Microsoft Word BT Hoa ly 1 docx Ho Chi Minh City University of Technology Department of Physicochemical Analytical Technologies Bài tập Hoá lý 1 (Physical Chemistry 1 Homework) Chương 1 Các khái niệ.
Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies Bài tập Hoá lý (Physical Chemistry - Homework) Chương Các khái niệm tính chất chung chất 1.11 The relative humidity is defined as the ratio of the partial pressure of water vapor to the pressure of water vapor at equilibrium with the liquid at the same temperature The equilibrium pressure of water vapor at 25 oC is 23.756 torr If the relative humidity is 49%, estimate the amount of water vapor in moles contained in a room that is 8.0 m by 8.0 m and 3.0 m in height Calculate the mass of the water n (H2O) = 120.2 mol, m (H2O) = 2.165 kg 1.17 a Find the fractional change in the volume of a sample of liquid water if its temperature is changed from 20 oC to 30 oC and its pressure is changed from bar to 26 bar b Estimate the percent change in volume of a sample of benzene if it is heated from oC to 45 oC at atm c Estimate the percent change in volume of a sample of benzene if it is pressurized at 55 oC from atm to 50 atm a ∆V/V ≈ 0.93 × 10−3, b ∆V/V ≈ 0.05567, c ∆V/V ≈ 0.00480 1.23 Assuming that the coefficient of thermal expansion of gasolines roughly equal to that of benzene, estimate the fraction of your gasoline expense that could be saved by purchasing gasoline in the morning instead of in the afternoon, assuming a temperature difference of oC ∆V/V = 0.006 1.25 The coefficient of thermal expansion of ethanol equals 1.12×10−3K−1 at 20 oC and atm The density at 20 oC is equal to 0.7893 g cm−3 a Find the volume of mol of ethanol at 10 oC and atm b Find the volume of 1mol of ethanol at 30 oC and atm a V(10 oC) = 57.72 cm3, b V(30 oC) = 59.02 cm3 1.33* a By differentiation, find an expression for the coefficient of thermal expansion of a gas obeying the van der Waals equation of state b Find the value of the coefficient of thermal expansion of nitrogen gas at 298.15 K and Vm = 24.4 L mol−1 b α = 3.363 × 10−3 K−1 Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 1.37 The experimental value of the compression factor Z = PVm/RT for hydrogen gas at T = 273.15 K and Vm = 0.1497 L/mol−1 is 1.1336 Find the values of Z predicted by the van der Waals, Dieterici, and Redlich–Kwong equations of state for these conditions Calculate the percent error for each Van der Waals: Z = 1.1434 (0.86% error) Dieterici: Z = 1.1255 (0.71% error) Redlich–Kwong: Z = 1.1153 (1.6% error) 1.39 Find the value of the isothermal compressibility of carbon dioxide gas at 298.15 K and a molar volume of 24.4 Lmol−1, a According to the ideal gas law b According to the truncated virial equation of state: 𝑃𝑉# 𝐵+ = + 𝑅𝑇 𝑉# For carbon dioxide at 298.15 K, B2 = −12.5 × 10−5 m3/mol a κT = 9.843 × 10−6 Pa−1, b κT = 9.945 × 10−6 Pa−1 1.41 a Use the van der Waals equation of state in terms of reduced variables, Eq (1.4-15), to calculate the pressure of 1.000 mol of CO2 in a volume of 1.000 L at 100.0 oC The critical constants are in Table A.5 in Appendix A Since the critical compression factor of carbon dioxide does not conform to the van der Waals value, Zc = 0.375, you must replace the experimental critical - molar volume by 𝑉#, = (0.375)RTc/Pc b Repeat the calculation using the ordinary form of the van der Waals equation of state a P = 28.8 bar, b P = 28.8 bar 1.43 The critical temperature of xenon is 289.73 K, and its critical pressure is 5.840 MPa a Find the values of the van der Waals constants a and b for xenon b Find the value of the compression factor, Z, for xenon at a reduced temperature of 1.35 and a reduced pressure of 1.75 a a = 0.4192 Pa m6 mol−2, b = 5.192 × 10−5 m3 mol−1, b Z = 0.7305 Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies Chương Nguyên lý thứ nhiệt động - Cân lượng hệ thống 2.1 Calculate the work done on the surroundings if mol of neon (assumed ideal) is heated from oC to 250 oC at a constant pressure of atm wsurr = 2079 J 2.3 Calculate the work done on 100.0 g of benzene if it is pressurized reversibly from 1.00 atm to 50 atm at a constant temperature of 293.15 K w = 4.79 J 2.7.* a Obtain a formula for the work done in reversibly and isothermally compressing mol of a vander Waals gas from a volume V1 to a volume V2 b Using the formula from part a, find the work done in reversibly compressing mol of carbon dioxide from 10 L to L at 298.15 K Compare with the result obtained by assuming that the gas is ideal c Using the formula from part a, calculate the work done on the surroundings if mol of carbon dioxide expands isothermally but irreversibly from L to 10 L at an external pressure of atm Compare with the result obtained by assuming that the gas is ideal b w = 1765 J, c wsurr = 507 J 2.13 a If a sample of mol of helium gas is isothermally and reversibly expanded at 298.15 K from a pressure of 2.5 atm to a pressure of atm, find w and q b If the sample of helium from part a is isothermally and irreversibly expanded from the same initial state to the same final state with Pext =1 atm, find w and q a q = −w = 4543 J, b q = −w = 2975 J 2.15 The normal boiling temperature of ethanol is 78.5 oC, and its molar enthalpy change of vaporization at this temperature is 40.3 kJ mol−1 Find q and w if mol of ethanol are reversibly vaporized at 78.5 oC and a constant pressure of atm Neglect the volume of the liquid compared with that of the vapor q = 120.9 kJ, w = −8.771 kJ 2.19 Calculate q, w, and ∆U for melting 100 g of ice at oC and a constant pressure of atm The density of ice is 0.916 g mL−1 q = 33.35 kJ, w = 0.92 J, ∆U = 33.35 kJ Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 2.21.* Consider the following three processes: (1) A sample of mol of helium gas is isothermally and reversibly expanded from a volume of 10 L and a temperature of 400 K to a volume of 40 L (2) The same sample is reversibly cooled at a constant volume of 10 L from 400 K to a temperature of 300 K, then expanded reversibly and isothermally to a volume of 40 L, and then heated reversibly from 300 K to 400 K at a constant volume of 40 L (3) The same sample is expanded irreversibly and isothermally at a temperature of 400 K from a volume of 10 L to a volume of 40 L with a constant external pressure of atm Calculate ∆U, q, and w for each process (1) q = −w = 9221 J, ∆U = 0, (2) q = −w = 6916 J, (3) q = −w = 3040 J 2.25 Find the final pressure if mol of nitrogen is expanded adiabatically and reversibly from a volume of 20 L to a volume of 40 L, beginning at a pressure of 2.5 atm Assume nitrogen to be ideal with CV,m = 5R/2 P2 = 0.947 atm 2.27 Find the final temperature and the final volume if mol of nitrogen is expanded adiabatically and reversibly from STP to a pressure of 0.6 atm Assume nitrogen to be ideal with CV,m = 5R/2 a T2 = 25.7 K, b V2 = 0.0705 m−3 2.41 A sample of 3.00 mol of argon is heated from 25.00 oC to 100.00 oC, beginning at a pressure of atm (101,325 Pa) a Find q, w, ∆U, and ∆H if the heating is done at constant volume b Find q, w, ∆U, and ∆H if the heating is done at constant pressure a w = 0, q = ∆U = 2806 J, b ∆U = 2806 J, q = 4677 J, w = −1871 J 2.43 a Find q, w, ∆U, and ∆H for heating mol of neon gas from 273.15 K to 373.15 K at a constant pressure of atm State any approximations and assumptions b Find q, w, ∆U, and ∆H for heating mol of neon gas from 273.15 K to 373.15 K at a constant volume of 22.4 L State any approximations and assumptions a q = ∆H = 2079 J, w = −831.45 J, ∆U = 1248 J b q = ∆U = 1247 J, w = 0, ∆H = 2079 J Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 2.45 The enthalpy change of fusion of mercury is 2331 J mol−1 Find ∆H for converting 100.0 g of solid mercury at−75.0 oC to liquid mercury at 25.0 oC at a constant pressure of 1.000 atm Assume that the heat capacities are constant and equal to their values in Table A.6 of the appendix ∆H = 5745 J 2.47 Find the value of q and the value of ∆H if mol of solid water (ice) at −10 oC is turned into liquid water at 80 oC, with the process at a constant pressure of atm Assume that the heat capacities are constant and equal to their values in Table A.6 of the appendix q = ∆H = 24.80 kJ Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies Chương Nguyên lý thứ nhiệt động - Entropy Section 3.1: The Second Law of Thermodynamics and the Carnot Heat Engine 3.1 a A Carnot engine contains 0.250 mol of a monatomic ideal gas as its working fluid Assume CV to be constant and equal to 3nR/2 If Th = 473 K, Tc = 373 K, V1 = 0.600 L, and if the compression ratio (the ratio V3/V1) equals 6.00, find the efficiency and the values of V2 and V4 b Calculate w for each of the steps in the cycle of part a a η = 0.211, V2 = 2.52 L, V4 = 0.857 L b w1 = −1411 J, w2 = −312 J, w3 = 1113 J, w4 = 312 J 3.3 Carbon monoxide is used as the fuel for a Carnot engine with a high temperature of 450 oC and a cool temperature of 100 oC Determine how high the combustion of 1.000 mol of CO could lift a 1.00 kg mass near the surface of the earth Assume that all of the heat from the combustion is transferred to the engine and assume that the combustion takes place at 450 oC h = 14.1 km 3.5 a A steam engine operates with its boiler at 200 oC and a pressure of 15.34 atm, and with its exhaust at a temperature of 100 oC and a pressure of 1.000 atm Find the Carnot efficiency for these temperatures What can you say about the efficiency of the steam engine? b The boiler is reinforced to operate at 360 oC and a pressure of 184 atm If the exhaust remains at 100 oC, find the percentage improvement in the Carnot efficiency c If the coal that the steam engine in part b burns is assumed to be pure graphite (not a good assumption) find the mass of coal required to produce 10.00 horsepower for 1.000 hour, assuming the Carnot efficiency horsepower = 746 watt = 746 J s−1 a ηc = 0.2114, b ηc = 0.4107, percentage improvement = 94.3%, c m = 1.996 kg 3.11 It has been proposed that a heat engine might economically operate using the temperature difference between sea water near the surface and at a depth of several hundred feet a Assume that such a heat engine has 50% of the efficiency of a Carnot engine and operates between 30 oC and 20 oC Find the efficiency of the engine b Assume that the heat engine drives an electric generator that produces 100 Mwatt (100 megawatts) Find the volume of sea water that must pass through the high-temperature heat exchanger per second if the heat exchanger lowers the temperature of the sea water from 30 oC to 20 oC Assume that the sea water has the same heat capacity as pure water at 298.15 K, 75.351 J K−1 mol−1, and density equal to 1.00 × 103 kg m−3 Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies a ηc = 0.01649, b dV/dt = 1.45 × 103 m3 s−1 Section 3.3: The Calculation of Entropy Changes 3.13 a Calculate ∆S for each step of the following cycle and sum the results to obtain ∆S for the cycle: Step 1: 1.000 mol of helium is expanded reversibly and isothermally at 298.15 K from 10.0 L to 20.0 L Step 2: The gas is heated reversibly at a constant volume from 298.15 K and 20.0 L to a temperature of 473.15 K Step 3: The gas is compressed reversibly and isothermally at 473.15 K from 20.0 L to 15.0 L Step 4: The gas is cooled reversibly at a constant volume of 15.0 L from 473.15 K to 373.15 K Step 5: The gas is compressed reversibly and isothermally at 373.15 K from a volume of 15.0 L to a volume of 10.0 L Step 6: The gas is cooled reversibly at a constant volume of 10.0 L from 373.15 K to 298.15 K b Repeat the calculation with all steps the same as in part a except that step is carried out isothermally and irreversibly with a constant external pressure of 1.000 atm a ∆S1 = 5.7632 J K−1, ∆S2 = 5.7587 J K−1, ∆S3 = −2.3919 J K−1, ∆S4 = −2.9612 J K−1, ∆S5 = −3.3712 J K−1, ∆S6 = −2.7985 J K−1 b All values are the same 3.15 A sample of 1.000 mol of helium gas (assumed ideal with CV,m = 3R/2) expands adiabatically and irreversibly from a volume of 3.000 L and a temperature of 500 K to a volume of 10.00 L against a constant external pressure of 1.000 atm Find the final temperature, ∆U, q, w, and ∆S for this process w = −1227J, q = 0, ∆U = −1227 J, Tf = 401.6 K, ∆S = 7.278 J K−1, ∆Srev = 0, qrev = 0, ∆Urev = −3441 J, wrev = −3441 J 3.17 a Find the change in entropy for the vaporization of 2.000 mol of liquid water at 100 oC and a constant pressure of 1.000 atm b Find the entropy change for the heating of 2.000 mol of water vapor at a constant pressure of 1.000 atm from 100 oC to 200 oC Use the polynomial representation in Table A.6 for the heat capacity of water vapor a ∆S = 217.98 J K−1, b ∆S = 16.54 J K−1 Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 3.19 a 1.000 mol of helium is compressed reversibly and isothermally from a volume of 100.00 L and a temperature of 298.15 K to a volume of 50.00 L Calculate ∆S, q, w, and ∆U for the process Calculate ∆Ssurr and ∆Suniv b Calculate the final temperature, ∆S, q, w, ∆U, ∆Ssurr, and ∆Suniv if the gas is compressed adiabatically and reversibly from the same initial state to a final volume of 50.00 L c The gas is compressed adiabatically and irreversibly from the same initial state to the same final volume with Pext = 1.000 atm What can you say about the final temperature, ∆S, q, w, ∆U, ∆Ssurr, and ∆Suniv? d The gas is compressed isothermally and irreversibly from the same initial state to the same final volume with Pext = 1.000 atm What can you say about ∆S, q, w, ∆U, ∆Ssurr, and ∆Suniv? a ∆S = −5.7632 J K−1, ∆U = 0, q = −1718.3 J, w = 1718.3 J, ∆Suniv = 0, ∆Ssurr = 5.7632 J K−1 b q = 0, ∆S = 0, ∆Ssurr = 0, ∆Suniv = 0, T2 = 473.3 K, ∆U = 2184.4 J, w = 2184.4 J c T2 > 473.3 K, ∆U > 2184.4 K, w > 2184.4 K, q = 0, ∆S > 0, ∆Ssurr = 0, ∆Suniv > d ∆S = −5.7632 J K−1, ∆U = 0, w < 5066 J, q > −5066 J, ∆Suniv > 0, ∆Ssurr > 5.7632 J K−1 3.21 a Calculate the entropy change for the following reversible process: 2.000 mol of neon (assume ideal with CV,m = 3R/2) is expanded isothermally at 298.15 K from 2.000 atm pressure to 1.000 atm pressure and is then heated from 298.15 K to 398.15 K at a constant pressure of 1.000 atm Integrate on the path representing the actual process b Calculate the entropy change for the reversible process with the same initial and final states as in part a, but in which the gas is first heated at constant pressure and then expanded isothermally Again, integrate on the path representing the actual process Compare your result with that of part a c Calculate the entropy change of the surroundings in each of the parts a and b d Calculate the entropy changes of the system and the surroundings if the initial and final states are the same as in parts a and b, but if the gas is expanded irreversibly and isothermally against an external pressure of 1.000 atm and then heated irreversibly with the surroundings remaining essentially at equilibrium at 400 K a ∆S = 23.55 J K−1, b ∆S = 23.55 J K−1, c ∆Ssurr = −23.55 J K−1 d ∆S = 23.55 J K−1, ∆Ssurr = −18.71 J K−1, ∆Suniv = 4.84 J K−1 Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 3.23 a A sample of 2.000 mol of neon is expanded reversibly and adiabatically from a volume of 10.00 L and a temperature of 500.0 K to a volume of 25.00 L Find the final temperature, q, w, ∆U, ∆S, and ∆Suniv for the process State any assumptions or approximations b The same sample is restored to its original state and is first expanded adiabatically and irreversibly at a constant external pressure of 1.000 atm to a volume of 25.00 L, then cooled reversibly to the same final temperature as in part a at a constant volume of 25.00 L Find the final temperature for the irreversible step, and find q, w, ∆U, and ∆S for this entire two-step process What can you say about ∆Suniv for each step of this two-step process? a T2 = 271.4 K, q = 0, ∆U = −5702 J, w = −5702 J, ∆S = 0, ∆Suniv = b T2 = 439.1 K, ∆S = 0, w = −1520 J, q = −4183 J, ∆U = −5703 J, ∆Suniv = 12.00 J K−1 3.25 A sample of 2.000 mol of a monatomic ideal gas is expanded and heated Its initial temperature is 300.0 K and its final temperature is 400.0 K Its initial volume is 20.00 L and its final volume is 40.00 L Calculate ∆S Does the choice of path between the initial and final states affect the result? ∆S = 18.71 J K−1 6–15 A steam power plant receives heat from a furnace at a rate of 280 GJ/h Heat losses to the surrounding air from the steam as it passes through the pipes and other components are estimated to be about GJ/h If the waste heat is transferred to the cooling water at a rate of 145 GJ/h, determine (a) net power output and (b) the thermal efficiency of this power plant Answers: (a) 35.3 MW, (b) 45.4 percent 6–18 The thermal efficiency of a general heat engine is 35 percent, and it produces 60 Hp At what rate is heat transferred to this engine, in kJ/s? 128 kJ/s 6–19 A 600-MW steam power plant, which is cooled by a nearby river, has a thermal efficiency of 40 percent Determine the rate of heat transfer to the river water Will the actual heat transfer rate be higher or lower than this value? Why? 900 MW In reality the amount of heat rejected to the river will be lower since part of the heat will be lost to the surrounding air from the working fluid as it passes through the pipes and other components 6–21 A heat engine with a thermal efficiency of 45 percent rejects 500 kJ/kg of heat How much heat does it receive? Answer: 909 kJ/kg Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 6–22 A steam power plant with a power output of 150 MW consumes coal at a rate of 60 tons/h If the heating value of the coal is 30,000 kJ/kg, determine the overall efficiency of this plant Answer: 30.0 percent 6–23 An automobile engine consumes fuel at a rate of 22 L/h and delivers 55 kW of power to the wheels If the fuel has a heating value of 44,000 kJ/kg and a density of 0.8 g/cm3, determine the efficiency of this engine Answer: 25.6 percent 6–24 In 2001, the United States produced 51 percent of its electricity in the amount of 1.878 x 1012 kWh from coalfired power plants Taking the average thermal efficiency to be 34 percent, determine the amount of thermal energy rejected by the coal-fired power plants in the United States that year 6–26 A coal-burning steam power plant produces a net power of 300 MW with an overall thermal efficiency of 32 percent The actual gravimetric air–fuel ratio in the furnace is calculated to be 12 kg air/kg fuel The heating value of the coal is 28,000 kJ/kg Determine (a) the amount of coal consumed during a 24-hour period and (b) the rate of air flowing through the furnace Answers: (a) 2.89 106 kg, (b) 402 kg/s 6–34C A heat pump that is used to heat a house has a COP of 2.5 That is, the heat pump delivers 2.5 kWh of energy to the house for each kWh of electricity it consumes Is this a violation of the first law of thermodynamics? Explain No The heat pump captures energy from a cold medium and carries it to a warm medium It does not create it 6–35C A refrigerator has a COP of 1.5 That is, the refrigerator removes 1.5 kWh of energy from the refrigerated space for each kWh of electricity it consumes Is this a violation of the first law of thermodynamics? Explain No The refrigerator captures energy from a cold medium and carries it to a warm medium It does not create it 6–39 Determine the COP of a heat pump that supplies energy to a house at a rate of 8000 kJ/h for each kW of electric power it draws Also, determine the rate of energy absorption from the outdoor air Answers: 2.22, 4400 kJ/h Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 6–42 An air conditioner removes heat steadily from a house at a rate of 750 kJ/min while drawing electric power at a rate of kW Determine (a) the COP of this air conditioner and (b) the rate of heat transfer to the outside air Answers: (a) 2.08, (b) 1110 kJ/min 6–43 A food department is kept at -12 oC by a refrigerator in an environment at 30 oC The total heat gain to the food department is estimated to be 3300 kJ/h and the heat rejection in the condenser is 4800 kJ/h Determine the power input to the compressor, in kW and the COP of the refrigerator 0.417kW, 2.2 6–44 A household refrigerator that has a power input of 450 W and a COP of 1.5 is to cool large watermelons, 10 kg each, to oC If the watermelons are initially at 28 oC, determine how long it will take for the refrigerator to cool them The watermelons can be treated as water whose specific heat is 4.2 kJ/kg·oC Is your answer realistic or optimistic? Explain Answer: 104 This answer is optimistic since the refrigerated space will gain some heat during this process from the surrounding air, which will increase the work load Thus, in reality, it will take longer to cool the watermelons 6–45 When a man returns to his well-sealed house on a summer day, he finds that the house is at 35 oC He turns on the air conditioner, which cools the entire house to 20 oC in 30 If the COP of the air-conditioning system is 2.8, determine the power drawn by the air conditioner Assume the entire mass within the house is equivalent to 800 kg of air for which cv = 0.72 kJ/kg·oC and cp = 1.0 kJ/kg·oC 1.71 kW 6–48 Bananas are to be cooled from 24 to 13 oC at a rate of 215 kg/h by a refrigeration system The power input to the refrigerator is 1.4 kW Determine the rate of cooling, in kJ/min, and the COP of the refrigerator The specific heat of banana above freezing is 3.35 kJ/kg·oC 132 kJ/min, 1.57 6–49 A heat pump is used to maintain a house at a constant temperature of 23 oC The house is losing heat to the outside air through the walls and the windows at a rate of 85,000 kJ/h while the energy generated within the house from people, lights, and appliances amounts to 4000 kJ/h For a COP of 3.2, determine the required power input to the heat pump Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies Answer: 7.03 kW 6–51 A household refrigerator runs one-fourth of the time and removes heat from the food compartment at an average rate of 800 kJ/h If the COP of the refrigerator is 2.2, determine the power the refrigerator draws when running 0.40 kW 6–54 Consider a building whose annual air-conditioning load is estimated to be 40,000 kWh in an area where the unit cost of electricity is $0.10/kWh Two air conditioners are considered for the building Air conditioner A has a seasonal average COP of 2.3 and costs $5500 to purchase and install Air conditioner B has a seasonal average COP of 3.6 and costs $7000 to purchase and install All else being equal, determine which air conditioner is a better buy Energy savings = 6280 kWh/year, cost savings = $628/year, cost difference = $1500 Discussion A cost conscious consumer will have no difficulty in deciding that the more expensive but more efficient airconditioner B is clearly the better buy in this case since air conditioners last at least 15 years But the decision would not be so easy if the unit cost of electricity at that location was much less than $0.10/kWh, or if the annual air-conditioning load of the house was much less than 40,000 kWh 6–55 Refrigerant-134a enters the condenser of a residential heat pump at 800 kPa and 35 oC at a rate of 0.018 kg/s and leaves at 800 kPa as a saturated liquid If the compressor consumes 1.2 kW of power, determine (a) the COP of the heat pump and (b) the rate of heat absorption from the outside air 2.64, 1.96 kW 6–76 A Carnot heat engine receives 650 kJ of heat from a source of unknown temperature and rejects 250 kJ of it to a sink at 24 oC Determine (a) the temperature of the source and (b) the thermal efficiency of the heat engine 772.2 K, 61.5% 6–77 A Carnot heat engine operates between a source at 1000 K and a sink at 300 K If the heat engine is supplied with heat at a rate of 800 kJ/min, determine (a) the thermal efficiency and (b) the power output of this heat engine Answers: (a) 70 percent, (b) 9.33 kW Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 6–82 In tropical climates, the water near the surface of the ocean remains warm throughout the year as a result of solar energy absorption In the deeper parts of the ocean, however, the water remains at a relatively low temperature since the sun’s rays cannot penetrate very far It is proposed to take advantage of this temperature difference and construct a power plant that will absorb heat from the warm water near the surface and reject the waste heat to the cold water a few hundred meters below Determine the maximum thermal efficiency of such a plant if the water temperatures at the two respective locations are 24 and oC 7.1% 6–83 A well-established way of power generation involves the utilization of geothermal energy— the energy of hot water that exists naturally underground—as the heat source If a supply of hot water at 140 oC is discovered at a location where the environmental temperature is 20 oC, determine the maximum thermal efficiency a geothermal power plant built at that location can have Answer: 29.1% 6–84C A homeowner buys a new refrigerator and a new air conditioner Which one of these devices would you expect to have a higher COP? Why? The difference between the temperature limits is typically much higher for a refrigerator than it is for an air conditioner The smaller the difference between the temperature limits a refrigerator operates on, the higher is the COP Therefore, an air-conditioner should have a higher COP 6–92 An air-conditioning system operating on the reversed Carnot cycle is required to transfer heat from a house at a rate of 750 kJ/min to maintain its temperature at 24 oC If the outdoor air temperature is 358C, determine the power required to operate this air-conditioning system Answer: 0.46 kW 6–93 An inventor claims to have developed a heat pump that produces a 200-kW heating effect for a 293 K heated zone while only using 75 kW of power and a heat source at 273 K Justify the validity of this claim Since the actual COP (2.67) is less than the maximum COP (14.7), the claim is valid Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 6–95 A refrigerator is to remove heat from the cooled space at a rate of 300 kJ/min to maintain its temperature at -8 oC If the air surrounding the refrigerator is at 25 oC, determine the minimum power input required for this refrigerator Answer: 0.623 kW 6–100 A refrigerator operating on the reversed Carnot cycle has a measured work input of 200 kW and heat rejection of 2000 kW to a heat reservoir at 27 oC Determine the cooling load supplied to the refrigerator, in kW, and the temperature of the heat source, in oC Answers: 1800 kW, -3 °C 6–104 A Carnot heat pump is to be used to heat a house and maintain it at 25 oC in winter On a day when the average outdoor temperature remains at about oC, the house is estimated to lose heat at a rate of 55,000 kJ/h If the heat pump consumes 4.8 kW of power while operating, determine (a) how long the heat pump ran on that day; (b) the total heating costs, assuming an average price of 11¢/kWh for electricity; and (c) the heating cost for the same day if resistance heating is used instead of a heat pump Answers: (a) 5.90 h, (b) $3.11, (c) $40.3 (1 USD = 100 cent) 6–107 The structure of a house is such that it loses heat at a rate of 3800 kJ/h per oC difference between the indoors and outdoors A heat pump that requires a power input of kW is used to maintain this house at 24 oC Determine the lowest outdoor temperature for which the heat pump can meet the heating requirements of this house Answer: -9.5 oC Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies Chương Phần - Chất khiết 3–20, 21, 23 Complete this table for H2O: 3–26 Complete this table for refrigerant-134a: Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 3–28 A 1.8-m3 rigid tank contains steam at 220 oC One-third 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 P = 2320 kPa, x = 0.0269, d = 287.8 kg/m3 3–29 A piston–cylinder device contains 0.85 kg of refrigerant-134a at 10 oC 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 until the temperature is 15 oC 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 P2 = 90.4 kPa, DV = 0.0205 m3, DH = 17.4 kJ/kg 3–31 10-kg of R-134a fill a 1.348-m3 rigid container at an initial temperature of -40 oC The container is then heated until the pressure is 200 kPa Determine the final temperature and the initial pressure Answers: 66.3 °C, 51.25 kPa 3–39 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 60 percent of the heat generated by the burner is transferred to the water during boiling, determine the rate of evaporation of water mevaporation = 0.80 x10-3 kg/s = 2.872 kg/h Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 3–51 A piston–cylinder device contains 0.005 m3 of liquid water and 0.9 m3 of water vapor in equilibrium at 600 kPa Heat is transferred at constant pressure until the temperature reaches 200 o C (a) What is the initial temperature of the water? (b) Determine the total mass of the water (c) Calculate the final volume (d) Show the process on a P-v diagram with respect to saturation lines T = 158.8 oC, mt = 7.395 kg, V2 = 2.604 m3 3–58 A rigid tank contains water vapor at 250 oC and an unknown pressure When the tank is cooled to 124 oC, the vapor starts condensing Estimate the initial pressure in the tank Answer: 0.30 MPa 3–61 100 grams of R-134a initially fill a weighted pistoncylinder device at 60 kPa and -20 oC The device is then heated until the temperature is 100 oC Determine the change in the device’s volume as a result of the heating Answer: 0.0168 m3 3–64 A piston-cylinder device initially contains 50 L of liquid water at 40 oC and 200 kPa Heat is transferred to the water at constant pressure until the entire liquid is vaporized (a) What is the mass of the water? (b) What is the final temperature? (c) Determine the total enthalpy change (d) Show the process on a T-v diagram with respect to saturation lines Answers: (a) 49.61 kg, (b) 120.21 °C, (c) 125,950 kJ Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies Chương Phần - Các chu trình nhiệt động 10–3 A steady-flow Carnot cycle uses water as the working fluid Water changes from saturated liquid to saturated vapor as heat is transferred to it from a source at 250 oC Heat rejection takes place at a pressure of 20 kPa Show the cycle on a T-s diagram relative to the saturation lines, and determine (a) the thermal efficiency, (b) the amount of heat rejected, and (c) the net work output Answers: (a) 36.3%, (b) 1092.3 kJ/kg, (c) 623.0 kJ/kg 10–5 Consider a steady-flow Carnot cycle with water as the working fluid The maximum and minimum temperatures in the cycle are 350 and 60 oC The quality of water is 0.891 at the beginning of the heatrejection process and 0.1 at the end Show the cycle on a T-s diagram relative to the saturation lines, and determine (a) the thermal efficiency, (b) the pressure at the turbine inlet, and (c) the net work output Answers: (a) 0.465, (b) 1.40 MPa, (c) 1623 kJ/kg 10–6C Consider a simple ideal Rankine cycle with fixed turbine inlet conditions What is the effect of lowering the condenser pressure on Heat rejected decreases; everything else increases Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 10–7C Consider a simple ideal Rankine cycle with fixed turbine inlet temperature and condenser pressure What is the effect of increasing the boiler pressure on Heat rejected decreases; everything else increases 10–8C Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures What is the effect of superheating the steam to a higher temperature on The pump work remains the same, the moisture content decreases, everything else increases 10–12 A steam power plant operates on a simple ideal Rankine cycle between the pressure limits of MPa and 50 kPa The temperature of the steam at the turbine inlet is 300 oC, and the mass flow rate of steam through the cycle is 35 kg/s Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the thermal efficiency of the cycle and (b) the net power output of the power plant 27.1%, 25.2 MW Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 10–13 Refrigerant-134a is used as the working fluid in a simple ideal Rankine cycle which operates the boiler at 2000 kPa and the condenser at 24 oC The mixture at the exit of the turbine has a quality of 93 percent Determine the turbine inlet temperature, the cycle thermal efficiency, and the back-work ratio of this cycle 67.5 oC, 10.7%, rbw = wP,in/wT,out = 0.0530 10–14 A simple ideal Rankine cycle which uses water as the working fluid operates its condenser at 40 oC and its boiler at 300 oC Calculate the work produced by the turbine, the heat supplied in the boiler, and the thermal efficiency of this cycle when the steam enters the turbine without any superheating 974.5 kJ/kg, 2573.4 kJ/kg, 0.375 10–16 Consider a 210-MW steam power plant that operates on a simple ideal Rankine cycle Steam enters the turbine at 10 MPa and 500 oC and is cooled in the condenser at a pressure of 10 kPa Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the quality of the steam at the turbine exit, (b) the thermal efficiency of the cycle, and (c) the mass flow rate of the steam Answers: (a) 0.793, (b) 40.2 percent, (c) 165 kg/s 11–3 A steady-flow Carnot refrigeration cycle uses refrigerant- 134a as the working fluid The refrigerant changes from saturated vapor to saturated liquid at 60 o C in the condenser as it rejects heat The evaporator pressure is 140 kPa Show the cycle on a T-s diagram relative to saturation lines, and determine (a) the coefficient of performance, (b) the amount of heat absorbed from the refrigerated space, and (c) the net work input Answers: (a) 3.23, (b) 106 kJ/kg, (c) 32.9 kJ/kg 11–7C In a refrigeration system, would you recommend condensing the refrigerant-134a at a pressure of 0.7 or 1.0 MPa if heat is to be rejected to a cooling medium at 15 oC? Why? Allowing a temperature difference of 10 oC for effective heat transfer, the condensation temperature of the refrigerant should be 25 oC The saturation pressure corresponding to 25 oC is 0.67 MPa Therefore, the recommended pressure would be 0.7 MPa Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 11–9C Consider two vapor-compression refrigeration cycles The refrigerant enters the throttling valve as a saturated liquid at 30 oC in one cycle and as subcooled liquid at 30 8C in the other one The evaporator pressure for both cycles is the same Which cycle you think will have a higher COP? The cycle that involves saturated liquid at 30 oC will have a higher COP because, judging from the T-s diagram, it will require a smaller work input for the same refrigeration capacity 11–13 An ideal vapor-compression refrigeration cycle that uses refrigerant-134a as its working fluid maintains a condenser at 800 kPa and the evaporator at -12 oC Determine this system’s COP and the amount of power required to service a 150 kW cooling load Answers: 4.87, 30.8 kW 11–14 Consider a 300 kJ/min refrigeration system that operates on an ideal vapor-compression refrigeration cycle with refrigerant-134a as the working fluid The refrigerant enters the compressor as saturated vapor at 140 kPa and is compressed to 800 kPa Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the quality of the refrigerant at the end of the throttling process, (b) the coefficient of performance, and (c) the power input to the compressor Answers: (a) 0.3225, (b) 3.969, (c) 1.260 kW 11–27 A space is kept at -15 oC by a vapor-compression refrigeration system in an ambient at 25 o C The space gains heat steadily at a rate of 3500 kJ/h and the rate of heat rejection in the condenser is 5500 kJ/h Determine the power input, in kW, the COP of the cycle and the secondlaw efficiency of the system 0.5556 kW, 1.75, hII = COPR/COPCarnot = 1.75/6.45 = 27.1% 11–28 Bananas are to be cooled from -8 oC to 12 oC at a rate of 1140 kg/h by a refrigerator that operates on a vaporcompression refrigeration cycle The power input to the refrigerator is 8.6 kW Determine (a) the rate of heat absorbed from the bananas, in kJ/h, and the COP, (b) the minimum power input to the refrigerator, and (c) the second-law efficiency for the cycle The specific heat of bananas above freezing is 3.35 kJ/kg·oC Answers: (a) 61,100 kJ/h, 1.97, (b) 0.463 kW, (c) 5.4 percent Ho Chi Minh City University of Technology Department of Physicochemical & Analytical Technologies 11–39 A heat pump that operates on the ideal vapor compression cycle with refrigerant-134a is used to heat a house and maintain it at 26 oC by using underground water at 14 oC as the heat source Select reasonable pressures for the evaporator and the condenser, and explain why you chose those values Assumptions: 1/ Steady operating conditions exist 2/ Kinetic and potential energy changes are negligible Analysis: Allowing a temperature difference of 10 oC for effective heat transfer, the evaporation and condensation temperatures of the refrigerant should be oC and 36 oC, respectively The saturation pressures corresponding to these temperatures are 338 kPa and 912 kPa Therefore, the recommended evaporator and condenser pressures are 338 kPa and 912 kPa, respectively 11–42 A heat pump that operates on the ideal vaporcompression cycle with refrigerant-134a is used to heat water from 15 to 45 oC at a rate of 0.12 kg/s The condenser and evaporator pressures are 1.4 and 0.32 MPa, respectively Determine the power input to the heat pump Answers: 2.97 kW 11–69 An ideal gas refrigeration cycle using air as the working fluid is to maintain a refrigerated space at -23 oC while rejecting heat to the surrounding medium at 27 oC If the pressure ratio of the compressor is 3, determine (a) the maximum and minimum temperatures in the cycle, (b) the coefficient of performance, and (c) the rate of refrigeration for a mass flow rate of 0.08 kg/s Answers: (a) 342.2 K, 219.0 K, (b) 2.74, (c) 2.49 kJ/s ... isothermally and irreversibly with a constant external pressure of 1. 000 atm a ∆S1 = 5.7632 J K? ?1, ∆S2 = 5.7587 J K? ?1, ∆S3 = −2.3 919 J K? ?1, ∆S4 = −2.9 612 J K? ?1, ∆S5 = −3.3 712 J K? ?1, ∆S6 = −2.7985 J K? ?1. .. Waals: Z = 1. 1434 (0.86% error) Dieterici: Z = 1. 1255 (0. 71% error) Redlich–Kwong: Z = 1. 115 3 (1. 6% error) 1. 39 Find the value of the isothermal compressibility of carbon dioxide gas at 298 .15 K and... 0.857 L b w1 = ? ?14 11 J, w2 = − 312 J, w3 = 11 13 J, w4 = 312 J 3.3 Carbon monoxide is used as the fuel for a Carnot engine with a high temperature of 450 oC and a cool temperature of 10 0 oC Determine