南昌大学材料热力学答案.doc

The problems of the first law
1.1 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 4.8kJ/mol. The molar heat capacity CP of lead may be taken as 29.3J/(mol K)
铅子弹射向一个寒冷的表面。在什么速度必须前往融化的影响,如果它的初始温度是25℃,加热的刚性表面刚性表面被忽视?铅的熔点为327℃。的摩尔熔化热铅是4.8焦每摩尔。摩尔热容CP的铅可能作为29.3 j /(摩尔K)
Solution:
1.2 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 the rate of 20 m/min
什么是平均功率的生产在一个人谁燃烧2500千卡的食品在一天的瓦特？估计平均加粉生产75公斤人谁是登高山以20米/分的速度
Solution
1.3 One cubic decimeter (1 dm3) of water is broken into droplets having a diameter of one micrometer (1 um) at 20℃.
(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 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)
水一立方分米（1立方分米）被分成20℃，直径一微米（1微米）的液滴。
（一）什么是液滴的总面积？
（b）计算需要产生的液滴的最小工作。假定液滴垫（具有零速度）
水具有72.75达因/厘米的表面张力在20℃（注：术语表面能量（烯/厘米2）也可用于表面张力达因/厘米）
Solution
1.4 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 pressure 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 the helium entering the quench chamber when the pressure in the tank has fallen to 1 atm?
气态氦被用于骤冷一热的金属片。氦是在存储在隔热的罐体积为50升和25℃的温度下，压力为10个大气压。假设氦是一种理想的气体。
（a）该阀打开，气体逃逸到激冷室中（压力=1atm）中，这将是第一气体的打试样的温度时？
（b）由于在氦气流，在罐中的压力下降。会是怎样进入骤冷室中的氦气的温度时，在罐中的压力降低到1个大气压？
Solution:
1.5 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 oðened and the surrounding gas is allowed to flow suickly into t(e tank until the pressure insi`e the tank is equals the pressure outside. Assume that no heat flow takes place. What is the0final tempeture kf tèe gaS in the tank? The heat cap!city mf the gas, Cp and Cv each íay be(assumed to be c/nsuantp and SvMhint: one way to approach the xroblem is to define the system as the gas ends up in the tank.
抽成真空（P= 0），辱骂箱由在温度T0的一个非常大的量的理想气体的（假定无限量包围。水箱上的阀是oðened和周围的气体被允许流动suickly成吨（例如罐，直到压力insi`e罐是等于外界压力。假定没有热流发生。这是the0final tempeture kf的TEE气？！在罐中的热帽城市MF的气体，Cp和CV每个IAY被（假定为c/ nsuantp和SvMhint：接近xroblem的一种方法是定义系统作为气体结束了在罐中。
solution
1.6 Calculate the heat of reaction of methane with oxygen at 298K, assuming that the products of reaction are CO2 and CH4 (gas)[This 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 1atm
计算的甲烷与氧气的反应热在298K，假定反应的产物是二氧化碳和甲烷（天然气）[反应的该热也被称为甲烷的低发热量]转换的答案为英制热量单位/ 1000的SCF联信甲烷。 SCF是指标准立方英尺在298和1大气压采取
NOTE: this value is a good approximation for the low calorific powder of natural gas
DATA:
solution1.7 Methane is delivered 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)
(a) Assuming complete combustion, 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) assuming 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 800K
甲烷输送在298K到玻璃工厂，而经营一个熔化炉，在1600 K的燃料与空气的量在298 K，这是10％的过量理论上所需要的完整的燃烧量（混合时，也空气是约21％的O 2和79％N 2）
（一）假设完全燃烧，什么是烟道气（燃气燃烧以下）的组成？
（二）什么是气体的温度，假设没有热损失？
（三）炉处理的玻璃2000公斤每小时，并且它的热损失到周围环境中的平均400000千焦耳/小时。在计算STP的燃油消耗（以m3/ h）的假设气体H1600-H298=1200KJ/ KG
（d）一个热交换器安装将一些烟道气的显热的燃烧空气。计算燃料消耗的降低，如果燃烧空气被加热到800K
DATA STP means T=298K, P=1atm

Solution

1.8 In an investigation of the thermodynamic 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 tempeture rang.
Solution
1.9 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 supplied to the furnace per cu. ft of exhaust gas

Solution
1.10 (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 air enter there burner at 298 K, what is the highest temperature the flame may attain (adiabatic flame temperature)?
（a）在该反应中，什么是在298K反应（）的焓？
（b）一种燃料气体，以组合物中50％的CO，50％的N 2是利用空气的化学计量量的燃烧。什么是烟道气的组合物？
（c）如果燃料气体和空气进入燃烧器有在298K，什么是火焰可能达到的最高温度（绝热火焰温度）？
DATA :standard heats of formation at 298 K

Heat capacities [J/(mol K)] to be used for this problem N2=33, O2=33, CO=34, CO2=57
Solution
1.11 a particular blast furnace gas has the following 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 is 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 dlaMe temperature be affected?
DaTA(k J?mol)
EMBED Equation.3 EMBED Equation.3 5
Solution

EMBED Equation.3
(b)repeat the calculation for 30% excess0combustion air at 298K
EMBED Equation.3 

(C)what is the adiabatic flame temperature when the blasp 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?

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
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)
氧化亚铜（氧化亚铜正被在一炉中于1000K降低氢，
（一）写为氧化亚铜的减少一摩尔化学反应
（二）有多少热量释放或每摩尔吸收反应的？鉴于热量和状态量的热量是否演变（放热反应）或吸收（吸热反应）
DATA: heat of formation of 1000K in cal/mol Cu2O=-41900 H2O=-59210
solution,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
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
Solution;
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
Solution:
1.17 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:
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?
Solution:
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
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:
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.
太阳能通量为约4J平方厘米/分钟。在没有聚焦集电极的表面温度可达到约900℃的值。如果操作使用集电极作为热源和低温贮存器的热机，在25℃，计算所需集电极的面积如果与热机是产生1马力。假设在发动机工作在最大效率。
Solution
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.
一台冰箱由0.25马力电机。如果该箱的内部被保持在-20℃ganister的35℃的最高表面温度，什么最大热泄漏（以瓦特为单位）到可容忍的盒子，如果马达连续运行？假定的性能系数为一可逆发动机的值的75％。
Solution:
2.3 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.
Solution:
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.
Solution:
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
如果化石燃料电厂的540和50℃运行提供了电力运行的热泵是25和5℃之间工作，什么是热抽的热量进入屋内每单位量的电厂中提取的金额锅炉。
（一）假设效率是等于最大理论值
（二）假设的电厂效率达到最大的70％，而热泵的性能系数是最大值的10％
（c）若一炉可以使用能量的化石敌人80％，以加热房子会是更经济的整体裂变燃料消耗使用热泵或熔炉的条件？做计算的情况下，A和B
solution:

2.6 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:
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?
Solution:
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) calcu