Fuel:n(CO)?0.12n(CO2)?0.24n(H2)?0.04n(N2)?0.6Air:Flue: n(O)?0.08 n(CO2)?0.36
2n(N2)?0.32n(H2O)?0.04n(N2)?0.92?H??HCO?CO2??HH2?H2O?0.12?(393.51?110.523)?0.04?(241.8?0)?43.6308KJ?CP,r,ini?0.36CCO2?0.04CH2O?0.92CN2?0.36?57?0.04?50?0.92?34?53.8(J/K)3
?T?43.6308?1053.8?810(K)T?1108.98(K)(b)repeat the calculation for 30% excess0combustion air at 298K
?H??HCO?CO2??HH2?H2O?0.12?(393.51?110.523)?0.04?(241.8?0)?43.6308KJ?CP,r,ini?0.36CCO2?0.04CH2O?1.016CN2?0.024CO2?0.36?57?0.04?50?1.016?34?0.024?34?57.88(J/K)?T?43.6308?1057.883?753.8(K)T?1051.8(K)Fuel:n(CO)?0.12n(CO2)?0.24n(H2)?0.04n(N2)?0.6Air: n(O2)?0.104
Flue:n(CO2)?0.36n(H2O)?0.04n(N2)?1.016n(O2)?0.024April 18, 2013
n(N2)?0.416
(C)what is the adiabatic flame temperature when the blasp furnace gas is preheated to 700K (the dry air is at 298K)
Fuel:n(CO)?0.12 n(O)?0.08 n(CO2)?0.36
2n(CO2)?0.24n(H2O)?0.04n(H2)?0.04n(N2)?0.6?H??HCO?CO2Air:Flue:n(N2)?0.32n(N2)?0.92??HH2?H2O??Hfuel700?298?0.12?(393.51?110.523)?0.04?(241.8?0)?(700?298)?(0.12?33?0.24?57?0.04?28?0.6?34)?59.373KJ
?CP,r,ini?0.36CCO2?0.04CH2O?0.96CN2?0.36?57?0.04?50?0.92?34?53.8(J/K)3?T?59.373?1053.8?1103.6(K)T?1401.6(K)(d) suppose the combustion air is not dry ( has partial pressure of water 15 mm Hg and a total pressure of 760 mm Hg) how will the flame temperature be affected?
Fuel:Air:Flue:n(CO)?0.12 n(O2)?0.08n(N2)?0.32n(CO2)?0.24n(H2)?0.04n(N2)?0.6 n(CO2)?0.36
n(H2O)?0.048150.4?0.008n(H2O)?760?15n(N2)?0.92?H??HCO?CO2??HH2?H2O?0.12?(393.51?110.523)?0.04?(241.8?0)?43.6308KJ?CP,r,ini?0.36CCO2?0.048CH2O?0.92CN23
?0.36?57?0.048?50?0.92?34?54.2(J/K)?T?43.6308?1054.2?805(K)T?1103(K)1.12 A bath of molten copper is super cooled to 5℃ below its true melting point. Nucleation of solid copper then takes place, and the solidification proceeds under adiabatic conditions. What percentage of the bath solidifies? DATA: Heat of fusion for copper is 3100 cal/mol at 1803℃(the melting point of copper) CP,L=7.5(cal/mol℃), CP,S=5.41+(1.5*10-3T )(cal/mol℃) Solution
18031798HHLS,1803LS,1798??1798CP,SdT??1803CP,LdT?HL,1798?0?3S
2?3100?5.41?5?1.5?10(18032?1798)?0.5?7.5?5?3103(cal/mol)1.13 Cuprous oxide (Cu2O) is being reduced by hydrogen in a furnace at 1000K, (a)write the chemical reaction for the reduced one mole of Cu2O
(b)how much heat is release or absorbed per mole reacted? Given the quantity of heat and state whether heat is evolved (exothermic reaction) or absorbed (endothermic reaction)
DATA: heat of formation of 1000K in cal/mol Cu2O=-41900 H2O=-59210 solution
Cu2O?H2?Cu?H2O?H?59210?41900?17310(cal/mol),exothermic reaction
1.14(a) what is the enthalpy of pure, liquid aluminum at 1000K?
(b) an electric resistance furnace is used to melt pure aluminum at the rate of 100kg/h. the furnace is fed with solid aluminum at 298K. The liquid aluminum leaves the furnace at 1000K. what is the minimum electric powder rating (kW) of furnace.
DATA : For aluminum : atomic weight=27g/mol, Cp,s=26(J/molK), Cp,L=29(J/molK), Melting point=932K, Heat of fusion=10700J/mol Solution
Hl,1000?9321000?298CP,SdT??932CP,LdT?HLS?26?(932?298)?29?(1000?932)?10700?27184(J/mol)P?2718427?1000?13600?279.7(W)?0.28(kW)
1.15 A waste material (dross from the melting of aluminum) is found to contain 1 wt% metallic aluminum. The rest may be assumed to aluminum oxide. The aluminum is finely divided and dispersed in the aluminum oxide; that is the two material are thermally connected.
If the waster material is stored at 298K. what is the maximum temperature to which it may rise if all the metallic aluminum is oxidized by air/ the entire mass may be assumed to rise to the same temperature. Data : atomic weight Al=27g/mol, O=16g/mol, Cp,s,Al=26(J/molK), Cp,s, Al2O3=104J/mol, heat formation of Al2O3=-1676000J/mol
1676000?127?21??16?1.5?2727102?99?104??TSolution;
?T?302(K)T?600(K)
1.16 Metals exhibit some interesting properties when they are rapidly solidified from the liquid state. An apparatus for the rapid solidification of copper is cooled by water. In the apparatus, liquid copper at its melting point (1356K) is sprayed on a cooling surface, where it solidified and cools to 400K. The copper is supplied to the apparatus at the rate of one kilogram per minute. Cooling water is available at 20℃, and is not allowed to raise above 80℃. What is the minimum flow rate of water in the apparatus, in cubic meters per minute? DATA; for water: Cp=4.184J/g k, Density=1g/cm3; for copper: molecular weight=63.54g/mol Cp=7cal/mol k, heat of fusion=3120 cal/mol
QCopper/min?[3120?7?(1356?400)]?100063.54?minSolution:QWater/min?1(80?20)V?3
V?2.573?10(m/min)31.17 water flowing through an insulated pipe at the rate of 5L/min is to be heated from 20℃ to 60℃ b an electrical resistance heater. Calculate the minimum power rating of the resistance heater in watts. Specify the system and basis for you calculation. DATA; For water Cp=4.184J/g k, Density=1g/cm3 Solution: W?4.184?(60?20)?5?100060?13947(W)
1.18 The heat of evaporation of water at 100℃ and 1 atm is 2261J/mol (a) what percentage of that energy is used as work done by the vapor?
(b)if the density of water vapor at 100℃ and 1 atm is 0.597kg/m3 what is the internal energy change for the evaporation of water?
P?V?101325?373273?0.0224?3101(J/mol)Solution:
%?31012261?18?7.6%
?U?W?Q??3101?2261?18?37597(J/mol)1.19 water is the minimum amount of steam (at 100℃ and 1 atm pressure) required to melt a kilogram of ice (at 0℃)? Use data for problem 1.20
Solution m(2261?4.18?100)?1000?334,m?125(g)
1.20 in certain parts of the world pressurized water from beneath the surface of the earth is available as a source of thermal energy. To make steam, the geothermal water at 180℃ is passed through a flash evaporator that operates at 1atm pressure. Two streams come out of the evaporator, liquid water and water vapor. How much water vapor is formed per kilogram of geothermal water? Is the process reversible? Assume that water is incompressible. The vapor pressure of water at 180℃ is 1.0021 Mpa( about 10 atm) Data: CP,L=4.18J/(g k), CP,v=2.00J/(g k), △HV=2261J/g, △Hm=334 J/g Solution:
(2261?2?80?4.18?80)x?4.18?80?(1000?x),x?138(g)irreversible
The problems of the second law
2.1 The solar energy flux is about 4J cm2/min. in no focusing collector the surface temperature can reach a value of about 900℃. If we operate a heat engine using the collector as the heat source and a low temperature reservoir at 25℃, calculate the area of collector needed if the heat engine is to produce 1 horse power. Assume the engine operates at maximum efficiency.
W?TH?TLTHWtQH?(90?25)90?273?4?10460StSolution
P??746(W)2
S?6.25(m)2.2 A refrigerator is operated by 0.25 hp motor. If the interior of the box is to be maintained at -20℃ ganister a maximum exterior temperature of 35℃, what the maximum heat leak (in watts) into the box that can be tolerated if the motor runs continuously? Assume the coefficient of performance is 75% of the value for a reversible engine.
W?TH?TLTHQHSolution:
0.75P?PL?34?TH?TLTL35?20
PL?0.25?746?643(W)273?202.3 suppose an electrical motor supplies the work to operate a Carnot refrigerator. The interior of the refrigerator is at 0℃. Liquid water is taken in at 0℃ and converted to ice at 0℃. To convert 1 g of ice to 1 g liquid. △H=334J/g is required. If the temperature outside the box is 20℃, what mass of ice can be produced in one minute by a 0.25 hp motor running continuously? Assume that the refrigerator is perfectly insulated and that the efficiencies involved have their largest possible value.
P?TH?TLTL27320PLSolution:
PL??0.25?746?334m
M?60m?457(g)2.4 under 1 atm pressure, helium boils at 4.126K. The heat of vaporization is 84 J/mol what size motor (in hp) is needed to run a refrigerator that must condense 2 mol of gaseous helium at 4.126k to liquid at the same temperature in one minute? Assume that the ambient temperature is 300K and that the coefficient of performance of the refrigerator is 50% of the maximum possible.
W?50%TH?TLTLTLQLPL?300?4.2164.216?84?2 60Solution:
0.5P'?P?TH?TLP'?393(W)?0.52(hp)2.5 if a fossil fuel power plant operating between 540 and 50℃ provides the electrical power to run a heat pump that works between 25 and 5℃, what is the amount of heat pumped into the house per unit amount of heat extracted from the power plant boiler.
(a) assume that the efficiencies are equal to the theoretical maximum values
(b) assume the power plant efficiency is 70% of maximum and that coefficient of performance of the heat pump
is 10% of maximum
(c) if a furnace can use 80% of the energy in fossil foe to heat the house would it be more economical in terms of
overall fissile fuel consumption to use a heat pump or a furnace ? do the calculations for cases a and b solution:
(a)P1?P2?TH,1?TL,1TH,1TH,2PH,1TH,2?TL,2
PH,2(b)P1?P2540?50540?273PH,1?25?5273?25PH,2 P?0.6286PH,2H,1(c)aisok,bisnot.
PH,2?8.98PH,12.6 calculate △U and △S when 0.5 mole of liquid water at 273 K is mixed with 0.5 mol of liquid water at 373 K and the system is allowed to reach equilibrium in an adiabatic enclosure. Assume that Cp is 77J /(mol K) from 273K to 373K Solution:
?U?0(J)?S?n1CPln(TET1)?n2CPln(TET2)?0.5CPln(323373)?0.5CPln(323273)?0.933(J/K)
2.7 A modern coal burning power plant operates with a steam out let from the boiler at 540℃ and a condensate temperature of 30℃.
(a) what is the maximum electrical work that can be produced by the plant per joule of heat provided to the
boiler?
(b) How many metric tons (1000kg) of coal per hour is required if the plant out put is to be 500MW (megawatts).
Assume the maximum efficiency for the plant. The heat of combustion of coal is 29.0 MJ/k g
(c) Electricity is used to heat a home at 25℃ when the out door temperature is 10℃ by passing a current
through resistors. What is the maximum amount of heat that can be added to the home per kilowatt-hour of electrical energy supplied?
(a)(c)TH?TLTHTLTH?TLQH?540?30540?301?0.89(J)
Solution:W(b)?
W?TH?TLTHQH1?19.9(J)
29.0m?500?3600QH?273?2525?10m?69371(kg)?69.3(ton)2.8 an electrical resistor is immersed in water at the boiling temperature of water (100℃) the electrical energy input into the resistor is at the rate of one kilowatt
(a) calculate the rate of evaporation of the water in grams per second if the water container is insulated that is no
heat is allowed to flow to or from the water except for that provided by the resistor
(b) at what rate could water could be evaporated if electrical energy were supplied at the rate of 1 kw to a heat
pump operating between 25 and 100℃
data for water enthalpy of evaporation is 40000 J/mol at 100℃; molecular weight is 18g/mol; density is 1g/cm3 solution:
(a)(b)m18m1840000?1000,m?0.45(g)40000?1000100?273100?25,m?2.23(g)
2.9 some aluminum parts are being quenched (cooled rapidly ) from 480℃ to -20℃ by immersing them in a
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