for the maximum most temperature T C,e . Assume that C p,H m H < C pC m C and T H,e = T C,i . Determine the entropy generated per kg of smaller heat capacity fluid Problem C85 Consider an adiabatic reversible compression from 1 to 2 via path A from volume v 1 to v 2 followed by irreversible adiabatic expansion from 2-3 and cooling from 3-1 (path B: 2-3 and 3-1). Apply Clausius in-equality for such a cycle and discuss the re- sult. D. CHAPTER 4 PROBLEMS (Unless otherwise stated assume T 0 = 25ºC and P 0 = 1 bar) Problem D1 Is the relation s(T o , p HO 2 ,o ) = s(T 0 ,p sat HO 2 , ) R ln (p HO 2 , o /p HO 2 ,sat ) equivalent to s(T o ,p HO 2 ,o ) = s o (T o ) – R ln (X HO 2 P/P o )? Problem D2 In the condenser part of a power plant, is there an irreversibility due to Q o ? Problem D3 Is it more practical to design for w opt than w s ? Problem D4 Is the notion of availability based on an isentropic concept? Problem D5 Is optimum work the same as reversible work? Problem D6 When is g ≡ ψ? Problem D7 Are ke and pe included in the definition of ψ? Problem D8 Describe the concept of chemical availability. Problem D9 Use an example to describe the availability for gasoline. Problem D10 Differentiate between the absolute (availability-Europe) and the relative availability (exergy). Problem D11 Explain the physical implications of the expression ψ= RT ln X k . Does this mean that ψ chem < 0? Problem D12 Is chemical equilibrium satisfied when µ = µ o ? Problem D13 What is the typical range of COP? Problem D14 What is the difference between isentropic and optimum work? Problem D15 What is the absolute stream availability? Can it have negative values? Does the value depend upon the reference condition used for the properties, such as h, s, etc.? 1 2 3 P v Figure C. 84 Problem D16 What is the (relative) stream availability or exergy? Can it have negative values? Does the value depend upon the reference condition used for the properties, such as h, s, etc.? Problem D17 What is the difference between closed system availability and open system availabil- ity ? Problem D18 Can we assume that P o ∆v ≈ 0 for liquids? Problem D19 What do we mean by useful and actual work? Problem D20 Consider the universe. As S → ∞, does φ → 0? Problem D21 What does a dead state imply? Problem D22 How are irreversibilities avoided in practice? Problem D23 For G to have a minimum value in a multicomponent system at specified values of T and P, what is the partial pressure of the species? Problem D24 Can the availability be completely destroyed? Problem D25 What are your thoughts regarding current oil consumption and availability? Problem D26 What is the implication of W u,opt for compression work? Problem D27 An irreversible expansion occurs in a piston–cylinder assembly with air as the me- dium. The initial and final specific volumes and temperatures are, respectively, 0.394 m 3 kg –1 and 1373 K, and 2.049 m 3 kg –1 and 813 K. Assume constant specific heats, c v0 = 0.717 kJ kg –1 K –1 and c p0 = 1.0035 kJ kg –1 K –1 . a) Determine the actual work delivered if the process is adiabatic and the adia- batic efficiency. b) Assume that this is a reversible process between the two given states (not necessarily adiabatic for which Pv n = constant). What is the value of n? De- termine the reversible work delivered. c) What is the maximum possible work if the only interactions are with the en- vironment, T amb = 300 K, and P amb = 100 kPa. What is the availability effi- ciency of this process? Is this the same as the adiabatic efficiency? d) What is the total entropy generated and the irreversibility? Problem D28 Water flows through a 30 m long insulated hose at the rate of 2 kg min –1 at a pressure of 7 bar at its inlet (which is a faucet). The water hose is well insulated. Determine the entropy generation rate. What could have been the optimum work? Problem D29 Steam enters a turbine at 5 bar and 240ºC (state 1). a) Determine the absolute availability at state 1? What is the absolute availabil- ity at the dead state (considering thermomechanical equilibrium)? b) What is the optimum work if the dead state is in mechanical and thermal equilibrium? c) What is the chemical availability? d) What is the optimum work if the steam eventually discharges at the dead state? The environmental conditions are 298 K, 1 bar, and air with a water vapor mole fraction of 0.0303. Problem D30 Saturated liquid water (the mother phase) is contained in a piston–cylinder assembly at a pressure of 100 kPa. An infinitesimal amount of heat is added to form a single vapor bubble (the embryo phase). a) If the embryo phase is assumed to be at the same temperature and pressure as the mother phase, determine the absolute availabilities ψ = h – T o s and Gibbs functions of the mother and embryo phases. b) If the pressure of the embryo (vapor) phase is 20 bar at 100ºC, while the mother phase is at 1 bar, what are the values of the availability and Gibbs function of the vapor embryo? (Assume the properties for saturated vapor at 100ºC and that the vapor phase behaves as an ideal gas from its saturated va- por state at 1 bar and 100ºC to 20 bar and 100ºC to determine the properties.) Problem D31 You’ve been engaged as a consultant for a manufacturing facility that uses steam. Their steam generator supplies high pressure steam at 800 psia, but they use the steam at 300 psia. How would you advise them to decrease the pressure such that they minimize irreversibilities? Be sure to explain your answer. If so, explain what and the mechanism responsible for the destruction. Show both the process and the throttling process on an h-s diagram and refer to it to illustrate your answer. Problem D32 Consider the energy from the sun at T R,1 and the ocean water at T 0 . Derive expres- sions for W opt . Look at Figure Problem D.32 and interpret your results in terms of the figure. Problem D33 Ice is to be heated at the North Pole where the ambient temperature is –30ºC to tem- perature of –25ºC, –20ºC, …, 90ºC. Determine the minimum work required. The heat of melting of ice is 334.7 kJ kg –1 , and c ice is 1.925 kJ kg –1 K –1 . Problem D34 A gas tank contains argon at T and P. a) Obtain an expression for the maximum possible work if an open system is used when tank pressure is T and P. Assume that there is negligible change in T and P of the tank and constant specific heats for the ideal gas. The ambient temperature is T o and the ambient pressure is P o . b) Suppose the gas is slowly transferred from the tank to a large piston–cylinder (PC) assembly in which the pressure and temperature decrease to the ambient values. Treat the tank and PC assembly as one closed system. What is the be- havior of φ/(RT o ) with respect to T/T o with P/P o as a parameter? Consider the case when the gas state is at 350 K and 150 bar, and T o = 298 K and P o = 100 kPa. Problem D35 Natural gas (that can be assumed to be methane) is sometimes transported over thou- sands of miles in pipelines. The flow is normally turbulent with almost uniform ve- locity across the pipe cross sectional area. There is a large pressure loss in the pipe due to friction. The friction also generates heat that raises the gas temperature, which can result in an explosion hazard. Assume that the pipes are well insulated and the specific heats are constant. Assume that initially P 1 = 10 bar and T 1 = 300 K, and fi- nally P 2 = 8 bar for a mass flow rate of 90 kg s –1 m –2 . What is the entropy change per unit mass? What is the corresponding result if the velocity changes due to the pressure changes? Problem D36 The adiabatic expansion of air takes place in a piston–cylinder assembly. The initial and final volume and temperature are, respectively, 0.394 kg m –3 and 1100ºC, and 2.049 kg m –3 and 813 K. Assume constant specific heats c v0 = 0.717 kJ kg –1 K –1 and c p0 = 1.0035 kJ kg –1 K –1 . a) What is the actual work? b) What is the adiabatic efficiency of the process? c) Assuming that a reversible path is followed between the same initial and fi- nal states according to the relation Pv n = constant, what is the work deliv- ered? Why is this different from the actual work? d) Now assume isentropic expansion from the initial state 1 to a volume of 2.333 kg m –3 and isometric reversible heat addition until the final tempera- ture is achieved. What is the heat added in this case? e) If the heat is first added isometrically and reversibly, and then isentropically expanded to achieve the final state, what is the value of the reversible work? HE Ambience at T 0 Dam T R,1 Ocean water + - 300 m Pump Battery Sun Figure Problem D.31 Relation between pressure and volume. f) What is the maximum possible work for a closed system if the ambient tem- perature is 300 K? What is the value of the irreversibility? Problem D37 Consider an ideal Rankine cycle nuclear power plant. The temperature of the heat source is 1400 K. The turbine inlet conditions are 6 MPa and 600ºC. The condenser pressure is 10 kPa. The ambient temperature is 25ºC. What is the irreversibility in KJ/kg and the maximum possible cycle work in KJ/kg? Problem D38 Steam enters a non-adiabatic steady state steady flow turbine at 100 bar as saturated vapor and undergoes irreversible expansion to a quality of 0.9 at 1 bar. The heat loss from the turbine to the ambience is known to be 50 kJ/kg. Determine the a) actual work, b) optimum work, and c) availability or exergetic or Second law efficiency for the turbine. Problem D39 Consider the generalized equation for work from a open system in terms of entropy generation. Using the Gauss divergence theorem, derive an expression for the work done per unit volume ′′w by a device undergoing only heat interaction with its envi- ronment and show that ′′w = –d/dt(e – T o s) – ∇(ρv(e T – T o s)) – T o σ. Obtain an ex- pression for the steady state maximum work. Problem D40 Water is heated from the compressed liquid state of 40ºC and 60 bar (state 1) to satu- rated vapor at a pressure P 2 . Heat is supplied from a large reservoir of burnt gases at 1200 K. If the final pressure P 2 = 60 bar, calculate s 2 –s 1 and the value of the reversible heat transfer q 12 to the water. If P 2 = 58 bar due to frictional losses (state 2´) but h 2 ´ = h 1 , calculate s 2 ´ – s 1 . Is this process internally reversible? Is there any entropy gener- ated and, if so, how much? If the value of Q H is identical for both cases (without and with frictional losses), what is the net entropy generated due to the irreversible heat transfer? Determine the changes in the availabilities (ψ 2 – ψ 1 ) and (ψ 2´ – ψ 1 ). Problem D41 A water drop of radius a at a temperature T l is immersed in ambient air at a tempera- ture T ∞ and it vaporizes. The temperature and water vapor mole fraction profile can in terms of the radial spatial coordinate r be expressed through the following expression under “slow evaporation” conditions X v /X v,s = (T–T ∞ )/(T l –T ∞ ) = a/r, where r ≥ a where X v denotes the mole fraction of the vapor and X v,s that at surface. Determine the difference between absolute availabilities at two locations r = a, and r = b. Plot the variation of availability in kJ/kg of mix with a/r where r is the radius. Problem D42 Electrical work is employed to heat 2 kg of water from 25ºC to 100ºC. The specific heat of water is 4.184 kJ kg –1 K –1 . Determine the electrical work required, and the minimum work required (e.g., by using a heat pump instead). Problem D43 Six pounds of air at 400ºF and 14.7 psia in a cylinder is placed in a piston-cylinder as- sembly and cooled isobarically until the temperature reaches 100ºF. Determine the optimum useful work, actual useful work, irreversibility and the availability or exer- getic or so called 2 nd law efficiency. Problem D44 An adiabatic turbine receives 95,000 lbm of steam per hour at location 1. Steam is bled off (for processing use) at an intermediate location 2 at the rate of 18,000 lbm per hour. The balance of the steam leaves the turbine at location 3. The surroundings are at a pressure and temperature of 14.7 psia and 77ºF, respectively. Neglecting the changes in the kinetic and potential energies and with the following information: P 1 = 400 psia, T 1 = 600ºF, P 2 = 50 psia, T 2 = 290ºF, P 3 = 2 psia, T 3 = 127 ºF, v 3 = 156.4 ft 3 lbm –1 , determine the maximum sssf work per hour, the actual work per hour, and the irreversibility. Problem D45 In HiTAC (High temperature Air Combustion systems), preheating of air to 1000ºC is achieved using either a recuperator or a regenerator. The recuperator is a counterflow heat exchanger while the regenerator is based on a ceramic matrix mounted in a tank through which hot gases and cold air are alternately passed. The hot gas temperature or this particular application is 1000 K. Assume c p to be constant for the hot gas, and for it to be the same as that for the cold air. If the recuperator is used, cold air enters it at 25ºC and the flowrate ratio of the hot to cold gases ˙ m H / ˙ m C = 0.5. The temperature differential between the air leaving the recuperator and the hot gases entering it is 50 K. Determine the availability efficiency for the recuperator. Will you recommend a regenerator instead? Why? Problem D46 Large and uniformly sized rocks are to be lifted in a quarry from the ground to a higher level. The weight of a standard rock is such that the pressure exerted by it alone on the surrounding air is 2 bar. The rocks are moved by a piston–cylinder as- sembly that contains three pounds of air at 300ºF when it is at ground level. Heat is transferred from a reservoir at 1000ºF until the temperature of the air in the cylinder reaches 600ºF so that piston moves up, thereby lifting a rock. Assume that air is an ideal gas with a constant specific heat. If the surrounding temperature and pressure are 60ºF and 14.7 psia, determine: a) The gas pressure. b) The work performed by the gas. c) The useful work (i.e., during the lifting of rocks) delivered by the gas. d) The optimum work. e) The optimum useful work. f) The irreversibility and the availability efficiency (based on the useful work). Problem D47 A jar contains 1 kg of pure water at 25ºC. It is covered with a nonporous lid and placed in a rigid room which contains 0.4 kg of dry air at a temperature and pressure of 25ºC and 1 bar. The lid is suddenly removed. The specific heat of water is 4.184 kJ kg –1 K –1 , and that of air is 0.713 kJ kg –1 K –1 . a) Determine the temperature and composition of the room, the atmosphere of which contains water vapor and dry air at equilibrium. Ignore the pressure change. b) The change in the availability. Problem D48 Hot combustion products enter a boiler at 1 bar and 1500 K (state 1). The gases trans- fer heat to water and leave the stack at 1 bar and 450 K (state 2). Water enters the boiler at 100 bar and 20ºC (state 3) and leaves as saturated vapor at 100 bar (state 4). The saturated vapor enters a non-adiabatic turbine at 100 bar and undergoes irreversi- ble expansion to a quality of 0.9 at 1 bar (state 5). The combustion gases may be ap- proximated as air. And the total gas flow is 20 kg s –1 . Determine the: [...]... vs Xk,l diagrams Assume the following vapor pressure relations: ln (Psat bar) = A - B/(T in K +C) where A, B and C are as follows: for O2: 8.273075661, 666.0 593 1 79, -9. 690 72568, respectively, and for N2: 6. 394 7322 29, 3 69. 1680573, and - 19. 6 199 74 09, respectively Use a spreadsheet program Determine (a) X1,e and X1 for the equilibrium phases at 100 K and 100 kPa b) T and X1 at 100 kPa and X1,e = 0.4 (c)... ∑ i-1 Aij (ρ - ρaj ) 10 i-1 + e-Eρ ∑ i -9 i -9  Aij ρ   Here, R = 4.6151 bar cm3/g K or 0.46151 J/g.K, τc/1000/Tc = 1.54 491 2, E = 4.8, and τaj = τc if j=1, τ aj = 2.5 if j>i, ρaj = 0.634 if j=1, ρaj =1.0 if j>i The coefficients for a0 in joules per gram are given as follows; C1 = 1857.065 C4 = 36.66 49 C7 = 46 C2 = 32 29. 12 C5 = -20.5516 C8 = -1011.2 49 C3 = -4 19. 465 C6 = 4.85233 Values for the coefficients... of water vapor in the gas mixture could be immediately determined The value of pO2 = 1 mm at –2 19 C, 10 mm at -210.6, 40 mm at -204.1ºC, 198 .8ºC at 100mm, -188.8 ºCat 400 mm and -182 .96 ºC at 760 mm; pN2 = 1 mm at 226.1ºC, 10 mm at -2 19. 1ºC, 40 mm at -214.0ºC, -2 09. 7ºC at 100mm, -200 .9 C at 400 mm and - 195 .8ºC at 760 mm (First evaluate the constants A, B and C for the Cox Antoine relation for N2 and... vaporized and burnt in a hazardous waste plant: H2SO4: 92 % by mass, Hydrocarbons: 4%, H2O: 4% Lump hydrocarbons with water The vapor pressure relations are as follows: ln (p) = A - B/(T(K)+C), with p expressed in units of bar The values of A, B and C are as follows: water: 11 .95 59, 398 4.8 49, - 39. 4856, respectively; H2SO4: 8.346772, 4240.275, -1 19. 155, respectively Determine the vapor phase mole fraction... from 1 bar and 300 K (state 1) to the engine pressure (state 2) Assume that for diesel fuel P c = 17 .9 bar, Tc = 6 59 K, ρ1 = 750 kg m–3, Cp1 = 2.1 kJ kg–1 K–1, ∆hc = 44500 kJ kg–1, L 298 = 360 kJ kg–1, L(T) = L 298 ((Tc – T)/(Tc – 298 ))0.38, and log10 Psat = a – b/(Tsat – c), where a = 4.12, b = 1626 K, c = 93 K Determine the specific volume of the liquid at 1 bar and 300 K Assume that the value of Zc can... lignin and the rest is hemi-cellulose, how will you determine the answers for (a) and (b)? Problem K 19 The body burns a mixture of glucose (C6H12O6, hf0 = -1260268 kJ/kmol, s( 298 ,s)=212 kJ/kmol K, HHV 2815832 kJ/kmol,1003 490 5.6 kJ/kmol and fat (C16H32O2, hf= 834 694 .4, s( 298 ,s) =452 kJ/kmol K, HHV = 1003 490 5.6 kJ/kmol K If inhaled air temperature is 25ºC, and exhaled air temperature is 37ºC Plot entropy... - Z)dP / P , where φ 1 is the partial molal fugacity coefficient of species 1 0 1 Problem H8 Determine u,h and f of H2O(Ρ) at T = 90 C and P =100 kPa., b) Determine u,h and f of H2O(Ρ) at T = 90 C and P = 50 kPa Assume that usat (90 C), vsat (90 C) are available Problem H9 Determine the chemical potential of CO2 at P = 34 bar, 320 K Assume real gas behavior For ideal enthalpy use h0 = cp0 (T- 273),... P.G Hill, and J.G Moore, Steam Tables, Wiley, New York, 196 9; L Haar, J.S Gallagher, and G.S Kell, NBS/NRC Steam Tables, Hemisphere, Washington, D.C., 198 4 The properties of water are determined in this reference using a different functional form for the Helmholtz function than given by Eqs (1)-(3) Problem G77 Ammonia is throttled from P1=1 69 bar and T1= 214 C to a very low pressure P2 ( . diesel fuel P c = 17 .9 bar, T c = 6 59 K, ρ 1 = 750 kg m –3 , C p1 = 2.1 kJ kg –1 K –1 , ∆h c = 44500 kJ kg –1 , L 298 = 360 kJ kg –1 , L(T) = L 298 ((T c – T)/(T c – 298 )) 0.38 , and log 10 . –30ºC to tem- perature of –25ºC, –20ºC, …, 90 ºC. Determine the minimum work required. The heat of melting of ice is 334.7 kJ kg –1 , and c ice is 1 .92 5 kJ kg –1 K –1 . Problem D34 A gas tank. piston–cylinder assembly. The initial and final volume and temperature are, respectively, 0. 394 kg m –3 and 1100ºC, and 2.0 49 kg m –3 and 813 K. Assume constant specific heats c v0 = 0.717 kJ kg –1 K –1