chapter6 phase equilibrium-1
曼昆微观经济学教材第六章练习英文答案
104WHAT’S NEW IN THE SIXTH EDITION:There is a new In the News feature on “Should Unpaid Internships Be Allowed ？”LEARNING OBJECTIVES ：By the end of this chapter ， students should understand:➢ the effects of government policies that place a ceiling on prices.➢ the effects of government policies that put a floor under prices 。
➢ how a tax on a good affects the price of the good and the quantity sold 。
➢ that taxes levied on sellers and taxes levied on buyers are equivalent 。
➢ how the burden of a tax is split between buyers and sellers.CONTEXT AND PURPOSE ：Chapter 6 is the third chapter in a three —chapter sequence that deals with supply and demand and how markets work 。
Chapter 4 developed the model of supply and demand 。
Chapter 5 added precision to the model of supply and demand by developing the concept of elasticity-the sensitivity of the quantity supplied and quantity demanded to changes in economic conditions 。
物理化学课件19-4化学平衡-符号
rGmθ RT ln K θ
三、rGmθ 的用途
1、计算平衡常数
Kθ
exp
r Gmθ RT
2、利用 rGmθ 估计反应的可能性
K θ Q spontaneous K θ Q can’t proceed forward
K θ Q eq.
dS系统 + dS环境 ≥0 dGT,p,W’=0 ≤0 ΣμBdnB ≤0 QP≤ Kpθ
aeq B B
意义：K = Qeq，是平衡位置的标志
二、影响K 的因素 (Effect factors of K)
1、温度： ln Kθ rGmθ
RT
d ln K θ dT
1 R
d dT
r
Gθ m
T
1
Hθ
r
m
R T2
Gibbs-Helmholtz formula
d ln Kθ dT
r
H
θ m
▲ 对高压气体反应： 须比较新状态时的Kθ和Q
3. 浓度对平衡的影响 表现为影响Q c反↑(or c产↓) eq→ c产↑(or c反↓) eq←
应用广泛： 例如，化工生产中不按计量比投料
A(廉价) + B(昂贵) →P
A过量
反应耦合
4. 惰性气体对平衡的影响：
(1) 等压下加入惰性气体： 相当于 p↓对eq的影响
1 x
1 x y
x2y x
(2) 2CH3OH(g) (CH3 )2 O(g) H2O(g)
x - 2y
y
1- x y
因为两个反应的 B 都等于零，所以 K θ (1) (x 2 y)x 0.00154
B
(1 x)(1 x y)
上海交通大学_材料科学基础第六章
纯金属结晶，液－固共存，f =0，说明结晶为恒温。 二元系金属结晶两相平衡，f =2-2+1=1，说明有一个可变因素(T)，表明 它在一定（T）范围内结晶。 二元系三相平衡，f =2-3+1=0，此时温度恒定，成分不变，各因素恒定。
Page 8
相率的应用
• 相律是检验、分析和使用相图的重要工具。利用它可以分 析和确定系统中可能存在的相数，检验和研究相图。
6.1.1 相平衡条件和相律
• 相平衡的条件：通过一些数学推导和系统平衡条件dG=0可 得：处于平衡状态下的多相(P个相)体系中，每个组元(共 有C个组元)在各相中的化学势（chemical potential）都彼此 相等。
• 相平衡(phase equilibrium)是一种动态平衡。
Page 6
第六章 单组元相图 及纯晶体的凝固
Page 1
本章要求掌握的内容
• 应掌握的内容:
– 纯金属凝固的过程和现象 – 结晶的热力学、动力学、能量、和结构条件 – 过冷度对结晶过程和结晶组织的影响；过冷度、临界过冷度、有效过
冷度、动态过冷度之间的区别。 – 几个重要概念：过冷度，临界晶核半径，临界形核功，形核率，均匀
Page 20
Page 21
6.2.2 晶体凝固的热力学条件
自由能
G H TS
dG Vdp SdT
在等压时，dp＝0， 所以可推导得：
dG S dT
由于熵S恒为正值，所以自由能是随温度增高而减小。
Page 22
在一定温度下，从一相转变为另一相的自由能变化为
G H TS
令液相转变为固相后的单位体积自由能变化为 GV ，则
曼昆经济学原理-第六章-供给、需求与政府政策
3. ..更少地由 Demand 生产者承担.
Quantity
供给缺乏弹性,需求富有弹性...
Price Price buyers pay Price without tax
Price sellers receive
1. 当需求比供给富有弹性时...
Supply
3. ...更少地由
Tax
消费者承担.
S1
没有税收时的均衡
Demand, D1
0
90 100
Quantity of
Ice-Cream Cones
工薪税
Wage
企业支付的工 资
没有税收时的 工资
工人得到的工资
税收楔子
0
Labor supply
Labor demand
Quantity of Labor
税收归宿
税收负担在市场参与者之间进行分 配的比例? 与向买者征税相比，向卖者征税的 效果如果？
向卖者征0.5美元的影响...
Price of Ice-Cream
Cone
Price buyers
pay
$3.30
Price without
tax
3.00 2.80
Price sellers receive
有税收时的均衡 Tax ($0.50)
向卖者征税使供给
S2 曲线向上移动，移
动幅度为税收量 ($0.50).
80
Quantity demanded
120
Quantity supplied
Demand
Quantity of Ice-Cream
Cones
Effects of a Price Floor
Chapter6 凝聚态物理导论(中科院研究生院)
Chapter 6 Magnetism of MatterThe history of magnetism dates back to earlier than 600 B.C., but it is only in the twentieth century that scientists have begun to understand it, and develop technologies based on this understanding. Magnetism was most probably first observed in a form of the mineral magnetite called lodestone, which consists of iron oxide-a chemical compound of iron and oxygen. The ancient Greeks were the first known to have used this mineral, which they called a magnet because of its ability to attract other pieces of the same material and iron.The Englishman William Gilbert(1540-1603) was the first to investigate the phenomenon of magnetism systematically using scientific methods. He also discovered that Earth is itself a weak magnet. Early theoretical investigations into the nature of Earth's magnetism were carried out by the German Carl Friedrich Gauss(1777-1855). Quantitative studies of magnetic phenomena initiated in the eighteenth century by Frenchman Charles Coulomb(1736-1806), who established the inverse square law of force, which states that the attractive force between two magnetized objects is directly proportional to the product of their individual fields and inversely proportional to the square of the distance between them.Danish physicist Hans Christian Oersted(1777-1851) first suggested a link between electricity and magnetism. Experiments involving the effects of magnetic and electric fields on one another were then conducted by Frenchman Andre Marie Ampere(1775-1836) and Englishman Michael Faraday(1791-1869), but it was the Scotsman, James Clerk Maxwell(1831-1879), who provided the theoretical foundation to the physics of electromagnetism in the nineteenth century by showing that electricity and magnetism represent different aspects of the same fundamental force field. Then, in the late 1960s American Steven Weinberg(1933-) and Pakistani Abdus Salam(1926-96), performed yet another act of theoretical synthesis of the fundamental forces by showing that electromagnetism is one part of the electroweak force. The modern understanding of magnetic phenomena in condensed matter originates from the work of two Frenchmen: Pierre Curie(1859-1906), the husband and scientific collaborator of Madame Marie Curie(1867-1934), and Pierre Weiss(1865-1940). Curie examined the effect of temperature on magnetic materials and observed that magnetism disappeared suddenly above a certain critical temperature in materials like iron. Weiss proposed a theory of magnetism based on an internal molecular field proportional to the average magnetization that spontaneously align the electronic micromagnets in magnetic matter. The present day understanding of magnetism based on the theory of the motion and interactions of electrons in atoms (called quantum electrodynamics) stems from the work and theoretical models of two Germans, Ernest Ising and Werner Heisenberg (1901-1976). Werner Heisenberg was also one of the founding fathers of modern quantum mechanics.Magnetic CompassThe magnetic compass is an old Chinese invention, probably first made in China during the Qin dynasty (221-206 B.C.). Chinese fortune tellers used lodestonesto construct their fortune telling boards.Magnetized NeedlesMagnetized needles used as direction pointers instead of the spoon-shaped lodestones appeared in the 8th century AD, again in China, and between 850 and 1050 they seemto have become common as navigational devices on ships. Compass as a Navigational AidThe first person recorded to have used the compass as a navigational aid was Zheng He (1371-1435), from the Yunnan province in China, who made seven ocean voyages between 1405 and 1433.有关固体磁性的基本概念和规律在上个世纪电磁学的发展史中就开始建立了。
Phase diagrams 相图
Chapter 6 – Phase diagrams
§6-1 General concept
§6-2 Level rule 杠杆规则
§6-3 One-component systems 单组分系统相图 §6-4 Two-component systems 二组分系统相图
§6-1 General concept
l
p
P
e
T
§6-1 General concept
The simplest application of thermodynamics to chemically significant systems are to the discussion of the phase transitions of pure substances Phase - 相 Phase diagram - 相图 Boundaries between regions – 边界 Vapor pressure – temperature Melting point – pressure A phase transition - the spontaneous conversion of one phase into another phase, occurs at a characteristic temperature for a given pressure. Transition temperature – is the temperature at which the two phases are in equilibrium and the Gibbs energy is minimized at the prevailing pressure
物理化学英文6相平衡 Phase Equilibrium
• the solute is non-volatile, i.e. the vapor phase is pure solvent.
• the solute is insoluble in the solid solvent, i.e. solid phases are pure substances.
p /torr
800
700
600
500
400
300
200
100
0
0.0
0.2
0.4
0.6
0.8
1.0
xethyl acetate
Raoult’s Law
• The vapor pressure of a substance varies linearly with its mole fraction in solution.\
p* DP
p
Vm (l)dp Vm (g)dp
p*
p*
p
Vm (l)DP RT dp / p p*
ln( p / p* ) VmDP RT
Phase Equilibrium
Binary mixtures
liq vap Eq. in Binary Mixtures
• Both the liquid and the vapor phase are binary mixtures of A and B.
• In pure liquid B, there are only B-B interactions.
• In solutions of A and B, there are A-B interactions as well.
经济学原理 曼昆课后答案 chapter 6
Problems and Applications1. If the price ceiling of $40 per ticket is below the equilibrium price, then quantitydemanded exceeds quantity supplied, so there’s a shortage of tickets. The policydecreases the number of people who attend classical music concerts, since supply islower because of the lower price.2. a. The imposition of a binding price floor in the cheese market is shown in Figure6-3. In the absence of the price floor, the price would be P1 and the quantitywould be Q1. With the floor set at P f, which is greater than P1, the quantitydemanded is Q2, while quantity supplied is Q3, so there is a surplus of cheese inthe amount Q3 - Q2.b. The farmers’ complaint that their total revenue has declined is correct ifdemand is elastic. With elastic demand, the percentage decline in quantitywould exceed the percentage rise in price, so total revenue would decline.c. If the government purchases all the surplus cheese at the price floor,producers benefit and taxpayers lose. Producers would produce quantity Q3of cheese, and their total revenue would increase substantially. Butconsumers would buy only quantity Q2 of cheese, so they are in the sameposition as before. Taxpayers lose because they would be financing thepurchase of the surplus cheese through higher taxes.Figure 6-33. a. The equilibrium price of frisbees is $8 and the equilibrium quantity is 6 millionfrisbees.b. With a price floor of $10, the new market price is $10 since the price floor isbinding. At that price, o nly 2 million frisbees are sold, since that’s thequantity demanded.c. If there’s a price ceiling of $9, it has no effect, since the market equilibriumprice is $8, below the ceiling. So the equilibrium price is $8 and theequilibrium quantity is 6 million frisbees.4. a. Figure 6-4 shows the market for beer without the tax. The equilibrium priceis P1 and the equilibrium quantity is Q1. The price paid by consumers is thesame as the price received by producers.Figure 6-4Figure 6-5b. When the tax is imposed, it drives a wedge of $2 between supply and demand,as shown in Figure 6-5. The price paid by consumers is P2, while the pricereceived by producers is P2 - $2. The quantity of beer sold declines to Q2.5. Reducing the payroll tax paid by firms and using part of the extra revenue to reducethe payroll tax paid by workers would not make workers better off because the division of the burden of a tax depends on supply and demand, not who must pay the tax.Since the tax wedge would be larg er, it’s likely that both firms and workers, who share the burden of any tax, would be worse off.6. If the government imposes a $500 tax on luxury cars, the price paid by consumers willrise less than $500, in general. The burden of any tax is shared by both producersand consumers−the price paid by consumers rises and the price received by producers falls, with the difference between the two equal to the amount of the tax. The onlyexceptions would be if the supply curve were perfectly elastic or the demand curvewere perfectly inelastic, in which case consumers would bear the full burden of the tax and the price paid by consumers would rise by exactly $500.7. a. It doesn’t matter whether the tax is imposed on producers or consumers−theeffect will be the same. With no tax, as shown in Figure 6-6, the demandcurve is D1 and the supply curve is S1. If the tax is imposed on producers, thesupply curve shifts up by the amount of the tax (50 cents) to S2. Then theequilibrium quantity is Q2, the price paid by consumers is P2, and the pricereceived (after taxes are paid) by producers is P2 - 50 cents. If the tax isinstead imposed on consumers, the demand curve shifts down by the amountof the tax (50 cents) to D2. The downward shift in the demand curve (whenthe tax is imposed on consumers) is exactly the same magnitude as theupward shift in the supply curve when the tax is imposed on producers. Soagain, the equilibrium quantity is Q2, the price paid by consumers is P2(including the tax paid to the government), and the price received byproducers is P2 - 50 cents.Figure 6-6Figure 6-7b. The more elastic is the demand curve, the more effective this tax will be inreducing the quantity of gasoline consumed. Greater elasticity of demandmeans that quantity falls more in response to the rise in the price of gasoline.Figure 6-7 illustrates this result. Demand curve D1 represents an elasticdemand curve, while demand curve D2 is more inelastic. To get the same tax wedge between demand and supply requires a greater reduction in quantitywith demand curve D1 than for demand curve D2.c. The consumers of gasoline are hurt by the tax because they get less gasolineat a higher price.d. Workers in the oil industry are hurt by the tax as well. With a lower quantityof gasoline being produced, some workers may lose their jobs. With a lowerprice received by producers, wages of workers might decline.8. a. Figure 6-8 shows the effects of the minimum wage. In the absence of theminimum wage, the market wage would be w1 and Q1 workers would beemployed. With the minimum wage (w m) imposed above w1, the marketwage is w m, the number of employed workers is Q2, and the number ofworkers who are unemployed is Q3 - Q2. Total wage payments to workers areshown as the area of rectangle ABCD, which equals w m times Q2.b. An increase in the minimum wage would decrease employment. The size ofthe effect on employment depends only on the elasticity of demand. Theelasticity of supply doesn’t matter, because there’s a surplus of labor.c. The increase in the minimum wage would increase unemployment. The sizeof the rise in unemployment depends on both the elasticities of supply anddemand. The elasticity of demand determines the quantity of labordemanded, the elasticity of supply determines the quantity of labor supplied,and the difference between the quantity supplied and demanded of labor is theamount of unemployment.d. If the demand for unskilled labor were inelastic, the rise in the minimum wagewould increase total wage payments to unskilled labor. With inelasticdemand, the percentage decline in employment would be less than thepercentage increase in the wage, so total wage payments increase. However,if the demand for unskilled labor were elastic, total wage payments woulddecline, since then the percentage decline in employment would exceed thepercentage increase in the wage.Figure 6-8Figure 6-99. a. Figure 6-9 shows the effect of a tax on gun buyers. The tax reduces thedemand for guns from D1 to D2. The result is a rise in the price buyers pay forguns from P1 to P2, and a decline in the quantity of guns from Q1 to Q2.Figure 6-10b. Figure 6-10 shows the effect of a tax on gun sellers. The tax reduces thesupply of guns from S1 to S2. The result is a rise in the price buyers pay forguns from P1 to P2, and a decline in the quantity of guns from Q1 to Q2.c. Figure 6-11 shows the effect of a binding price floor on guns. The increase inprice from P1 to P f leads to a decline in the quantity of guns from Q1 to Q2.There is excess supply in the market for guns, since the quantity supplied (Q3) exceeds the quantity demanded (Q2) at the price P f.Figure 6-11Figure 6-12d. Figure 6-12 shows the effect of a tax on ammunition. The tax on ammunitionreduces the demand for guns from D1 to D2, because ammunition and guns arecomplements. The result is a decline in the price of guns from P1 to P2, and adecline in the quantity of guns from Q1 to Q2.10. a. Programs aimed at making the public aware of the dangers of smoking reducethe demand for cigarettes, shown in Figure 6-13 as a shift from demand curveD1 to D2. The price support program increases the price of tobacco, which isthe main ingredient in cigarettes. As a result, the supply of cigarettes shifts tothe left, from S1 to S2. The effect of both programs is to reduce the quantityof cigarette consumption from Q1 to Q2.Figure 6-13b. The combined effect of the two programs on the price of cigarettes isambiguous. The education campaign reduces demand for cigarettes, whichtends to reduce the price. The tobacco price supports raise the cost ofproduction of cigarettes, which tends to increase the price.c. The taxation of cigarettes further reduces cigarette consumption, since itincreases the price to consumers. As shown in the figure, the quantity falls toQ3.11. a. The effect of a 50 cent per cone subsidy is to shift the demand curve up by 50cents at each quantity, since at each quantity a consumer’s willingness to payis 50 cents higher. The effects of such a subsidy are shown in Figure 6-14.Before the subsidy, the price is P1. After the subsidy, the price received bysellers is P S and the effective price paid by consumers is P D, which equals P Sminus 50 cents. Before the subsidy, the quantity of cones sold is Q1; after thesubsidy the quantity increases to Q2.Figure 6-14b. Because of the subsidy, consumers are better off, since they consume more ata lower price. Producers are also better off, since they sell more at a higherprice. The government loses, since it has to pay for the subsidy.。
第六章 相平衡(二)
19
§6-7 二组分固态不互 溶系统液－固平衡相图
20
二组分液态完全互溶而固态完 全不互溶系统液－ 全不互溶系统液－固相图 具有低共熔点的固态不互溶凝聚系统
21
一、相图分析
a、b—纯物质熔点 E—低共熔点 纯物质熔点 低共熔点 aE、bE—溶液凝固点随溶液 aE、bE 溶液凝固点随溶液 组成变化关系；固体A 组成变化关系 ； 固体 A、B 在 溶液中的溶解度随温度的变 S’ 化关系。 化关系。 CED—三相平衡线 CED 三相平衡线 F＝2－3＋1＝0 冷却过程: 冷却过程 c→d B(s) 析出 →e nL/nS=eS’/eL’ →f l→A(s)+B(s) 过f点：液相消失 点
23
24
讨论： 讨论：
由上述冷却曲线可以看到 转折点（ 1）若冷却曲线上出现转折点（即曲线斜率发生改变）， ）若冷却曲线上出现转折点 即曲线斜率发生改变）， 则系统内必发生了相数的改变（有新相生成或旧相消失） 则系统内必发生了相数的改变（有新相生成或旧相消失） 相数的改变 2）若冷却曲线上出现水平线段，则系统的自由度数 若冷却曲线上出现水平线段 水平线段， F=0，若单组分系统是两相共存， 为F=0，若单组分系统是两相共存，二组分系统是三 相共存。 相共存。
30
L1
l+C(s) A(s)+C(s) Q l+B(s) C(s)+B(s)
L2
c’
A
C
xB
点、线、面
H2SO4·4H2O
H2SO4·H2O H2SO4·2H2O
水−硫酸二元系相图
31
二、生成不稳定化合物
d e d e 分解温度— 分解温度 不相合熔点
O1
关于教案的确切定义和内容
关于“教案”1999年版《辞海》下册第4177页对“教案”的定义：教案——教师以课时或课题为单位编制的教学具体方案。
上课的重要依据，保证教学质量的重要措施。
可分为课题计划和课时计划。
有时仅指课时计划，一般包括班级、学科名称、课时和教学目标、课的类型、课的进程（包括教学内容、教学方法、时间分配、作业题、师生活动设计）、教具等。
课程教学方案（简称教案）内容1．课程简介●课程名称：分离工程(Separation Processes)●课程类型：专业课●课程内容简介分离工程在化工生产中占有十分重要的地位，在提高生产过程的经济效益和产品质量中起举足轻重的作用。
对大型的石油工业和以化学反应为中心的石油化工生产过程，分离装置的费用占投资的50%—90%。
分离工程是化工类本科生在学习物理化学、化工原理及化工热力学的基础上开设的一门重要的课程。
研究和处理分离过程开发和设计中遇到的工程问题，包括适宜分离方法的选择，分离流程和操作条件的确定。
分离过程的实验研究方法和设计计算等。
有利于学生工程能力的培养。
●课时：32●学分：2●班级：化学工程与工艺、三年级●教材：Separation Process Principles, J.D. Seader, Ernest J. Henley, 化学工业出版社，北京，2002.●参考书：Chemical Engineering Volume 2, 5th Edition, J F Richardson, J H Harker, John Backhurst, Butterworth-Heinemann, Oxford, 2002《化工分离工程》，邓修，吴俊生主编，科学出版社，北京，2000●考核方式：闭卷考试●教师姓名：陈鸿雁2．教学大纲与教学进程●本讲教学内容章、节教学内容：见教学大纲（Separation Processes Syllabus）●教学日历：见教学日历和教学简历3．教学具体方案（每“两节课”为“一讲”，每讲填一张表）●本讲教学内容●本讲知识点、重点、难点●本讲教学方法与教学手段●本讲多媒体（或ppt）课件●本讲师生互动设计●本讲作业题●本讲与上一讲衔接，与下一讲的联系华东理工大学课堂教学方案设计表华东理工大学课堂教学方案设计表华东理工大学课堂教学方案设计表华东理工大学课堂教学方案设计表华东理工大学课堂教学方案设计表。
物理专业英语名词解释
part one mechanics力学chapter 1 kinematics—uniformly accelerated motion运动学，匀加速运动frame of reference: 参照系position vector and displacement 位置向量和位移speedvelocity 速度instantaneous velocity瞬时速度velocity components速度分量acceleration 加速度graphical interpretation图像释义uniformly accelerated motion along a straight line 匀加速直线运动acceleration due to gravity (g) 重力加速度projectile problems落体问题relative motion相对运动chapter 2 dynamics-- newton's laws of motion动力学- 牛顿运动定律general properties of forces in mechanics:力的基本性质1 the law of universal gravitation万有引力定律2the weight 重量3 the tensile force 拉力4 the normal force 法向力5 the friction force 摩擦力6 dimensional analysis三维分析chapter 3 equilibrium平衡concurrent forces共点力are forces whose lines of action all pass through a common point. the forces acting on a point object are concurrent because they all pass through the same point, the point object.equilibrium 平衡rigid body刚体the torque (or moment) 转矩或力矩the two conditions for equilibrium 平衡的两个条件the center of gravity 重心axis轴chapter 4 work and energy功和能kinetic energy (ke) 动能conservative force保守力⑵gravitational (weight) potential energy (peg) 重力（重量）势能⑵elastic potential energy 弹性势能the efficiency 效率chapter 5 impulse and momentumthe linear momentum 冲量与动量an impulse 冲量collisions and explosions碰撞和爆炸a perfectly elastic collision 完全弹性碰撞coefficient of restitution恢复系数the center of mass重心chapter 6 rotation转动the angular speed 角速度the angular acceleration 角加速度tangential 【数】切线;正切centripetal acceleration ( )加速度the centripetal force 向心力chapter 7 rigid-body rotation刚体转动the moment of inertia 转动惯量parallel-axis theorem平行轴定理chapter 8 elasticity弹性elasticity弹性;弹力the stress 【物】应力[u][c]strain 应变the elastic limit弹性极限the shear modulus 切变模量standard atmospheric pressure标准大气压the hydrostatic pressure静水压力equation of continuity连续性方程the viscosity 粘度spring弹簧a restoring force 恢复力simple harmonic motion 简谐运动vibratory motion 振动运动the period ( ) 【数】循环节;周期the frequency ( ) 频率the elastic potential energy 弹性势能the simple pendulum 单摆chapter 11 wave motion波动a propagating wave 波传播wave terminology波术语in-phase vibrations同相振动standing waves驻波conditions for resonance共振的条件longitudinal (compressional) waves 纵向（挤压）波chapter 12 sound声音the intensey （i）强度loudness 响度beats节拍doppler effect 多普勒效应interference effects 干扰效应part two thermodynamics热力学chapter 1 the kinetic theory of gases第1章气体动力学理论avogadro's number ( ) 阿伏伽德罗数（）the root mean square speed根均方速度the absolute temperature绝对温度the mean free path (m.f.p.) 平均自由程（m.f.p.）the equipartition theorem of energy 能量均分定理ideal gas law理想气体定律heat 热the internal energy 内部能量an isobaric process is a process carried out at constant pressure. 等压过程是恒压进行的过程。
多恩布什《宏观经济学》(英文第八版)答案-第六章
Chapter 6 Solutions to the Problems in the Textbook:Conceptual Problems:1. The aggregate supply curve and the Phillips curve describe very similar relationships and bothcurves can be used to analyze the same phenomena. The AS-curve shows a relationship between the price level and the level of output. The Phillips curve shows a relationship between the rate of inflation and the unemployment rate, given certain inflationary expectations. For example, a movement along the AS-curve depicts an increase in the price level that is associated with an increase in the level of output. As output increases, the rate of unemployment decreases (see Okun’s law).Therefore, with a larger increase in the price level (a higher level of inflation) there will be a decrease in unemployment, creating a downward-sloping Phillips curve.This downward sloping Phillips curve shifts whenever inflationary expectations change. If one assumes that workers will change their wage demands whenever their inflationary expectations change, one can conclude that a shift in the Phillips curve corresponds to a shift in the upward sloping AS-curve, since higher wages mean higher cost of production.2. In the short run, when wages and prices are assumed to be fixed, there can be no inflation and thusthe Phillips curve makes no sense over this very brief time frame. But in the medium run (in this chapter also often referred to as the short run), the Phillips curve is downward sloping as inflationary expectations are assumed to be constant. In the long run, the Phillips curve is vertical at the natural rate of unemployment, which corresponds to the vertical long-run AS-curve at the full-employment level of output.3. A variety of explanations are given in this chapter for the stickiness of wages in the short orintermediate run. One is that workers have imperfect information and nobody knows the actual price level. People don’t know whether a change in their nominal wage is the result of an increase in prices or in the real wage they receive for the work they provide. Due to this uncertainty, labor markets will not clear immediately. Another argument relies on coordination problems, that is, different firms within an economy cannot coordinate price changes in response to monetary policy changes.Individual firms change their prices only reluctantly, since they are afraid of losing market share. The efficiency wage theory argues that employers pay above market-clearing wages to motivate their workers to work harder. Firms are also reluctant to change wages because of the perceived menu costs involved. There are long-term relations between firms and workers and wages are usually set in nominal terms by wage contracts, which are renegotiated only periodically. Thus real wages fluctuate over time as the price level changes. Finally, the insider-outsider model argues that firms negotiate only with their own employees but not with unemployed workers. Since a turnover in the labor force is costly to firms, they are willing to offer above market-clearing wages to the currently employed rather than hiring the unemployed who may be willing to work for lower wages.These different views are not necessarily mutually exclusive and it is up to students to decide which of the arguments presented here they find most plausible. The explanations differ mainly in their assumption of how fast markets clear and whether employment variations are voluntary.4.a. Stagflation is defined as a period of high unemployment accompanied by high inflation.4.b. Stagflation can occur in time periods when people have high inflationary expectations. If theeconomy goes into a recession, the actual rate of inflation will fall below the expected rate of inflation.However, the actual inflation rate may still be very high while the rate of unemployment is increasing.For example, the Fed may have let money supply grow much too fast in the past, so everyone expectsa high inflation rate. If a supply shock occurs, we will see an increase in the rate of unemploymentwhile inflationary expectations and actual inflation remain very high. This scenario occurred during the 1970s. Once we have reached such a situation, it becomes necessary to design policies that will reduce inflationary expectations to shift the Phillips curve back to the left.5. Assume a disturbance occurs and the AD-curve shifts to the right. Unemployment decreases andinflation increases, and we move along the downward sloping Phillips curve to the left. However, as soon as people realize that actual inflation is higher than their inflationary expectations, they adjust their inflationary expectations upward and the downward-sloping Phillips curve shifts to the right, eventually returning unemployment back to its natural rate. In other words, the economy adjusts back at the full-employment level of income.If an adverse supply shock occurs (the upward-sloping AS-curve shifts to the left), unemployment and inflation increase simultaneously. This will correspond to a shift of the downward-sloping Phillips curve to the right. However, when people realize that actual inflation is less than expected inflation, then the downward-sloping Phillips curve starts to shift back and the economy adjusts back to the natural rate of unemployment in the long run.6.The expectations-augmented Phillips curve predicts that inflation will rise above the expected levelwhen unemployment drops below its natural rate. However, if people know that this is going to happen, why don’t they immediately adjust to it? And if people immediately adjusted to it, wouldn’t this imply that anticipated monetary policy would be ineffective to cause any deviation from the full-employment level of output? In reality, however, even if people have rational expectations, they may not be able to adjust immediately. One reason is that wage contracts often set wages for an extended time period. Similarly, prices cannot always be changed right away and the costs of changing prices may outweigh the benefits. A further argument is that even rational people make forecasting mistakes and learn only slowly.In other words, the location of the expectations-augmented Phillips curve is determined by the level of expected inflation, which is set by recent historical experience. A shift in this curve caused by changing inflationary expectations occurs only gradually. The rational expectations model, on the other hand, assumes that the Phillips curve shifts almost instantaneously as new information about the near future becomes available.Technical Problems:1. A reduction in the supply of money leads to excess demand for money and increased interest rates,reducing the level of private spending (especially investment). Therefore the AD-curve shifts to the left. This causes an excess supply of goods and services at the original price level so the price level starts to decrease. Since the AS-curve is upward sloping, a new short-run macro-equilibrium is reached at a lower level of output (and thus a higher level of unemployment) and a lower price level.PP1However, the higher level of unemployment eventually puts downward pressure on wages, reducing the cost of production and shifting the upward-sloping AS-curve to the right. Alternatively, since this equilibrium output level is below the full-employment level, prices will continue to fall, and the upward-sloping AS-curve will shift to the right. As long as output is below the full-employment level Y*, the upward-sloping AS-curve will continue to shift to the right, which means that the price level will continue to decline. Eventually a new long-run equilibrium will be reached at the full-employment level of output (Y*) and a lower price level.2. According to the rational expectations theory, an announced change in monetary policy wouldimmediately change people’s perception in regard to the expected inflation rate. If people could adjust immediately to this change in inflationary expectations, then the rate of unemployment or the output level would remain the same. In other words, we would immediately move from point 1 to point 3 in the diagram used to explain the previous question and the Fed would be unable to affect the unemployment rate. In reality, however, even if people have rational expectations and can anticipate the effects of a policy change correctly, they may not be able to immediately adjust due to wage contracts, etc. Thus, there will always be some deviation from the full-employment output level Y*.3.a. A favorable supply shock, such as a decline in material prices, shifts the upward-sloping AS-curve tothe right, leading to excess supply at the existing price level. A new short-run equilibrium is reached at a higher level of output and a lower price level. But since output is now above the full-employment level Y*, there is upward pressure on wages and prices and the upward-sloping AS-curve shifts back to the right. A new long-run equilibrium is reached back at the original position (Y*), and the original price level (assuming that the change in material prices did not affect the full-employment level of output). Since nominal wages (W) will have risen but the price level (P) will not have changed, real wages (W/P) will have increased.PP1P20 13.b. Lower material prices lower the cost of production, shifting the upward-sloping AS-curve shiftsto the right, and leading to an increase in output and a lower price level. Since unemployment is now below its natural rate, there is a shortage of labor, providing upward pressure on wages. This will increase the cost of production again, eventually shifting the upward-sloping AS-curve back to the original long-run equilibrium (assuming that potential GDP has not been affected).Additional Problems:1. Explain the long-run effect of an increase in nominal money supply on the amount of realmoney balances available in the economy.In the very short run, the price level is fixed, so if nominal money supply (M) increases, a higher level of real money balances is available, causing interest rates to fall and the level of investment spending to increase. This leads to an increase in aggregate demand. The shift to the right of the AD-curve causes the price level (P) to increase, leading to a reduction in real money balances (M/P). In the medium run (an upward-sloping AS-curve), we reach a new equilibrium at a higher output level and a higher price level. Since prices have gone up proportionally less than nominal money supply, real money balances have increased. However, to reach a new long-run equilibrium, prices have to increase further, and as a result, the level of real money balances will decrease further. When the new long-run equilibrium at Y* is finally reached, the price level will have risen proportionally to nominal money supply and the level of real money balances will be back at its original level.2. Assume the economy is in a recession. Describe an adjustment process that will ensure that theeconomy eventually will return to full employment. How can the government speed up this process?If the economy is in a recession, there will be downward pressure on wages and prices, which will bring the economy back to the full-employment output level. The upward-sloping AS-curve will shift to the right due to lower production costs. However, this process may take a fairly long time. The government can shorten this adjustment process with the help of expansionary fiscal or monetary policies to stimulate aggregate demand. The resulting shift to the right of the AD-curve implies that the final long-run equilibrium will be at a higher price level. In other words, the reduction in unemployment can only be achieved at the cost of higher inflation.3. "The stickiness of wages implies that policy makers can achieve low unemployment only if theyare willing to put up with high inflation." Comment on this statement.There are several explanations of why wages and prices adjust only slowly. One is that workers have imperfect information, so they do not realize that lower prices mean higher real wages. Another is that firms are reluctant to change prices and wages since they are unsure about the behavior of their competitors and want to avoid the perceived cost of making these changes. Finally, wage contracts tend to be long-term and staggered, so it takes time to adjust wages to price changes. Some firms may pay their workers above market-clearing wages to keep them happy and productive. For these reasons, wages and prices tend to be rigid in the short run. Thus it takes time for the economy to adjust back to full-employment.If there were a stable Phillips-curve relationship, a low rate of unemployment could only be achieved by allowing inflation to increase. However, such a stable relationship does not exist. Wages tend to be rigid in the short run, so expansionary policies lower unemployment and increase inflation in the short run. In the long run, however, the economy will adjust back to the natural rate of unemployment, so expansionary policies simply lead to a higher price level.4. "If we assume that people have rational expectations, then fiscal policy is always irrelevant.But monetary policy can still be used to affect the rate of inflation and unemployment."Comment on this statement.Individuals and firms with rational expectations consistently make optimal decisions based on all information available. As long as a policy change is anticipated, people are able to assess its long-run outcome and will try to immediately adjust. Since fiscal policy doesn't affect inflation or unemployment in the long run, it is also ineffective in the short run if wages and prices are assumed to be flexible. An anticipated change in monetary growth, on the other hand, will be reflected in a change in the inflation rate. If wages are flexible, workers will adjust their wage demands immediately and no significant change in the unemployment rate will occur. However, even if people have rational expectations, wages tend to be fairly rigid in the short run due to wage contracts. Therefore, it will take time for the economy to adjust back to a long-run equilibrium. This implies that both fiscal and monetary policy can affect the rate of inflation and unemployment to some degree in the short run.5. "Inflation cannot accelerate in a recession, when the rate of unemployment is above its naturalrate." Comment on this statement.Inflation can accelerate even in a recession, that is, when the unemployment is high, if a supply shock occurs. An oil price increase will increase the cost of production, so the upward-sloping AS-curve will shift to the left. This will increase the inflation rate and the rate of unemployment simultaneously, as firms increase their product prices and cut their production. If the Fed tries to accommodate the supply shock with expansionary monetary policy in an effort to stimulate the economy, then inflation will accelerate even more, as the AD-curve shifts to the right.6. Comment on the following statement:"The coordination approach to the Phillips curve focuses on the problems that the administration has in coordinating its fiscal policies with the monetary policies of the Fed." The coordination approach has nothing to do with fiscal or monetary policy but is simply one explanation of why wages adjust slowly. This view asserts that firms generally are unable to coordinate wage and price changes in response to a monetary policy change. For example, any firm that cuts workers' wages in response to monetary contraction while other firms don't, will anger its employees who may then choose to leave. Firms are also reluctant to change their prices since they are unsure about their competitors' behavior. Thus wages and prices change only slowly in response to a change in aggregate demand. This implies an upward-sloping (short-run) AS-curve.7. Comment on the following statement:"The unemployment rate is zero at the full-employment level of output."With a higher price level real wages decline, increasing the quantity of labor demanded. Therefore the nominal wage rate is bid up until the real wage rate is restored to its unique equilibrium level. Similarly, if prices fall, real wages increase, leading to unemployment. The nominal wage rate falls to bring the real wage rate back to its equilibrium level. So the nominal wage rate changes in proportion to the price level to maintain a real wage rate that clears the labor market. At this wage rate, the full-employment level of output is produced. However, at the full-employment output level the unemployment rate is not zero. Due to frictions in the labor market, there is always a positive unemployment rate, as workers switch between jobs. This is called the natural rate of unemployment.8. Briefly state the reason for the slow adjustment of wages to changes in aggregate demand. The reasons for the slow adjustment of nominal wages can be explained in several ways. One explanation is that workers have imperfect information, that is, they do not immediately realize whether a change in their nominal wage is the result of an increase in prices or in the real wage they receive for the work they provide. Another explanation is that coordination problems exist, that is, different firms within an economy are unsure about the behavior of their competitors and thus they only reluctantly change wages or prices. The efficiency wage theory, on the other hand, argues that firms pay above market-clearing wages to motivate their workers to work harder. Firms are also reluctant to change wages due to the perceived cost of doing so. Another argument is that wage contracts tend to be long-term, so real wages tend to fluctuate over the length of the contract and output adjusts only slowly to price changes. Finally, the insider-outsider model argues that firms negotiate only with their employees but not the unemployed. Since a turnover of the labor force is costly to firms, they are willing to offer above market-clearing wages to the currently employed rather than hiring the unemployed who may be willing to work for less. These various explanations are not mutually exclusive, and they all imply that the AS-curve is positively sloped, that is, that a change in aggregate demand will affect both output and prices in the short run.9. True or false? Why?"There is no frictional unemployment at the natural rate of unemployment."False. The natural rate of unemployment is the rate at which the labor market is in equilibrium. But there is always some unemployment due to new entrants into the labor force, people between jobs, and the like.This rate of unemployment is considered normal, due to frictions in the labor market, and is often called frictional unemployment.10. "If everyone in this economy had rational expectations, then wages would be flexible andunemployment could not occur." Comment on this statement.The new Keynesian models argue that even if people have rational expectations, socially undesirable outcomes may still occur due to imperfect competition and the existence of wage contracts. Prices may not change freely, since firms in imperfectly competitive markets are reluctant to change them, due to the menu costs involved. Nominal wages are set by contracts over a period of time, so the economy may adjust only slowly to a decrease in aggregate demand. Thus a rate of unemployment higher than the natural rate can exist over an extended period of time.11. True or false? Why?"If nominal wages were more flexible, expansionary policies would be more effective in reducing the rate of unemployment."False. In Chapter 5 we learned that in the classical case (where nominal wages are completely flexible) the AS-curve is vertical, whereas in the Keynesian case (where wages do not change, even if unemployment persists) the AS-curve is horizontal. From this we can conclude that more flexible nominal wages imply a steeper upward-sloping AS-curve. Any type of expansionary demand-side policy will shift the AD-curve to the right and this will cause the level of output and prices to increase (at least in the short-run). A steeper upward-sloping AS-curve results in a larger price increase and a smaller increase in output. But a smaller increase in the level of output results in a smaller reduction in unemployment. In either case, the economy will settle back at the full-employment level of output in the long run. In the long run, the rate of unemployment always goes back to its natural level.12. Explain the short-run and long-run effects of an increase in the level of government spendingon output, unemployment, interest rates, prices, and real money balances.An increase in government spending increases aggregate demand, shifting the AD-curve to the right. Because there is excess demand, the price level increases, which reduces the level of real money balances. Therefore interest rates increase, leading to some crowding out of investment. Due to this real balance effect, the increase in output is less than the shift in the AD-curve. Assuming an upward-sloping AS-curve, a new equilibrium is reached at a higher price level, a higher level of output, a lower unemployment rate and a higher interest rate. Since output is now above the full-employment level, wages and prices will continue to rise and the upward-sloping AS-curve will start shifting to the left. This process will continue until a new long-run equilibrium is reached at the full-employment level of income Y*, that is, until unemployment is back at its natural rate. At this point the price level, nominal wages, and interest rates will be higher than previously and real money balances will be lower.13. Briefly explain why there seems to be so much interest in finding ways to shift theupward-sloping aggregate supply curve to the right.Shifting the upward-sloping AS-curve to the right seems to be the only way to offset the effects of an adverse supply shock without any negative side effects. An adverse supply shock, such as an increase in oil prices, causes a simultaneous increase in unemployment and inflation, and policy makers have only two options for demand-management policies. Expansionary fiscal or monetary policy will help to achieve full employment faster but will raise the price level, while restrictive fiscal or monetary policy will reduce inflationary pressure but increase unemployment. Therefore, any policy that would shift the upward sloping AS-curve back to the right seems preferable, since it might bring the economy back to the original equilibrium by simultaneously lowering inflation and unemployment.14. Use an AD-AS framework to show the effect of monetary restriction on the level of output,prices and the interest rate in the medium and the long run.A decrease in nominal money supply will increase interest rates, leading to a decrease in investment spending. This will shift the AD-curve to the left, creating an excess supply of goods and services. Therefore price level will decrease and real money balances will increase. A new equilibrium will be achieved at the intersection of the new AD-curve and the upward-sloping AS-curve at an output level that is below the full-employment level.In the long run, higher unemployment will cause downward pressure on wages. As the cost of production decreases, the upward-sloping AS-curve will keep shifting to the right until a new long-run equilibrium is established at the full-employment level of output, that is, where the new AD-curve intersects the long-run vertical AS-curve at Y*. At this point, real output, the real interest rate, real money balances, and the real wage rate will be back at their original level. Nominal money supply, the price level and the nominal wage rate will all have decreased proportionally.A simplified adjustment can be shown as follows:1-->2: Ms down ==> i up ==> I down ==> Y down ==> the AD-curve shifts left ==>excess supply ==> P down ==> real ms up ==> i down ==> I up ==> Y up(The first line describes a policy change, that is, a shift in the AD-curve; the second line describes the price adjustment, that is, a movement along the AD-curve.)Short-run effect:Y down, i up, P down2-->3: Since Y < Y* ==> downwards pressure on nominal wages ==> cost of production down ==> the short run AS-curve shifts right ==> excess supply of goods ==> P down ==> real ms up==> i down ==> I up ==> Y up (This process continues until Y = Y*)Long-run effect:Y stays at Y*, i remains the same, P down.Note: Even though only one shift of the short-run AS-curve to the new long-run equilibrium is shown here, this shift is actually a combination of many shifts.P2P1P2P30 215. Briefly discuss the importance of Okun’s law in evaluating the cost of unemployment.Okun’s law states that a reduction in the unemployment rate of 1 percent will increase the level of output by about 2 percent. This relationship allows us to measure the cost to society (in terms of lost production) of a given rate of unemployment.16. True or false? Why?"If monetary policy accommodates an adverse supply shock, it will worsen any inflationary effects."True. An adverse supply shock shifts the upward-sloping AS-curve to the left. There is excess demand for goods and services at the original price level and prices start to rise, leading to lower real money balances, higher interest rates, and lower output. If no policy is implemented, then unemployment will force the nominal wage down to restore equilibrium at the original position. If the government views this adjustment process as too slow, it can respond by implementing expansionary policies. Accommodating the supply shock in this way shifts the AD-curve to the right and a new equilibrium can be reached at full-employment but at a higher price level. It is unlikely, though, that the economy will remain there for long since workers will realize that their purchasing power has been diminished by higher prices and will demand a wage increase. If they are successful, the cost of production will increase and the upward-sloping AS-curve will shift to the left again. In other words, we will enter a wage-price spiral.PP3P2P1217. Assume oil prices decline. What kind of monetary policy should the Fed undertake if its goal isto stabilize the level of output while keeping inflation low? Show with the help of an AD-AS diagram and briefly explain the adjustment process.1-->2: As oil prices decline, the cost of production decreases and the upward-sloping AS-curve shifts to the right, causing excess supply of goods. Thus the price level decreases, real money balances increase, and the interest rate declines.2-->3: A decrease in money supply will increase the interest rate, decrease private spending, and shift the AD-curve to the left. This means that prices will decrease even further and the level of output will decline. (We assume, for simplicity, that it goes back to the full-employment level Y*, so no long-run adjustment is needed.) Overall, the level of output has remained at its full-employment level but the level of prices and the interest rate have decreased.PP1P2218. Comment on the following statement:"A favorable oil shock causes lower inflation and lower unemployment."A decrease in material prices (or any other favorable supply shock) shifts theupward-sloping AS-curve to the right, and prices begin to decrease. The new equilibrium is at a lower price level and a higher level of output (a lower level of unemployment).Since output is now above the full-employment level, there will be upward pressure on nominal wages and prices, and the upward-sloping AS-curve will start shifting back to its original position (assuming that potential output was not affected). In the long run, unemployment will be back at its natural rate but the price level will have decreased (and thus real wages increased).19. “Falling oil prices will lead to increased employment, higher wage rates an dincreased real money balances.” Comment on this statement with the help of an AD-AS diagram and explain the short-run and long-run adjustment processes.A decline in material prices shifts the upward-sloping AS-curve to the right, leading to excess supply at the existing price level. A new equilibrium is reached at a higher level of output and a lower price level. But since output is now above the full-employment level Y*, there is upward pressure on wages and prices and the upward-sloping AS-curve starts shifting back to the right. A new long-run equilibrium is reached back at the original position (Y*), and the original price level (assuming that the change in material prices did not affect the full-employment level of output). Since nominal wages (W) will have risen but the price level (P) will not have changed, real wages (W/P) will have increased.PP1P2Y*Y2Y。
Chapter 7 Phase Equilibrium
Ⅱ 如果选用二项Virial EOS计算，则计算结果是
BPis ln is RT
24
i 4、 组分 i 在液相中的活度系数
组分 i 在液相中的活度系数是通过关系式 1 ( nG E ) ln i RT ni T , P ,n[ i ] 用液相的 GE 模型进行计算。在Chapter 6中已经介绍了目前 比较流行的几种活度系数模型。如Wilson 模型
f (T , P , x ( ) , x ( ) ) 0
3
7.1 相平衡判据与相律公式
已经证明，相平衡判据是：
T (1) T ( 2) T ( ) P (1) P ( 2) P ( )
(j1) (j2) (j )
m0
0
xi
1
9
Constant Temperature
负偏差体系
Liquid
Pi Pis xi
P
Vapor
0
xi
1
10
Constant Temperature Liquid
a
具有最高压力 恒沸物体系
Pi Pi xi
s
P
Azeotrope
存在 a 点， xi yi
Dew Line(P - y)
ˆi 2、组分 i 在汽相中的逸度系数 V ˆ V是通过混合物中组分逸度系数计算公式
i
dP ˆ ln i ( Z i 1) P 0
P
用汽相的EOS进行计算的。
21
ˆ Ⅰ 如果选用Cubic EOS计算 iV ，则计算公式是
P RT ˆ RT ln i dVt RT ln Z n Vt i T , P , n[ i ]
胶体与界面化学英文1Colloid and SurfaceInterface Chemistry—Scope and Variables
1
Contents
Chapter 1: Colloid and Surface/Interface Chemistry—Scope and Variables Chapter 2: Sedimentation and Diffusion and Their Equilibrium Chapter 3: Solution Thermodynamics: Osmotic and Donnan Equilibia Chapter 4: The Rheology of Dispersions
Reverse hexagonal liquid crystal
17
The exchange of main structures of aggregation
vesicle
18
4. Impact of Colloid and Surface Chemistry in Science,Engineering and Technology
5
The linear dimension is size range, rather than particle weight or the number of atoms in a particle.
The properties of colloid system and surface phenomena of colloid system depend mainly on the specific surface area of colloid particle, little or lightly on the colloid structure and density of a particle.
大学热动专业英语1-2章翻译
Specialized English for Thermal Energy & Power EngineeringCOURSE OUTLINETextbook: 热能与动力工程专业英语（Specialized English for Thermal Energy & Power Engineering）(3th) 阎维平，中国电力出版社（第三版）COURSE OUTLINECourse Goals:1.To understand the basic characteristics of Specialized English.2.To recognize some technical words in thermal energy and power engineering.3.To know how to write the abstract for a paper or a thesis (P155).Grading:Exercises in the class 20%Final exam 80%ContentsChapter 1 Introduction to Thermal Sciences1.1 Fundamental of engineering thermodynamics1.2 Fundamental of fluid mechanics1.3 Fundamental of heat transferChapter 2 Boiler2.1 Introduction2.2 Development of utility boiler2.3 Fuel and combustion2.4 Pulverizing system2.5 System arrangement and key components2.6 On-load cleaning of boilers2.7 Energy balanceChapter 1 Introduction to Thermal Sciences1.1 Fundamental of engineering thermodynamics•Thermodynamics is a science in which the storage, transformation, and transfer of energy are studied. Energy is stored as internal energy( associated with temperature), kinetic energy( due to motion), potential energy (due to elevation) and chemical energy( due tochemical composition); it is transformed from one of these forms to another; and it is transferred across a boundary as either heat or work.第一章热科学介绍1.1 工程热力学基础热力学是一门研究能量储存、转换及传递的科学。
第6章 多组分多级分离的严格计算 化学分离工程
H (Heat Balance Equation) ——热量衡算方程
对于第j级的MESH方程：
7
对第j级： 共有（2C＋3）个方程 （1）物料衡算方程（M－eq.） C个 (6-1)
GiM , j = L j -1 xi , j -1 V j 1 yi , j 1 Fj zi , j - ( L j U j ) xi , j - (V j Wj ) yi , j = 0
RETURN
16
6.1平衡级的理论模型
3、同时校正法：先将MESH方程用泰勒级数展开， 并取其线性项，然后用NewtonRaphson法联解。 适用过程：（1）宽沸程的精馏过程； （2）非理想性较强的精馏过程； 如：萃取精馏、共沸精馏 （3）有化学反应的分离过程； 如：反应精馏和催化精馏等 按解决问题的策略不同分为：NC-SC法和GS-SC法 见6.3内容
三对角 泡点法(BP法)—窄沸程 (分块求解法) 矩阵法 流率加和法(SR法)—宽沸程 同时校正法 Naphthali-Sandholm（NC-SC）法
(同时求解) Goldstein-Standfield（GS-SC）法
GO
ROSE松弛法
14
6.1平衡级的理论模型
1、逐级计算法：将每一级的M和E方程组合为一组， 运用试差的方法，按级求解，得到组成断面。常 用的两种方法： (A)流量平衡法：(Lewis-Matheson法) 特点：交替使用相平衡和物料平衡方程进行逐板 计算类似于二元精馏的图解法。 属于设计型计算。（表6-1） (B)比流量法（Thiele-Geddes法） 特点：以比流量的形式建立M和E联立的工作方程 (li/di)，从塔顶到进料板，从塔釜到进料 板逐级进行计算。 属于操作型计算。 （表6-1） RETURN 15
第六章 水和水蒸气的性质
饱和状态：汽化与凝结的动态平衡
At the equilibrium state, the pressure corresponding to only one temperature. That is, . Saturation temperature 饱和温度Ts 饱和压力ps Saturation pressure
6.3.1 P=constant (压力 p 是定值)
§6-3 水蒸气的定压发生过程
t < ts
未饱和水
t = ts
t = ts
t = ts
t > ts
v > v’’ h > h’’ s > s’’
过热
饱和水 饱和湿蒸汽 饱和干蒸汽 过热蒸汽
v < v’ h < h’ s < s’
v = v’ v ’< v <v’’ v = v’’ h = h’ h ’< h <h’’ h = h’’ s = s’ s ’< s <s’’ s = s’’
(气体和液体均处在饱和状态下)
Evaporation occurs at any temperature and pressure. （蒸发可在任何温度和压力下发生．） Evaporation rate depends on the free surface area, the temperature, the flow rate above, etc. （蒸发的速度与自由液面表面积，液体温度，液面风速等有关．
t ts
t
v
t过热 t ts
注意：水蒸气定压发生过程说明
(1) (2)
Q U W U pdV 只有熵加热时永远增加 U pV U ( pV ) H S Sf Sg 0
物理化学-相平衡
3
组分数：定义为 K＝ S – R – R’
例如：金属Zn的冶炼
4
例如：金属Zn的冶炼 ZnS(矿石)
灼烧
ZnO(s)
用C还原 ～1200℃
Zn
Zn(g)+CO(g)+CO2(g)
ZnO
(s) C (s)
Φ=3
S=5
5
反应① ZnO+C → CO+Zn 反应② 2ZnO+C → CO2+2Zn ③=2①－②
p V (g) 等T下： T m
①
∴
p
pv↑
23
②
pV p
T
值很小，表明pV对p 不敏感
结论：液体蒸汽压pV与p有关，但影响很 小；但pV对T敏感。 如：蒸馏易加压操作。 凝聚系统对压强变化不敏感。
24
6－4 纯物质的相图 (Phase diagram for pure substance )
液相线：直线，p～xB(sln) 气相线：曲线，p-yB(g) 相区： 物系点和相点：定义；在 单相区，物系点与相点重 合；在两相区，物系点与 两个相点在同一条水平线 上。
38
pA*
xB→
B
二、 T-x -y图（沸点－组成图） (Boiling point-composition diagram)
Clausius - Clapeyron Equation （克－克方
19
2、s-g平衡
d ln{p} gs H m dT RT 2
克－克方程
描述固体蒸气压与温度的关系 3、s-l平衡
dp ls H m l dT TsVm
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每一个相的变量数为：T、p、(S-1)浓度 总变量数：
因为P个相，浓度就有P(S-1)个，平衡各相
温度、压强T、p相同，温度压强为2个变量，
总变量数为：P(S-1)+2
不变量数： 对每一种物质(B)：相平衡时，在P 个 相间平衡，所以有(P-1)个不变量: B(Ⅰ) = B(Ⅱ) = … = B(P) 整个系统有S种物质，共有 S(P-1)个不变量。 若还有独立的化学反应R个： R个化学方程关系式 若还有浓度限制条件R’个： R´个浓度关系式 总不变量数: S(P-1)+ R+ R´
第六章 相平衡
phase equilibrium
相平衡在日常生活中常遇到，相平衡受什么条件的约束 呢？在化工生产中常用到相平衡，在石油工业中遇到相平 衡的问题，如开采时，由于地层T，p变化，造成沥青质等 固体的沉积堵塞缝隙；储运是管道输油的条件，不同油品 的分段输送，炼油过程不同馏分的分离。
本章主要讲：单组分系统、 双组分系统、 三组分系统
f= C-P+2 =2-3+2 =1
例:在一个抽空的容器中放有过 量的NH4I(s)，同时存在下列平 衡： NH4I(s) = NH3(g) + HI(g)
2HI(g) = H2(g) + I2(g)
求此系统的自由度数。
解：此系统的P = 2，S = 5，R =2，四种气体的 分压之间存在下列定量关系式：
则有
显然，
μ*(α,B*,T,p) + dμ*(α)＝μ*(β,B*,T,p) + dμ*(β)
d μ*( α) ＝ d μ*(β) dG = - SdT + Vdp 可得
由热力学基本方程式
- Sm*(α)dΤ+ Vm*(α)dp = - Sm*(β)dT + Vm*(β)dp
移项，整理得， ( ) Sm ( ) S dp Sm m dT Vm ( ) Vm ( ) V m
t/℃ -15 -10 285.7 260.0 110.4 -5 0.01 20 100 374 22.04 p*/Pa g ↔ l 190.5 ×106 s ↔ g 165.5 s↔l 156.0 421.0 610.5 401.7 610.5 59.8 610.5 ×106 (MPa) 2337.8 101325
读图：线： OC线：g OB线：g OA线： s
p l 汽 - 液平衡F = 1，
b 汽 – 固平衡 s
A
C
p = f (T )， F = 1， p = f ( T ) l 固 - 液平衡，F = 1。
l
a
sC` B OFra bibliotekgT
647K
OC`线：是过冷水线
AOC 区域，液相区，F = 2；
面：BOC 区域，汽相区，F = 2，C点对应的温度是临界温度； AOB 区域，固相区，F = 2，A点以上固相区变得复杂。 点：O点：纯水的三相点。此处固液气三相平衡，F = 0， t = 0.0098℃，p = 610.5Pa。 利用相图可说明水在温度或压强变化时的相变化，如 a→b。
(2) 由任意量的 CaCO3 (s), CaO (s), CO2 (g)建立如下反应平衡： CaCO3 (s) = CaO(s) + CO2(g) 试求(1) 、(2)两种情况下，系统的组分数 C=？自由度数 f =?
解： (1) C = S - R -R’ = 3-1- 0 = 2
f = C-P+2=2-3+2 =1 (2) C = S - R - R’ = 3 - 1 - 0 = 2
Na2CO3(s) 的水化物与 Na2CO3 水溶液及 冰平衡共存。
§6.2 液体的饱和蒸气压和沸点 饱和蒸气压：在温度T，某液体物质 气液平衡时的蒸气压Ps。 沸点：液体饱和蒸气压等于外压的 气液平衡时的温度。 正常沸点：饱和蒸气压为101325Pa 时的温度。
A(l) A(g)
同一温度下，挥发性大的物质饱和 蒸气压大。
p(NH3) = p(HI) +2p(H2)；p(H2) = p(I2)
分压的限制条件也就是气相组成的限制条件，故 R′=2，所以
C = S-R-R′= 5-2-2 = 1
f = C – P + 2 =1- 2 + 2 = 1
自由度数 f 为1，说明本题的多相平衡系统中， p、T及四种气体的分压六个变量中，只有其中一 个变量在维持系统相数不变的情况下，可以在一 定范围内独立变化。 f = 1
所以,组分数与物种数的选择无关，组分数C总是 不变。
③.自由度数（f degrees of freedom ）
系统中能够维持原有相数而可以 独立改变的变量的数目（如：温度、
压强、浓度等）。
f=独立变量数=总变量数-不独立变量数
2. 相律的推导
设平衡系统中有：S 种化学物质，分 布于P 个相中，且在各相中各物质分子 形态相同。
单组分系统的相图 很多，如硫、碳等，由 于它们有多种晶型，所 以相图也要复杂一些。
硫有两种晶型，正交硫 s1和单斜硫 s2。图中 有三个三相点：B、 C、E。
F
P / kPa
s1
E l B s2 C D
A
g
T/ K
②.克拉佩龙-克劳修斯方程
在单组分系统的两相平衡时，F = 1， 即 p = f (T )，这个函数关系就是克拉佩 龙方程。
例: 由任意量的 NH4Cl (s) 、NH3(g)、 HCl(g) 建立如下反应平衡：
NH4Cl (s) =NH3(g)+HCl(g)
试求系统的 组分数 C=？自由度数f=?
解：
C = S - R - R´= 3 - 1 - 0 =2 f = C - P + 2 =2 - 2 + 2 = 2
例.(1) 仅由CaCO3(s)部分分解，建立如下反 应平衡： CaCO3 (s) = CaO(s) + CO2(g)
1. 单组分系统相图
在单组分系统中， f=1 – P + 2，f = 3- P， 因此fmax= 2。
可用平面直角坐标系表示系统的相与温度、压强的 关系。
①.水的相图 相图的绘制， H2O在中常压强下可以以气（水蒸气）、液、固 三种不同的相态存在，相应存在冰水、冰水蒸气及 水水蒸气三种两相平衡。
实验测得三种两相平衡的温度和压强数据如下：
当系统中只有一个相时，P =1， f = 2，即T、p在有限的范围内可以 同时改变而不会产生新相和使旧相 消失，这就是双变量均相系统。
当P = 2，即有两个相，则 f =1， 这时，T、p 中只有一个能独立改变， 且p与T互为函数关系，这种函关系 是我们在本节中要点研究的热力学 方程。 当P =3，则f=0，这时三相平衡共 存，T、p为定值。对于任何平衡系 统，自由度 f 的最小值只能是零， 所以单组分系统最多只可能有三个
C = S – R - R’ = 3 – 1 - 1 = 1
又如：在真空容器中定量的NH4HCO3 (s) 部分
分解，有如下反应平衡：
NH4HCO3 (s) = NH3(g) + H2O(g) + CO2 (g)
∵ Kp=PNH3PH2OPCO2 ，本来有三个变量PNH3PH2OPCO2
，知
道一个另2个就知道了。少了2个变量 ∴ R′= 2
1）同一物质的饱和蒸气压Ps随温度
的升高而增加； 2). 同一外压下不同液体可有不同
沸点；
3). 同一液体在不同外压下沸点不 同，外压降低，沸点降低。
§6.3 单组分系统相平衡
单组分系统相图 单组分系统热力学
由于单组分系统中只存在一种纯化 学物质，故C =S =1，相律的表示式 可写成：
f = C-P+2 = 1-P-2 = 3-P
如果有其他n个影响因素 ,则相律表 示如下： f = C – P + n 这就是吉布斯相律。
关于相律有几点说明：
a. 式中的2，就是温度和压强，若还有其它因素， 则为n； b.当所有物种不是全部分布于所有相时，上式仍 成立。
c.外压对固液相平衡系统的影响很小，在 101.325kPa压强下 研究固液平衡时，可不考虑外压对固液平衡的影 响，故这时系统的条件自由度数为 f′= C-P +1 （5-2-2）
F=独立变量数=自由度数
F= [P (S - 1) + 2 ] - [ S( P - 1) + R + R´ ] = S – R - R´ – P + 2
=C – P + 2
--------Gibbs 相律
相律的中文表述：
在只受环境的温度和压强影响的热力 学多相平衡系统中，自由度等于组分数 减去相数再加上2（温度和压强两个变 量）。 f = C – P + 2 (温度和压强）
C = S – R - R’ = 4 – 1 - 2 = 1
(2)当把电解质在溶液中的离子亦视为物种时， 但存在电离平衡的关系。 如： H2O = H+ + OH-
S = 3， R =1， R′= 1，因为： x(H+) = x(OH-)=10-7 C = S – R - R’ = 3-1- 1= 1
所以:C = S – R -R′= 5- 3 – 0 = 2
因为压强已固定，有 f′=C-P+1 ，因为 f′= 0时P最大，
所以
0 = C-P +1 = 2-P +1= 3-P，P =3
这三个相中，除Na2CO3的水溶液（液相） 及 冰 H2O(s) 外 ， 还 有 一 个 相 ， 这 就 是
Na2CO3(s)的水化物，即最多只能有一种
一般说来，混合气体在一起是一个相；