材料热力学习题答案1

1、The problems of the first law1. a lead bullet is fired at a frigid surface. At what speed must it travel to melt on impact, if its initial temperature is 25 and heating of the rigid surface of the rigid surface is neglected? The melting point of lead is 327. The molar heat of fusion of the lead is 4

2、.8kJ/mol. The molar heat capacity CP of lead may be taken as 29.3J/(mol K) (1.1)Solution: 2. what is the average power production in watts of a person who burns 2500 kcal of food in a day? Estimate the average additional powder production of 75Kg man who is climbing a mountain at eh rate of 20 m/min

3、 (1.2)Solution 3 One cubic decimeter (1 dm3) of water is broken into droplets having a diameter of one micrometer (1 um) at 20. (1.3)(a) what is the total area of the droplets?(b) Calculate the minimum work required to produce the droplets. Assume that the droplets are rest (have zero velocity)Water

4、 have a surface tension of 72.75 dyn/cm at 20 (NOTES: the term surface energy (ene/cm2) is also used for surface tension dyn/cm)Solution 4.Gaseous helium is to be used to quench a hot piece of metal. The helium is in storage in an insulated tank with a volume of 50 L and a temperature of 25, the pre

5、ssure is 10 atm. Assume that helium is an ideal gas.(a) when the valve is opened and the gas escapes into the quench chamber (pressure=1 atm), what will be the temperature of the first gas to hit the specimen?(b) As the helium flows, the pressure in the tank drops. What will be the temperature of th

6、e helium entering the quench chamber when the pressure in the tank has fallen to 1 atm? (1.4)Solution: 5 An evacuated (P=0), insulted tank is surrounded by a very large volume (assume infinite volume) of an ideal gas at a temperature T0. The valve on the tank is opened and the surrounding gas is all

7、owed to flow quickly into the tank until the pressure inside the tank is equals the pressure outside. Assume that no heat flow takes place. What is the final tempeture of the gas in the tank? The heat capacity of the gas, Cp and Cv each may be assumed to be constant over the temperature rang spanned

8、 by the experiment. You answer may be left in terms of Cp and Cvhint: one way to approach the problem is to define the system as the gas ends up in the tank. (1.5)solution 6. Calculate the heat of reaction of methane with oxygen at 298K, assuming that the products of reaction are CO2 and CH4 (gas)Th

9、is heat of reaction is also called the low calorific power of methane convert the answer into unites of Btu/1000 SCF of methane. SCF means standard cubic feet, taken at 298 and 1atmNOTE: this value is a good approximation for the low calorific powder of natural gas (1.6)DATA: solution7. Methane is d

10、elivered at 298 K to a glass factory, which operates a melting furnace at 1600 K. The fuel is mixed with a quantity of air, also at 298 K, which is 10% in excess of the amount theoretically needed for complete combustion (air is approximately 21% O2 and 79% N2) (1.7)(a) Assuming complete combustion,

11、 what is the composition of the flue gas (the gas following combustion)?(b) What is the temperature of the gas, assuming no heat loss?(c) The furnace processes 2000kg of glass hourly, and its heat losses to the surroundings average 400000 kJ/h. calculate the fuel consumption at STP (in m3/h) assumin

12、g that for gas H1600-H298=1200KJ/KG(d) A heat exchanger is installed to transfer some of the sensible heat of the flue gas to the combustion air. Calculate the decrease in fuel consumption if the combustion air is heated to 800KDATA STP means T=298K, P=1atm Solution8.In an investigation of the therm

13、odynamic properties of a-manganese, the following heat contents were determined:H700-H298=12113 J/(g atom)H1000-H298=22803 J/(g atom)Find a suitable equation for HT-H298 and also for CP as a function of temperature in the form (a+bT) Assume that no structure transformation takes place in the given t

14、empeture rang. (1.8)Solution 9.A fuel gas containing 40% CO, 10% CO2, and the rest N2 (by volume) is burnt completely with air in a furnace. The incoming and ongoing temperatures of the gases in the furnace are 773K and 1250K,respectively. Calculate (a) the maximum flame temperature and (b) heat sup

15、plied to the furnace per cu. ft of exhaust gas (1.9) Solution 10. (a) for the reaction ,what is the enthalpy of reaction () at 298 K ?(b) a fuel gas, with composition 50% CO, 50% N2 is burned using the stoichiometric amount of air. What is the composition of the flue gas?(c) If the fuel gas and the

16、air enter there burner at 298 K, what is the highest temperature the flame may attain (adiabatic flame temperature)?DATA :standard heats of formation at 298 K (1.10)Heat capacities J/(mol K) to be used for this problem N2=33, O2=33, CO=34, CO2=57Solution 11.a particular blast furnace gas has the fol

17、lowing composition by (volume): N2=60%, H2=4, CO=12%, CO2=24% (a) if the gas at 298K is burned with the stochiometric amount of dry air at 298 K, what is the composition of the flue gas? What is the adiabatic flame temperature?(b) repeat the calculation for 30% excess combustion air at 298K(C)what i

18、s the adiabatic flame temperature when the blast furnace gas is preheated to 700K (the dry air is at 298K)(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? DATA(k J/mol) （1.11） Solution 12

19、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 copp

20、er)CP,L=7.5(cal/mol), CP,S=5.41+(1.5*10-3T )(cal/mol) （1.12）Solution13Cuprous 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

21、whether heat is evolved (exothermic reaction) or absorbed (endothermic reaction)DATA: heat of formation of 1000K in cal/mol Cu2O=-41900 H2O=-59210 （1.13）solution,exothermic reaction14. (a) what is the enthalpy of pure, liquid aluminum at 1000K?(b) an electric resistance furnace is used to melt pure

22、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 fusi

23、on=10700J/mol (1.14)Solution15 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 was

24、ter 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 o

25、f Al2O3=-1676000J/mol (1.15)Solution;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 surf

26、ace, 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=

27、4.184J/g k, Density=1g/cm3; for copper: molecular weight=63.54g/molCp=7cal/mol k, heat of fusion=3120 cal/mol (1.16)Solution: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 (1.17)Solution: 18 The heat of evaporation of water at 100 and 1 atm is 2261J/mol(a) what percentage of that e