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.
Trang 1Bài tập Hoá lý 1 (Physical Chemistry 1 - Homework) Chương 1 Các khái niệm và tính chất chung của các 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
a Find the volume of 1 mol of ethanol at 10 oC and 1 atm
b Find the volume of 1mol of ethanol at 30 oC and 1 atm
Trang 21.37 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#
𝑅𝑇 = 1 +
𝐵+
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 m 6 mol −2 , b = 5.192 × 10 −5 m 3 mol −1 , b Z = 0.7305
Trang 3Chương 2 Nguyên lý thứ nhất nhiệt động - Cân bằng năng lượng của hệ thống
2.1 Calculate the work done on the surroundings if 1 mol of neon (assumed ideal) is heated from 0 oC to 250 oC at a constant pressure of 1 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
q = 120.9 kJ, w = −8.771 kJ
2.19 Calculate q, w, and ∆U for melting 100 g of ice at 0 oC and a constant pressure of 1 atm The density of ice is 0.916 g mL−1
q = 33.35 kJ, w = 0.92 J, ∆U = 33.35 kJ
Trang 42.21.* Consider the following three processes:
(1) A sample of 2 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 1 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 2 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 2 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 1 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
Trang 52.45 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 2 mol of solid water (ice) at −10 oC is turned into liquid water at 80 oC, with the process at a constant pressure of 1 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
Trang 6Chương 3 Nguyên lý thứ 2 của 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 1 horsepower = 746 watt = 746 J s−1
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
Trang 7a ηc = 0.01649, b dV/dt = 1.45 × 103 m 3 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 1 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 =
a ∆S = 217.98 J K −1 , b ∆S = 16.54 J K −1
Trang 83.19
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 > 0
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
Trang 93.23 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 = 0
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?
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
Trang 106–22 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 1012kWh 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 3 106 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 1 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 1 kWh of electricity it consumes Is this a violation of the first law
Answers: 2.22, 4400 kJ/h
Trang 116–42 An air conditioner removes heat steadily from a house at a rate of 750 kJ/min while drawing electric power at a rate of 6 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 5 large watermelons, 10 kg each, to 8 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 min
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 min 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