Chapter 5 Solution Properties
罗斯 公司理财 英文第九版Chap005
5-8
5.4 The Internal Rate of Return
IRR: the discount rate that sets NPV to zero Minimum Acceptance Criteria:
Ranking Criteria:
Accept if the IRR exceeds the required return Select alternative with the highest IRR
Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.
Must exceed a MINIMUM acceptance criteria
5-2
5.1 Why Use Net Present Value?
Accepting positive NPV projects benefits shareholders.
NPV
uses cash flows NPV uses all the cash flows of the project NPV discounts the cash flows properly
Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g., acquiring an accounting system.
RANK all alternatives, and select the best one.
中级微观经济学_Ch5
16
5.2 Solutions to the Consumer’s Problem: Demand Function
The optimal choice is called the consumer’s ORDINARY DEMAND （一般需求）at the given prices and income. Ordinary demand function are denoted by x1*(p1,p2,m) and x2*(p1,p2,m).
18
Example 2: Quasi-linear Utility Function
Suppose a consumer has quasi-linear utility function: u(x1,x2)=aln x1+x2, a>0. The prices of x1 and x2 are p1 and p2, respectively, and consumer’s income is denoted by m. Also, x1 and x2 are nonnegative. What is the optimal consumptionnditions simultaneously you can get the interior solutions.
11
Solving for Interior Solution (method 2)
The conditions may be obtained by using the Lagrangian multiplier method, i.e., constrained optimization in calculus. How to do it? see supplement.
斯蒂芬·威廉森-宏观经济学第五版答案chapter5
Chapter 5A Closed-Economy One-PeriodMacroeconomic Model⏹Teaching GoalsThere are three key points to be learned from this chapter. The first point is that when we allow the consumers and firms that we studied in Chapter 4 to interact with each other and with the government, the economy is able to achieve equilibrium through price adjustment. In this particular case, the “price” is the relative price of leisure, the real wage. The second important point is that the equilibrium that markets settle upon is a favorable one, in the sense of Pareto optimality. This point is in keeping with Adam Smith’s notion that the “invisible hand” of self-interested individuals, meeting in a competitive market, can work for the common good. The third point is that we can directly discover the equilibrium position of a market economy by solving an economic planner problem. Although students may find this point to be somewhat arcane, stress the point that it will be much simpler to solve problems (e.g., exam problems) by working with a planner problem as opposed to directly solving general equilibrium problems. The students, however, need to be aware when this solution method is not applicable. The section about the Laffer curve is a good way to show when social and private optima do not coincide.Once students have mastered the mechanics of the model, the two problems for which this model is best suited are the analyses of changes in government spending and total factor productivity. In working these problems, stress the applicability of these results to historical applications and as a guide to understanding current events.A key tactic of the textbook’s approach is the critical assessment of the usefulness and credibility of competing models. Therefore, it is important to stress the extent to which models fit the facts. Does this model fit the facts of long-run growth? Does this model fit the facts of the typical business cycle? These kinds of questions come up again and again in the course of macroeconomic study. Stress again and again that scientific study needs to relate to observations, in our case the stylized facts of Chapter 2.⏹Classroom Discussion TopicsAn alternative approach to this material is to start with the example of Robinson Crusoe (or Castaway, Gilligan’s Island, etc.). Does an isolated individual have any economic choices? What would guide these choices? Would you rather be on an island with a more plentiful food supply? A pure income effect can then be presented in the form of extra food (or a volleyball) washing up on shore, or in the form of “pirates” (government?) demanding tribute. An increase in total factor productivity can be in the form of obtaining a fishing net or a ladder to climb coconut trees. A change in capital can be the consequence of a hurricane, etc. The next step would be to ask the students about the likely consequences of additional individuals on the island. If they are all identical, and there are no economies to team production, will there be any reason for markets to exist? Could a market improve things? How and why? Typically, markets improve things onlyChapter 5 A Closed-Economy One-Period Macroeconomic Model 39 to the extent that people are different. However, these types of differences are what we are willing toignore when we adopt the fiction of a representative consumer.OutlineI. Competitive EquilibriumA. A One-Period Model1. No Borrowing or Lending2. G = TB. Equilibrium Modeling1. Endogenous Variables2. Exogenous Variables3. Hypothetical ExperimentsC. Properties of a Competitive Equilibrium1. Representative Consumer Maximizes Utility Subject to Budget Constraint2. Representative Firm Maximizes Profits3. Markets Clear4. Government Budget Constraint Satisfied5. ,,l C l CN w MRS MRT MP === II. OptimalityA. Pareto OptimalityB. Welfare Theorems1. 1st Theorem: A Competitive Equilibrium Can Be Pareto Optimal2. 2nd Theorem: A Pareto Optimum Can Be a Competitive EquilibriumC. Inefficiencies1. Externalities2. Distorting Taxes3. Monopoly PowerD. Using the Second Theorem1. Pareto Optima Are Easier to Identify2. Effects of Disturbances on Pareto OptimaIII. Effects of an Increase in Government SpendingA. Impact Effect1. Parallel Downward Shift in PPF2. Pure Income EffectB. Equilibrium Effects1. Reduced Consumption2. Reduced Leisure and Increased Hours of Work3. Increased Output4. Lower Real WageC. Crowding-OutD. Government Spending a Source of Business Cycles?40 Williamson • Macroeconomics, Fifth Edition1. Government Spending Shocks Wrongly Predict Countercyclical Consumption2. Government Spending Shocks Wrongly Predict Countercyclical Real WagesIV. Effects of an Increase in Total Factor ProductivityA. Impact Effect1. Upward Shift in PPF2. Steeper PPF3. Income and Substitution EffectsB. Equilibrium Effects1. Increased Consumption2. Leisure and Hours Worked May Rise or Fall3. Increased Output4. Higher Real WageC. Productivity and Long-Run Growth1. Consumption Grows over Time2. Hours Worked Remain about Constant3. Output Increases over Time4. Real Wages Rise over TimeD. Productivity as Source of Business Cycles?1. Consumption Is Procyclical2. Cyclical Properties of Hours Workeda. Procyclical Hours Worked Is a Business Cycle Factb. Need Strong Substitution Effect to Predict Procyclical Hoursc. Intertemporal Substitution of Leisure3. Increased Output Defines the Cycle4. Procyclical Real Wage RateV. Income Tax Revenue and the Laffer CurveA. Tax Revenue1. The Tax Base Depends on the Proportional Tax Rate2. The Laffer Curve Measures Tax Revenue as a Function of the Tax Rate3. Unless the Tax Rate Is Optimal, Two Tax Rates Yield the Same Tax Revenue4. Supply-Side Economists Claim the U.S. Economy Is at the Bad Tax Rate5. Empirical Evidence Tends to Prove Supply-Side Economists WrongVI. A Model of Public Goods: How Large Should the Government Be?A. Effects of higher GDP on optimal government spending.B. Better government technology: what happens to optimal government spending and private spending?Chapter 5 A Closed-Economy One-Period Macroeconomic Model 41 Solutions to End-of-Chapter Problems1. Although we often think about the negative externalities of congestion and pollution in cities, theremay also be some positive externalities. A concentrated population is better able to support the arts and professional sports; cities typically have a greater variety of good restaurants, etc. Perhaps a more basic issue is that there may be some increasing returns to scale at low output levels that makeindustrial production more costly in small towns. There may also be externalities in production in being located close to other producers. One example would be the financial industry in financialcenters like New York, London, Tokyo, etc. Another example would be large city medical centers that enhance coordination between primary physicians and specialists.One market test of whether productivity is higher in cities would be to look at the wages in cities versus the wages in smaller towns and rural areas. Wages are often higher in cities for individuals of comparable skills. Market efficiency suggests that the higher wages be reflective of a higher marginal product of labor, and that the higher wages compensate those choosing to live in cities for thenegative externalities that they face.2. In a one period model, taxes must be exactly equal to government spending. A reduction in taxes istherefore equivalent to a reduction in government spending. The result is exactly opposite of the case of an increase in government spending that is presented in the text. A reduction in governmentspending induces a pure income effect that induces the consumer to consume more and work less. At lower employment, the equilibrium real wage is higher because the marginal product of labor rises when employment falls. Output falls, consumption rises, employment falls and the real wage rises. 3. The only impact effect of this disturbance is to lower the capital stock. Therefore, the productionpossibility frontier shifts down and the marginal product of labor falls (PPF is flatter).(a) The reduction in the capital stock is depicted in the figure below. The economy starts at point Aon PPF1. The reduction in the capital stock shifts the production possibilities frontier to PPF2.Because PPF2 is flatter, there is a substitution effect that moves the consumer to point D. Theconsumer consumes less of the consumption good and consumes more leisure. Less leisure alsomeans that the consumer works more. Because the production possibilities frontier shifts down,there is also an income effect. The income effect implies less consumption and less leisure (more work). On net, consumption must fall, but leisure could decrease, remain the same, or increase,depending on the relative strengths of the income and substitution effect. The real wage must also fall. To see this, we must remember that, in equilibrium, the real wage must equal the marginalrate of substitution. The substitution effect implies a lower marginal rate of substitution. Theincome effect is a parallel shift in the production possibilities frontier. As the income effectincreases the amount of employment, marginal product of labor must fall from point D topoint B. This reinforces the reduction in the marginal rate of substitution from point A to point D.42 Williamson • Macroeconomics, Fifth Edition(b) Changes in the capital stock are not likely candidates for the source of the typical businesscycle. While it is easy to construct examples of precipitous declines in capital, it is more difficult to imagine sudden increases in the capital stock. The capital stock usually trends upward, and this upward trend is important for economic growth. However, the amount of new capital generatedby a higher level of investment over the course of a few quarters, of a few years, is very small in comparison to the existing stock of capital. On the other hand, a natural disaster that decreasesthe stock of capital implies lower output and consumption, and also implies lower real wages,which are all features of the typical business cycle contraction.4. Government Productivity. First consider the benchmark case in which 1,z = and there is no effect ofchanges in z on government activities. Now suppose that z increases. This case of an increase in z is depicted in the figure below. The original production possibilities frontier is labeled PPF 1 and the competitive equilibrium is at point A. If the increase in z only affects the economy through thechange in (,),zF K N then the new production possibilities frontier is PPF 2. The diagram shows a case in which the income and substitution effects on leisure exactly cancel out, and the economy moves to point B. The equation for the production possibilities frontier is (,).C zF K h l T =−− In the benchmark case, T G = and so we have (,).C zF K h l G =−− For this problem, /,T G z = and so the production possibilities frontier is given by (,)/.C zF K h l G z =−− When 1,z = the two PPFscoincide. When z increases, the vertical intercept of the PPF increases by /.G z ∆ Therefore, the new PPF is PPF 3 in the figure below. The competitive equilibrium is at point C . There is an additional income effect that provides an additional increase in equilibrium consumption, and a reinforcedincome effect that tend to make leisure increase. Therefore, relative to the benchmark case, there is a larger increase in consumption, and either a smaller decrease in leisure or a larger increase in leisure.Chapter 5 A Closed-Economy One-Period Macroeconomic Model 435. Change in preferences.(a) At the margin, the consumer decides that leisure is more preferred to consumption. That is, theconsumer now requires a bigger increase in consumption to willingly work more (consume less leisure). In more intuitive language, the consumer is lazier.(b) To work out the effects of this change in tastes, we refer to the figure below. The productionpossibility frontier in this example is unchanged. The consumer now picks a new point at which one of the flatter indifference curves is tangent to the production possibilities frontier. That is,equilibrium will shift from point A to point B. Consumption falls and leisure rises. Therefore, the consumer works less and produces less. Because employment has fallen, it also must be the case that the real wage increases.44 Williamson • Macroeconomics, Fifth Edition(c) This disturbance, which some might characterize as a contagious outbreak of laziness, wouldhave the appearance of a recession, as output and employment both fall. The consequentreduction in consumption is also consistent with a typical recession. However, in this case thereal wage would rise, which is inconsistent with the business cycle facts. Therefore, this type of preference change is not a cause of recessions.6. Production-enhancing aspects of government spending.(a) The increase in government spending in this example has two separate effects on the productionpossibilities frontier. First, the increase in government spending from G1 to G2 implies a parallel downward shift in the production possibilities frontier. Second, the productive nature ofgovernment spending is equivalent to an increase in total factor productivity that shifts theproduction possibilities frontier upward and increases its slope. The figure below draws theoriginal production possibilities frontier as PPF1 and the new production possibilities frontier as PPF2. If the production-enhancing aspects of the increase in government spending are largeenough, representative consumer utility could rise, as in this figure.Chapter 5 A Closed-Economy One-Period Macroeconomic Model 45(b) There are three effects at work in this example. First, there is a negative income effect from theincrease in taxes needed to pay for the increased government spending. This effect tends to lower both consumption and leisure. Second, there is a substitution effect due to the productive effect of the increase in G, which is drawn as the movement from point A to point D. This effect tends to increase both consumption and leisure. Third, there is a positive income effect from the increase in G on productivity. This effect tends to increase both consumption and leisure. In the figure above, the movement from point D to point B is the net effect of the two income effects. Ingeneral, consumption may rise or fall, and leisure may rise or fall. The overall effect on output is the same as in any increase in total factor productivity. Output surely rises.46 Williamson • Macroeconomics, Fifth Edition7. (a) If households dedicate a hours to education today, it reduces the hours available for leisure andwork to h−a. The PPF has to start form point (−G, h−a). Graphically, this corresponds to thefigure in the answer of question 6(b). The consequence is thus a reduction in consumption,leisure, employment, aggregate output, but an increase in the real wage.(b) In the future, workers will be more efficient, which corresponds to an increase in total factorproductivity. Thus we have the case described in Figure 5.9 of the textbook. There is an increase in future consumption, aggregate output and the real wage. Changes in employment and leisureare ambiguous.(c) An increase in education leads to an immediate loss in welfare, as both leisure and consumptionare reduced. But this is compensated by an increase in future consumption, and possibly ofleisure, too. Whether this is worth doing depends on the preferences of households over currentand future utility.8. We need to analyze each case separately. Start with the good equilibrium. As government expensesincrease, more tax revenue needs to be raised, and thus the tax rate needs to be increased. As shown in the figure below, this tilts down the linear PPF. The new equilibrium leads to a lower indifferencecurve. This leads to a negative income effect and a lower wage (remember, it is z(1 − t)), thus asubstitution effect. The income effect lowers consumption and leisure, the substitution effectdecreases consumption and increases leisure. All in all, consumption is lower and leisure is higher, as we know that the substitution effect dominates the income effect. This means that the labor supply is reduced, and thus equilibrium labor and output.The story is different in the bad equilibrium. To increase tax revenue, one needs to reduce the tax rate. Then all the changes discussed above are exactly in the opposite direction.9. We know from previous analysis that an improvement in total factor productivity pushes up the PPF,and thus leads to an increase in consumption, a decrease in leisure, and thus an increase in thequantity of labor supplied. This increases the tax base, and thus allows a reduced tax rate to achieve the same tax revenue, or in other words, it pushes the left portion of the Laffer curve to the left. The reduction in the tax rate has then a further impact on the variables of interest: as we saw in question 7, first part with a reversal of all signs: consumption increases even more and leisure decrease yet more, leading to an even higher quantity of labor. All in all, as both labor and total factor productivityincrease, output increases.Chapter 5 A Closed-Economy One-Period Macroeconomic Model 47 10. a) With perfect substitutes preferences, indifference curves are straight lines with slope –b, where b is the marginal rate of substitution. If b > 1/q, so that the indifference curves are steeper than the PPF, then the optimal choice for the government is G=qY, so that C = 0. Thus if b is relatively large (the consumer cares relatively more about public goods relative to private goods) and q is relatively large (the government is relatively efficient), then all production should be carried on by the government. Alternatively if b < 1/q, then G = 0 and C = Y, so that government is inactive. Thus, if b increases or q increases, this makes it more likely that b > 1/q and we have the first case, where all production comes from the government.b) With perfect complements, indifference curves are as depicted in Figure 10.1, and the initial equilibrium is at point A. If a increases, then the equilibrium shifts from A to B in Figure 10.2. An increase in a represents a greater preference for private goods relative to public goods, and in Figure 10.2, this results in less public goods and more private consumption in equilibrium. If q increases, this shifts the PPF out as in Figure 10.3, and the equilibrium shifts from A to B. Both C and G increase, driven by income effects.Figure 10.1Figure 10.248 Williamson • Macroeconomics, Fifth Edition ©2014 Pearson Education, Inc.Figure 10.311. (a) If public goods and private goods are perfect substitutes, then the consumer always chooses C and l so that C = dl , and so given the production possibilities frontier, we must haveC C h G d =−− and so()1d h G C d −=+ and 1h G l d −=+ Therefore, consumption and leisure both decrease when government spending increases – a pure incomeeffect.(b) However, suppose that public goods and private goods are perfect complements. As in part (a), it is always optimal for the consumer to choose C and l so that C = dl. But the consumer faces a tax T = G , and the wage is w=1. So, if the consumer chooses the C = dl and the budget constraint is satisfied, then ()1d h G C d −=+ and1h G l d −=+,just as in part (a). This is the only optimum if,C aG ≤orChapter 5 A Closed-Economy One-Period Macroeconomic Model 49 ©2014 Pearson Education, Inc.(1)dh G a d d ≥++ But, if (1)dh G a d d≤++ Then, it is optimal for the consumer to chooseC aG = and aG l d=. In this case, the consumption bundle of the consumer actually lies inside the production possibilitiesfrontier, and government spending has a Keynesian effect. More government spending implies greater consumption.。
Michael-quirk-半导体制造技术-第五章-半导体制造中的化学品
30 20
40 50
10 00
70 80
High
High
temperature pressure
30 20
40 50
10 0
70 80
Moveable piston
Volume increase
Semiconductor Manufacturing Technology
by Michael Quirk and Julian Serda
Properties of Materials
• Temperature • Pressure and Vacuum • Condensation • Vapor Pressure • Sublimation and
Deposition • Density • Surface Tension • Thermal Expansion • Stress
by Michael Quirk and Julian Serda
© 2001 by Prentice Hall
Objectives
After studying the material in this chapter, you will be able to:
1. Identify and discuss the four states of matter.
Sublimation
Dry ice (CO2)
Semiconductor Manufacturing Technology
by Michael Quirk and Julian Serda
Figure 5.7
© 2001 by Prentice Hall
Deposition
流体力学英文版复习
p K V / V 6 6 3.110 0.110 (998 1000) /1000 1.5 109 (Pa)
7
2018/10/14
(5) Viscosity
Viscosity is an internal property of a fluid that offers resistance to shear deformation. It describes a fluid's internal resistance to flow and may be thought as a measure of fluid friction. The resistance of a fluid to shear depends upon its cohesion( 内 聚 力 ) and its rate of transfer of molecular momentum(分子动量交换).
dp
The bulk modulus of elasticity ( 体积弹性模量 ) K is the reciprocal of coefficient of volume compressibility p.
dp K p dV / V
2018/10/14
1
（Pa）
(1.16)
6
Example 1.1 A mineral oil in cylinder has a volume of 1000cm3 at 0.1MN/m2 and a volume of 998 cm3 at 3.1MN/m2. What is its bulk modulus of elasticity?
spaced parallel plates（平行板）. The lower plate is fixed, the upper plate with area A move with a constant velocity V, a force F is applied to the upper plate.
fluent湍流管道流动教程
Preparation
1. Copy the le
fluent_inc fluent5 tut elbow elbow.msh
from the FLUENT tutorial CD to your working directory. 2. Start the 2D version of FLUENT.
Prerequhave little experience
with FLUENT, but that you are generally familiar with the interface. If you are not, please review the sample session in Chapter 1 of the User's Guide.
b Click on Scale to scale the grid. The reported values of the Domain Extents will be reported in the default SI units of meters.
【金属基复合材料】第五章,复合材料基体与增强体
Introduction
The possibility of taking advantage of particular properties of the constituent materials to meet specific demands is the most important motivation for the development of composites. The terms matrix and reinforcement are often used. The matrix is a percolating “soft” phase (with in general excellent ductility, formability and thermal conductivity) in which are embedded the “hard” reinforcements (high stiffness, hardness, and low thermal expansion). The reinforcements can be continuous or discontinuous, orientated or disorientated. The composites are classified by: (1) their matrix (polymer, ceramic, metal), (2) their reinforcement, which includes the chemical nature (oxides, carbides, nitrides), shape (continuous fibers, short fibers, whiskers, particulates) and orientation, (3) their processing routes.
Solution_国际财务管理_切奥尔尤恩_课后习题答案_第五章
CHAPTER 5 THE MARKET FOR FOREIGN EXCHANGESUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTERQUESTIONS AND PROBLEMSQUESTIONS1. Give a full definition of the market for foreign exchange.Answer: Broadly defined, the foreign exchange (FX) market encompasses the conversion of purchasing power from one currency into another, bank deposits of foreign currency, the extension of credit denominated in a foreign currency, foreign trade financing, and trading in foreign currency options and futures contracts.2. What is the difference between the retail or client market and the wholesale or interbank market for foreign exchange?Answer: The market for foreign exchange can be viewed as a two-tier market. One tier is the wholesale or interbank market and the other tier is the retail or client market. International banks provide the core of the FX market. They stand willing to buy or sell foreign currency for their own account. These international banks serve their retail clients, corporations or individuals, in conducting foreign commerce or making international investment in financial assets that requires foreign exchange. Retail transactions account for only about 14 percent of FX trades. The other 86 percent is interbank trades between international banks, or non-bank dealers large enough to transact in the interbank market.3. Who are the market participants in the foreign exchange market?Answer: The market participants that comprise the FX market can be categorized into five groups: international banks, bank customers, non-bank dealers, FX brokers, and central banks. International banks provide the core of the FX market. Approximately 100 to 200 banks worldwide make a market in foreign exchange, i.e., they stand willing to buy or sell foreign currency for their own account. These international banks serve their retail clients, the bank customers, in conducting foreign commerce or making international investment in financial assets that requires foreign exchange. Non-bank dealers are large non-bank financial institutions, such as investment banks, mutual funds, pension funds, and hedge funds, whose size and frequency of trades make it cost- effective to establish their own dealing rooms totrade directly in the interbank market for their foreign exchange needs.Most interbank trades are speculative or arbitrage transactions where market participants attempt to correctly judge the future direction of price movements in one currency versus another or attempt to profit from temporary price discrepancies in currencies between competing dealers.FX brokers match dealer orders to buy and sell currencies for a fee, but do not take a position themselves. Interbank traders use a broker primarily to disseminate as quickly as possible a currency quote to many other dealers.Central banks sometimes intervene in the foreign exchange market in an attempt to influence the price of its currency against that of a major trading partner, or a country that it “fixes” or “pegs” its currency against. Intervention is the process of using foreign currency reserves to buy one’s own currency in order to decrease its supply and thus increase its value in the foreign exchange market, or alternatively, selling one’s own currency for foreign currency in order to increase its supply and lower its price.4. How are foreign exchange transactions between international banks settled?Answer: The interbank market is a network of correspondent banking relationships, with large commercial banks maintaining demand deposit accounts with one another, called correspondent bank accounts. The correspondent bank account network allows for the efficient functioning of the foreign exchange market. As an example of how the network of correspondent bank accounts facilities international foreign exchange transactions, consider a U.S. importer desiring to purchase merchandise invoiced in guilders from a Dutch exporter. The U.S. importer will contact his bank and inquire about the exchange rate. If the U.S. importer accepts the offered exchange rate, the bank will debit the U.S. importer’s account for the purchase of the Dutch guilders. The bank will instruct its correspondent bank in the Netherlands to debit its correspondent bank account the appropriate amount of guilders and to credit the Dutch exporter’s bank account. The importer’s bank will then debit its books to offset the debit of U.S. importer’s account, reflecting the decrease in its correspondent bank account balance.5. What is meant by a currency trading at a discount or at a premium in the forward market?Answer: The forward market involves contracting today for the future purchase or sale of foreign exchange. The forward price may be the same as the spot price, but usually it is higher (at a premium) or lower (at a discount) than the spot price.6. Why does most interbank currency trading worldwide involve the U.S. dollar?Answer: Trading in currencies worldwide is against a common currency that has international appeal. That currency has been the U.S. dollar since the end of World War II. However, the euro and Japanese yen have started to be used much more as international currencies in recent years. More importantly, trading would be exceedingly cumbersome and difficult to manage if each trader made a market against all other currencies.7. Banks find it necessary to accommodate their clients’ needs to buy or sell FX forward, in many instances for hedging purposes. How can the bank eliminate the currency exposure it has created for itself by accommodating a client’s forward transaction?Answer: Swap transactions provide a means for the bank to mitigate the currency exposure in a forward trade. A swap transaction is the simultaneous sale (or purchase) of spot foreign exchange against a forward purchase (or sale) of an approximately equal amount of the foreign currency. To illustrate, suppose a bank customer wants to buy dollars three months forward against British pound sterling. The bank can handle this trade for its customer and simultaneously neutralize the exchange rate risk in the trade by selling (borrowed) British pound sterling spot against dollars. The bank will lend the dollars for three months until they are needed to deliver against the dollars it has sold forward. The British pounds received will be used to liquidate the sterling loan.8. A CD/$ bank trader is currently quoting a small figure bid-ask of 35-40, when the rest of the market is trading at CD1.3436-CD1.3441. What is implied about the trader’s beliefs by his prices?Answer: The trader must think the Canadian dollar is going to appreciate against the U.S. dollar and therefore he is trying to increase his inventory of Canadian dollars by discouraging purchases of U.S. dollars by standing willing to buy $ at only CD1.3435/$1.00 and offering to sell from inventory at the slightly lower than market price of CD1.3440/$1.00.9. What is triangular arbitrage? What is a condition that will give rise to a triangular arbitrage opportunity?Answer: Triangular arbitrage is the process of trading out of the U.S. dollar into a second currency, then trading it for a third currency, which is in turn traded for U.S. dollars. The purpose is to earn an arbitrageprofit via trading from the second to the third currency when the direct exchange between the two is not in alignment with the cross exchange rate.Most, but not all, currency transactions go through the dollar. Certain banks specialize in making a direct market between non-dollar currencies, pricing at a narrower bid-ask spread than the cross-rate spread. Nevertheless, the implied cross-rate bid-ask quotations impose a discipline on the non-dollar market makers. If their direct quotes are not consistent with the cross exchange rates, a triangular arbitrage profit is possible.10. Over the past six years, the exchange rate between Swiss franc and U.S. dollar, SFr/$, has changed from about 1.30 to about 1.60. Would you agree that over this six-year period, the Swiss goods have become cheaper for buyers in the United States? (UPDATE? SF has gone from SF1.67/$ to SF1.04/$ over the last six years.)CFA Guideline Answer:The value of the dollar in Swiss francs has gone up from about 1.30 to about 1.60. Therefore, the dollar has appreciated relative to the Swiss franc, and the dollars needed by Americans to purchase Swiss goods have decreased. Thus, the statement is correct.PROBLEMS1. Using Exhibit 5.4, calculate a cross-rate matrix for the euro, Swiss franc, Japanese yen, and the Britishpound. Use the most current American term quotes to calculate the cross-rates so that the triangular matrix resulting is similar to the portion above the diagonal in Exhibit 5.6.Solution: The cross-rate formula we want to use is:S(j/k) = S($/k)/S($/j).The triangular matrix will contain 4 x (4 + 1)/2 = 10 elements.¥ SF £ $Euro 159.91 1.6317 .7478 1.4744 Japan (100) 1.0204.4676 .9220 Switzerland.4583 .9036 U.K 1.97172. Using Exhibit 5.4, calculate the one-, three-, and six-month forward cross-exchange rates between theCanadian dollar and the Swiss franc using the most current quotations. State the forward cross-rates in“Canadian” terms.Solution: The formulas we want to use are:F N (CD/SF) = F N ($/SF)/F N ($/CD)orF N (CD/SF) = F N (CD/$)/F N (SF/$).We will use the top formula that uses American term forward exchange rates.F 1(CD/SF) = .9052/.9986 = .9065F 3(CD/SF) = .9077/.9988 = .9088F 6(CD/SF) = .9104/.9979 = .91233. A foreign exchange trader with a U.S. bank took a short position of £5,000,000 when the $/£ exchange rate was 1.55. Subsequently, the exchange rate has changed to 1.61. Is this movement in the exchange rate good from the point of view of the position taken by the trader? By how much has the bank’s liability changed because of the change in the exchange rate? UPDATE TO CURRENT EX-RATES?CFA Guideline Answer:The increase in the $/£ exchange rate implies that the pound has appreciated with respect to the dollar. This is unfavorable to the trader since the trader has a short position in pounds.Bank’s liability in dollars initially was 5,000,000 x 1.55 = $7,750,000Bank’s liability in dollars now is 5,000,000 x 1.61 = $8,050,0004. Restate the following one-, three-, and six-month outright forward European term bid-ask quotes in forward points.1.3431-1.3436SpotOne-Month 1.3432-1.3442Three-Month 1.3448-1.3463Six-Month 1.3488-1.3508Solution:One-Month 01-06Three-Month 17-27Six-Month 57-725. Using the spot and outright forward quotes in problem 3, determine the corresponding bid-ask spreads in points.Solution:5SpotOne-Month 10Three-Month 15Six-Month 206. Using Exhibit 5.4, calculate the one-, three-, and six-month forward premium or discount for the Canadian dollar versus the U.S. dollar using American term quotations. For simplicity, assume each month has 30 days. What is the interpretation of your results?Solution: The formula we want to use is:f N,CD = [(F N($/CD) - S($/CD/$)/S($/CD)] x 360/Nf1,CD = [(.9986 - .9984)/.9984] x 360/30 = .0024f3,CD = [(.9988 - .9984)/.9984] x 360/90 = .0048f6,CD = [(.9979 - .9984)/.9984] x 360/180 = -.0060The pattern of forward premiums indicates that the Canadian dollar is trading at a premium versus the U.S. dollar for maturities up to three months into the future and then it trades at a discount.7. Using Exhibit 5.4, calculate the one-, three-, and six-month forward premium or discount for the U.S. dollar versus the British pound using European term quotations. For simplicity, assume each month has 30 days. What is the interpretation of your results?Solution: The formula we want to use is:f N,$ = [(F N (£/$) - S(£/$))/S(£/$)] x 360/Nf1,$ = [(.5076 - .5072)/.5072] x 360/30 = .0095f3,$ = [(.5086 - .5072)/.5072] x 360/90 = .0331f6,$ = [(.5104 - .5072)/.5072] x 360/180 = .0757The pattern of forward premiums indicates that the dollar is trading at a premium versus the British pound. That is, it becomes more expensive to buy a U.S. dollar forward for British pounds (in absolute and percentage terms) the further into the future one contracts.8. A bank is quoting the following exchange rates against the dollar for the Swiss franc and the Australian dollar:SFr/$ = 1.5960--70A$/$ = 1.7225--35An Australian firm asks the bank for an A$/SFr quote. What cross-rate would the bank quote?CFA Guideline Answer:The SFr/A$ quotation is obtained as follows. In obtaining this quotation, we keep in mind that SFr/A$ = SFr/$/A$/$, and that the price (bid or ask) for each transaction is the one that is more advantageous to the bank.The SFr/A$ bid price is the number of SFr the bank is willing to pay to buy one A$. This transaction (buy A$—sell SFr) is equivalent to selling SFr to buy dollars (at the bid rate of 1.5960 and the selling those dollars to buy A$ (at an ask rate of 1.7235). Mathematically, the transaction is as follows:bid SFr/A$ = (bid SFr/$)/(ask A$/$) = 1.5960/1.7235 = 0.9260The SFr/A$ ask price is the number of SFr the bank is asking for one A$. This transaction (sell A$—buy SFr) is equivalent to buying SFr with dollars (at the ask rate of 1.5970 and then simultaneously purchasing these dollars against A$ (at a bid rate of 1.7225). This may be expressed as follows:ask SFr/A$ = (ask SFr/$)/(bid A$/$) = 1.5970/1.7225 = 0.9271The resulting quotation by the bank isSFr/A$ = 0.8752—0.87639. Given the following information, what are the NZD/SGD currency against currency bid-ask quotations?AmericanTermsTerms EuropeanBidAskAskQuotations BidBankNew Zealand dollar .7265 .7272 1.3751 1.3765Singapore dollar .6135 .6140 1.6287 1.6300Solution: Equation 5.12 from the text implies S b(NZD/SGD) = S b($/SGD) x S b(NZD/$) = .6135 x 1.3751 = .8436. The reciprocal, 1/S b(NZD/SGD) =S a(SGD/NZD) = 1.1854. Analogously, it is implied that S a(NZD/SGD) = S a($/SGD) x S a(NZD/$) = .6140 x 1.3765 = .8452. The reciprocal, 1/S a(NZD/SGD) = S b(SGD/NZD) = 1.1832. Thus, the NZD/SGD bid-ask spread is NZD0.8436-NZD0.8452 and the SGD/NZD spread is SGD1.1832-SGD1.1854.10. Doug Bernard specializes in cross-rate arbitrage. He notices the following quotes:Swiss franc/dollar = SFr1.5971?$Australian dollar/U.S. dollar = A$1.8215/$Australian dollar/Swiss franc = A$1.1440/SFrIgnoring transaction costs, does Doug Bernard have an arbitrage opportunity based on these quotes? If there is an arbitrage opportunity, what steps would he take to make an arbitrage profit, and how would he profit if he has $1,000,000 available for this purpose.CFA Guideline Answer:A. The implicit cross-rate between Australian dollars and Swiss franc is A$/SFr = A$/$ x $/SFr = (A$/$)/(SFr/$) = 1.8215/1.5971 = 1.1405. However, the quoted cross-rate is higher at A$1.1.1440/SFr. So, triangular arbitrage is possible.B. In the quoted cross-rate of A$1.1440/SFr, one Swiss franc is worth A$1.1440, whereas the cross-rate based on the direct rates implies that one Swiss franc is worth A$1.1405. Thus, the Swiss franc is overvalued relative to the A$ in the quoted cross-rate, and Doug Bernard’s strategy for triangular arbitrage should be based on selling Swiss francs to buy A$ as per the quoted cross-rate. Accordingly, the steps Doug Bernard would take for an arbitrage profit is as follows:i.Sell dollars to get Swiss francs: Sell $1,000,000 to get $1,000,000 x SFr1.5971/$ =SFr1,597,100.ii.Sell Swiss francs to buy Australian dollars: Sell SFr1,597,100 to buy SFr1,597,100 x A$1.1440/SFr = A$1,827,082.40.iii.Sell Australian dollars for dollars: Sell A$1,827,082.40 for A$1,827,082.40/A$1.8215/$ = $1,003,064.73.Thus, your arbitrage profit is $1,003,064.73 - $1,000,000 = $3,064.73.11. Assume you are a trader with Deutsche Bank. From the quote screen on your computer terminal, you notice that Dresdner Bank is quoting €0.7627/$1.00 and Credit Suisse is offering SF1.1806/$1.00. You learn that UBS is making a direct market between the Swiss franc and the euro, with a current €/SF quote of .6395. Show how you can make a triangular arbitrage profit by trading at these prices. (Ignore bid-ask spreads for this problem.) Assume you have $5,000,000 with which to conduct the arbitrage. What happens if you initially sell dollars for Swiss francs? What €/SF price will eliminate triangulararbitrage?Solution: To make a triangular arbitrage profit the Deutsche Bank trader would sell $5,000,000 to Dresdner Bank at €0.7627/$1.00. This trade would yield €3,813,500= $5,000,000 x .7627. The Deutsche Bank trader would then sell the euros for Swiss francs to Union Bank of Switzerland at a price of €0.6395/SF1.00, yielding SF5,963,253 = €3,813,500/.6395. The Deutsche Bank trader will resell the Swiss francs to Credit Suisse for $5,051,036 = SF5,963,253/1.1806, yielding a triangular arbitrage profit of $51,036.If the Deutsche Bank trader initially sold $5,000,000 for Swiss francs, instead of euros, the trade would yield SF5,903,000 = $5,000,000 x 1.1806. The Swiss francs would in turn be traded for euros to UBS for €3,774,969= SF5,903,000 x .6395. The euros would be resold to Dresdner Bank for $4,949,481 = €3,774,969/.7627, or a loss of $50,519. Thus, it is necessary to conduct the triangular arbitrage in the correct order.The S(€/SF) cross exchange rate should be .7627/1.1806 = .6460. This is an equilibrium rate at which a triangular arbitrage profit will not exist. (The student can determine this for himself.) A profit results from the triangular arbitrage when dollars are first sold for euros because Swiss francs are purchased for euros at too low a rate in comparison to the equilibrium cross-rate, i.e., Swiss francs are purchased for only €0.6395/SF1.00 instead of the no-arbitrage rate of €0.6460/SF1.00. Similarly, when dollars are first sold for Swiss francs, an arbitrage loss results because Swiss francs are sold for euros at too low a rate, resulting in too few euros. That is, each Swiss franc is sold for €0.6395/SF1.00 instead of the higher no-arbitrage rate of €0.6460/SF1.00.12. The current spot exchange rate is $1.95/£ and the three-month forward rate is $1.90/£. Based on your analysis of the exchange rate, you are pretty confident that the spot exchange rate will be $1.92/£ in three months. Assume that you would like to buy or sell £1,000,000.a. What actions do you need to take to speculate in the forward market? What is the expected dollar profit from speculation?b. What would be your speculative profit in dollar terms if the spot exchange rate actually turns out to be $1.86/£.Solution:a. If you believe the spot exchange rate will be $1.92/£ in three months, you should buy £1,000,000 forward for $1.90/£. Your expected profit will be:$20,000 = £1,000,000 x ($1.92 -$1.90).b. If the spot exchange rate actually turns out to be $1.86/£ in three months, your loss from the long position will be:-$40,000 = £1,000,000 x ($1.86 -$1.90).13. Omni Advisors, an international pension fund manager, plans to sell equities denominated in Swiss Francs (CHF) and purchase an equivalent amount of equities denominated in South African Rands (ZAR).Omni will realize net proceeds of 3 million CHF at the end of 30 days and wants to eliminate the risk that the ZAR will appreciate relative to the CHF during this 30-day period. The following exhibit shows current exchange rates between the ZAR, CHF, and the U.S. dollar (USD).Currency Exchange RatesZAR/USD ZAR/USD CHF/USD CHF/USDMaturity Bid Ask Bid AskSpot 6.2681 6.2789 1.5282 1.534330-day 6.2538 6.2641 1.5226 1.528590-day 6.2104 6.2200 1.5058 1.5115a.Describe the currency transaction that Omni should undertake to eliminate currency riskover the 30-day period.b.Calculate the following:• The CHF/ZAR cross-currency rate Omni would use in valuing the Swiss equityportfolio.• The current value of Omni’s Swiss equity portfolio in ZAR.• The annualized forward premium or discount at which the ZAR is trading versus theCHF.CFA Guideline Answer:a.To eliminate the currency risk arising from the possibility that ZAR will appreciateagainst the CHF over the next 30-day period, Omni should sell 30-day forward CHF against 30-day forward ZAR delivery (sell 30-day forward CHF against USD and buy 30-day forward ZAR against USD).b.The calculations are as follows:• Using the currency cross rates of two forward foreign currencies and three currencies(CHF, ZAR, USD), the exchange would be as follows:--30 day forward CHF are sold for USD. Dollars are bought at the forward sellingprice of CHF1.5285 = $1 (done at ask side because going from currency intodollars)--30 day forward ZAR are purchased for USD. Dollars are simultaneously sold topurchase ZAR at the rate of 6.2538 = $1 (done at the bid side because going fromdollars into currency)--For every 1.5285 CHF held, 6.2538 ZAR are received; thus the cross currency rate is1.5285 CHF/6.2538 ZAR = 0.244411398.• At the time of execution of the forward contracts, the value of the 3 million CHFequity portfolio would be 3,000,000 CHF/0.244411398 = 12,274,386.65 ZAR.• To calculate the annualized premium or discount of the ZAR against the CHF requires comparison of the spot selling exchange rate to the forward selling price of CHF forZAR.Spot rate = 1.5343 CHF/6.2681 ZAR = 0.24477912030 day forward ask rate 1.5285 CHF/6.2538 ZAR = 0.244411398The premium/discount formula is:[(forward rate – spot rate) / spot rate] x (360 / # day contract) =[(0.244411398 – 0.24477912) / 0.24477912] x (360 / 30) =-1.8027126 % = -1.80% discount ZAR to CHFMINI CASE: SHREWSBURY HERBAL PRODUCTS, LTD.Shrewsbury Herbal Products, located in central England close to the Welsh border, is an old-line producer of herbal teas, seasonings, and medicines. Its products are marketed all over the United Kingdom and in many parts of continental Europe as well.Shrewsbury Herbal generally invoices in British pound sterling when it sells to foreign customers in order to guard against adverse exchange rate changes. Nevertheless, it has just received an order from a large wholesaler in central France for £320,000 of its products, conditional upon delivery being made in three months’ time and the order invoiced in euros.Shrewsbury’s controller, Elton Peters, is concerned with whether the pound will appreciate versus the euro over the next three months, thus eliminating all or most of the profit when the euro receivable is paid. He thinks this is an unlikely possibility, but he decides to contact the firm’s banker for suggestions about hedging the exchange rate exposure.Mr. Peters learns from the banker that the current spot exchange rate is €/£ is €1.4537, thus the invoice amount should be €465,184. Mr. Peters also learns that the three-month forward rates for the pound and the euro versus the U.S. dollar are $1.8990/£1.00 and $1.3154/€1.00, respectively. The banker offers to set up a forward hedge for selling the euro receivable for pound sterling based on the €/£ forward cross-exchange rate implicit in the forward rates against the dollar.What would you do if you were Mr. Peters?Suggested Solution to Shrewsbury Herbal Products, Ltd.Note to Instructor: This elementary case provides an intuitive look at hedging exchange rate exposure. Students should not have difficulty with it even though hedging will not be formally discussed until Chapter 8. The case is consistent with the discussion that accompanies Exhibit 5.9 of the text. Professor of Finance, Banikanta Mishra, of Xavier Institute of Management – Bhubaneswar, India contributed to this solution.Suppose Shrewsbury sells at a twenty percent markup. Thus the cost to the firm of the £320,000 order is £256,000. Thus, the pound could appreciate to €465,184/£256,000 = €1.8171/1.00 before all profit was eliminated. This seems rather unlikely. Nevertheless, a ten percent appreciation of the pound (€1.4537 x 1.10) to €1.5991/£1.00 would only yield a profit of £34,904 (= €465,184/1.5991 - £256,000). Shrewsbury can hedge the exposure by selling the euros forward for British pounds at F3(€/£) = F3($/£) ÷ F3($/€) = 1.8990 ÷ 1.3154 = 1.4437. At this forward exchange rate, Shrewsbury can “lock-in” a price of £322,217 (= €465,184/1.4437) for the sale. The forward exchange rate indicates that the euro is trading at a premium to the British pound in the forward market. Thus, the forward hedge allows Shrewsbury to lock-in a greater amount (£2,217) than if the euro receivable was converted into pounds at the current spotIf the euro was trading at a forward discount, Shrewsbury would end up locking-in an amount less than £320,000. Whether that would lead to a loss for the company would depend upon the extent of the discount and the amount of profit built into the price of £320,000. Only if the forward exchange rate is even with the spot rate will Shrewsbury receive exactly £320,000.Obviously, Shrewsbury could ensure that it receives exactly £320,000 at the end of three-month accounts receivable period if it could invoice in £. That, however, is not acceptable to the French wholesaler. When invoicing in euros, Shrewsbury could establish the euro invoice amount by use of the forward exchange rate instead of the current spot rate. The invoice amount in that case would be €461,984 = £320,000 x 1.4437. Shrewsbury can now lock-in a receipt of £320,000 if it simultaneously hedges its euro exposure by selling €461,984 at the forward rate of 1.4437. That is, £320,000 =€461,984/1.4437.。
胶体与界面化学英文5Static and Dynamic Light Scattering and Other Radiation Scattering
establish: the information on the diffusion coefficients of the particles, particle size, particles size distribution and etc.
16
§ 5.3 Scattering by small particles: Theory of Rayleigh scattering
1. Scattering by single molecules and gases
light
transmitted light
absorption light scattering light
17
(1) Rayleigh theory
A. The scattering centers are small in dimension compared to the wavelength of the radiation (about 1/20). B. The refractive index gradient (dn/dc) is not very large. C.The particles moves independently (exp. gas).
At sunset, we see mostly transmitted light. Since the blue has been most extensively removed from sunset light by scattering, the sky appears red at sunset.
第五章 -结构表征
粉末衍射结构分析的科学意义
（1）自然界存在的和人工合成的绝大多数固体 材料是多晶体。
（2）新材料研究中最先得到的大多是多晶。 （3）由于易生成孪晶、包晶、生长条件苛刻等
原因 , 很多材料的单晶生长都不容易甚至不 可能 。 （4）粉末衍射能方便进行高温、低温、强电磁 场、高压下的实验, 研究物质的相变。
Powder X-ray diffraction
Purpose: to identify crystalline phase---Bragg’s law:
n = 2dsin （d为晶面间距，θ为入射角，λ为波长，n为反射级数）
Bragg 对晶体衍射的处理是将晶体点阵看作由相当于半透明的镜面构成 的，一部分射线被反射，其余部分则透过平面，被其它平面相继反射。
XPREP
Direct method or Heavy-atom method
XS
Structure analysis Shelxtl program
Structure refinement
XL
晶体生长 挑选单晶体
安装晶体 预测量 搜集数据 解析结构 图文报告
Approach of the crystal growth
Producing good quality crystals of a suitable size is the first and most important step in determining any crystal structure. Crystallization is the process of arranging atoms or molecules that are in a fluid or solution state into an ordered solid state. This process occurs in two steps--nucleation and growth.
【金属基复合材料】第五章,复合材料基体与增强体
Introduction
The possibility of taking advantage of particular properties of the constituent materials to meet specific demands is the most important motivation for the development of composites. The terms matrix and reinforcement are often used. The matrix is a percolating “soft” phase (with in general excellent ductility, formability and thermal conductivity) in which are embedded the “hard” reinforcements (high stiffness, hardness, and low thermal expansion). The reinforcements can be continuous or discontinuous, orientated or disorientated. The composites are classified by: (1) their matrix (polymer, ceramic, metal), (2) their reinforcement, which includes the chemical nature (oxides, carbides, nitrides), shape (continuous fibers, short fibers, whiskers, particulates) and orientation, (3) their processing routes.
专业英语电子版教材
注意事项 (2)专业英语课程简介 ................................................................................................................ 错误！未定义书签。
Chapter 1 Matter and Measurement (2)1.1. Classification of Matter (3)1.2. Properties of Matter (3)1.3 Atoms, Molecules and Compounds (4)1.4. Numbers in Physical Quantities (5)1.5 Units of Measurement (8)1.6 The Dimensional Method (11)Word and sentence: (12)Chapter 2 Nomenclature of Inorganic Chemistry (13)2.1 Chemical Language (13)2.2 Nomenclature of Elements (14)2.3 Nomenclature of Inorganic Compounds (21)Chapter 3 Inorganic Chemistry (28)3.1 The Atomic Nature of Matter (28)3.2 Electronic Structure of Atoms (30)3.3 Periodicity of Atomic Properties (33)3.5 Molecular Geometry and Bonding Theories......................................................... 错误！未定义书签。
3.6 Chemical Reactions................................................................................................. 错误！未定义书签。
微积分第五章课件
▪ 5.1 Areas and Distances
The area problem
Area of rectangle Area of trapezoid 1. Areas of curved trapezoid Suppose the curved trapezoid is bounded by
Next we assume that f(x) is not a constant function. Since f(x) is continuous on [a, b], f(x) takes on the minimum and the maximum values on [a, b]. Let f(u) = m and f(v) = M be the
1 0
x2
dx
lim
0
n
i 1
i
2xi
y
y x2
lim
n
1 3
o
i 1x
n
Example 2. Use the definition to evaluate Solution: Use
to divide [1, 3] into n subintervals of equal width. We choose
and Find the area of A .
y f (x)
A?
Method:
1) Partition:
a x0 x1 x2 xn1 xn b
Use the lines x xi to divide A into small curved trapezoid;
2) Approximation: i [xi1 , xi ]
letter in place of x without changing the value of
Solutions溶液
SolutionsThis section will focus on what you need to know about solutions, solution concentrations, and colligative properties in order to be successful on the SAT II Chemistry test. This material is closely tied in with the material from the first half of this chapter and “The Structure of Matter.”Properties of Solutions A solution is a homogenous mixture of two or more substances that exist in a single phase. There are two main parts to any solution. The solute is the component of a solution that is dissolved in the solvent; it is usually present in a smaller amount than the solvent. The solvent is the component into which the solute is dissolved, and it is usually present in greater concentration. For example, in a solution of salt water, salt is the solute and water is the solvent. In solutions where water is the solvent, the solution is referred to as an aqueous solution. A solution does not have to involve liquids. For instance, air is a solution that consists of nitrogen, oxygen, carbon dioxide, and other trace gases, and solder is a solution of lead and tin. The general rule of thumb for solutions is the idea that like dissolves like. Polar, ionic substances are soluble in polar solvents, while nonpolar solutes are soluble in nonpolar solvents. For example, alcohol and water, which are both polar, can form a solution and iodine and carbon tetrachloride, which are both nonpolar, make a solution. However, iodine will not readily dissolve in polar water. In a solution, the particles are really small—anywhere from 0 to 100 nm. They never settle on standing, they cannot be separated by filtering, and light will pass through a solution unchanged. One type of mixture that is not a solution is known as the colloid. In a colloid, particles are between 100 and 1000 nm in size—still too small for our eyes to distinguish, but particles this small will not settle. As is the case in solutions, the particles cannot be filtered, but they do scatter light. Some examples of colloids include gelatin, fog, smoke, and shaving cream. Another type of mixture that is not considered a solution is known as a suspension. Suspensions have much larger particles: usually over 1000 nm. Particles in a suspension will settle on standing, can often be separated by a filter, and may scatter light, but they are usually not transparent. Some examples of suspensions are muddy water, paint, and some medicines, like Pepto-Bismol. The Solution Process In order for a solute to be dissolved in a solvent, the attractive forces between the solute and solvent particles must be great enough to overcome the attractive forces within the pure solvent and pure solute. The solute and the solvent molecules in a solution are expanded compared to their position within the pure substances.The process of expansion, for both the solute and solvent, involves a change in the energy of the system: this process can be either exothermic or endothermic. After dissolving, the solute is said to be fully solvated (usually by dipole-dipole or ion-dipole forces), and when the solvent is water, the solute is said tobe hydrated. The separation of the solute particles from one another prior to dissolving is an endothermic process for both solvent and solute (steps 1 and 2), but when the solute and solvent combine with each other, this is an exothermic process (step 3). If the energy released in step 3 is greater than the energy absorbed in steps 1 and 2, the solution forms and is stable.The term solubility refers to the maximum amount of material that will dissolve in a given amount of solvent at a given temperature to produce a stable solution. By looking at the plot of solubilities below, you can see that most solids increase in solubility with an increase in temperature.Gases, however, decrease in solubility with an increase in temperature. Degrees of Saturation When referring to solutions, there are three degrees of saturation—unsaturated, saturated, and supersaturated. If a solutionis unsaturated, the solvent is capable of dissolving more solute. When the solution is saturated, the solvent has dissolved the maximum amount of solute that it can at the given temperature. At this point we say that the solution is in a state of dynamic equilibrium—the processes of dissolving and precipitation are happening at the same rate. A supersaturated solution is one in which the solvent contains more solute than it can theoretically hold at a given temperature. Supersaturated solutions are often formed by heating a solution and dissolving more solute, then cooling the solution down slowly. These solutions are unstable and crystallize readily. Concentration Terms Solutions are often referred to as being concentrated or dilute. These two terms are very general.While concentrated indicates that there is a lot of solute dissolved in the solvent (perhaps the solution is near to being saturated) and dilute indicates that a small amount of solute is dissolved in the solvent, we often need to be exact with quantities in chemistry. The units of concentration that you should be familiar with for the SAT II exam are reviewed below.Molarity (M )The molarity of a solution is a measure of the number of moles of solute per liter of solution. This is the most common concentration unit used in chemistry. For instance, you might see an expression that looks like this:[NaCl] = 0.75which means that 0.75 mole of NaCl is dissolved per 1.00 L of solution. The brackets around the number indicate that the concentration is expressed in terms of molarity. Let’s now run through how you calculate the molarity of a solution. Example Calculate the molarity of a solution prepared by dissolving 20.0 g of solid NaOH in enough water to make 100 mL of solution. Explanation Convert grams to moles:Then convert mL to liters:Then divide:Dilution Dilution is the process of taking a more concentrated solution and adding water to make it less concentrated. The more concentrated solution before the dilution is performed is known as the stock solution. You can relate the concentration of the stock solution to the concentration of the diluted solution using the equation below:M1V1 = M2V2where M is molarity and V is the volume, in liters, of the solution. Try the following example using this equation. Example What volume of 6.0 M sulfuric acid (H2SO4) must be used to prepare 2.0 L of a 0.10 M H2SO4 solution? Explanation Just plug the numbers into the formula! Be careful to read closely.M1V1 = M2V2(6.0 M) (V1) = (0.10 M) (2.0 L)V1 = 0.033 Lor 33 mL should be measured out and then diluted by adding enough water to make 2.00 L total volume.Mass Percent (Weight Percent)The mass percent of a solution is another way of expressing its concentration. Mass percent is found by dividing the mass of the solute by the mass of the solution and multiplying by 100; so a solution of NaOH that is 28% NaOH by mass contains 28 g of NaOH for each 100 g of solution. Here’s the equation:Now try a problem involving the equation:Example A solution is prepared by mixing 5.00 g ethanol (C2H5OH) with 100.0 g water. Calculate the mass percent of ethanol in this solution. Explanation Plugging the values we were given into the mass percent equation, we get:Molality (m)The molality of a solution is a measure of the number of moles of solute per kilogram of solvent. Whereas the molarity of a solution is dependent on the volume of the solution, the molality is dependent on the mass of the solvent in the solution. Do not get these confused, and when you see either term on the SAT II Chemistry test, double-check to make sure which one they’re talking about—the words look similar, too! Try an example: Example A solution is prepared by mixing 80.0 g of sodiumhydroxide (NaOH) with 500.0 g of water. Calculate the molality of this solution. Explanation Convert grams of solute to moles:Convert grams of solvent to kg:Divide:Electrolytes Certain solutions are capable of conducting an electric current and these solutions are referred to as electrolytes. Generally speaking, we say that there are three classes of electrolytes (solutions that conduct a current): acids, bases, and salts.✧Strong electrolytes consist of solutes that dissociate completely in solution. Strong acids, strong bases, and soluble salts are in this category. (We will discuss acids and bases in chapter 6.)✧Nonelectrolytes are substances that are predominantly covalently bonded, generally will not produce ions in solution, and therefore are considered nonconductors.✧Weak electrolytes consist of solutes that dissociate only a little in solution. Weak acids, weak bases, and slightly soluble salts are in this category.The greater the degree of dissociation of the solute, the greater the conductivity of the solution. Consider two acid solutions that have the same concentration—hydrochloric acid and acetic acid. Hydrochloric acid ionizes completely, while only about 2% of the acetic acid molecules ionize. If a conductivity apparatus were used to test the two solutions, HCl would conduct an electric current to a much greater degree because there is more available charge in solution. Below is a figure showing the ionization of barium chloride; as you can see, the Ba+ and Cl- ions are floating free in solution, and this makes barium chloride an electrolyte.Colligative Properties Properties of solutions that depend on the number of solute particles present per solvent molecule are called colligative properties. The concentration of solute in a solution can affect various physical properties of the solvent including its freezing point, boiling point, and vapor pressure. For the SAT II you will only need to be familiar with the first two. Freezing Point Depression The freezing point of a substance is defined as the temperature at which the vapor pressure of the solid and the liquid states of that substance are equal. If the vapor pressure of the liquid is lowered, the freezing point decreases.Why is a solution’s freezing point depressed below that of a pure solvent? The answer lies in the fact that molecules cluster in order to freeze. They must be attracted to one another and have a spot in which to cluster; if they act as a solvent, solute molecules get in the way and prevent them from clustering tightly together. The more ions in solution, the greater the effect on the freezing point. We can calculate the effect of these solute particles by using the following formula:DT f = K f m solute iWhereDT f = the change in freezing pointK f = molal freezing point depression constant for the substance (for water = 1.86oC/m)m = molality of the solutioni = number of ions in solution (this is equal to 1 for covalent compounds and is equal to the number of ions in solution for ionic compounds)Boiling Point Elevation As you learned earlier in this chapter, the boiling point of a substance is the temperature at which the vapor pressure equals atmospheric pressure. Because vapor pressure is lowered by the addition of a nonvolatile solute, the boiling point is increased. Why? Since the solute particles get in the way of the solvent particles trying to escape the substance as they move around faster, it will take more energy for the vapor pressure to reach atmospheric pressure, and thus the boiling point increases. We can calculate the change in boiling point in a way that’s similar to how we calculate the change in freezing point:DT b = K b msolute iWhereK b = molal boiling point elevation constant (for water = 0.51 C/m)Now try a problem that deals with freezing point depression and boiling point elevation. Example Calculate the freezing point and boiling point of asolution of 100 g of ethylene glycol (C2H6O2) in 900 g of water. Explanation Calculate molality:Freezing point depression = (m)(K f)(i)T f = (1.79)(1.86)(1) = 3.33oCFreezing point = 0oC - 3.33oC = -3.33oCBoiling point elevation = (m)(Km)(i)T b = (1.79)(0.51)(1) = 0.91oCBoiling point = 100oC + 0.91oC = 100.91oC。
Chapter_05
※ The two vortices tend to drag the surrounding air with them, and this secondary movment induces a small component is called downwash(下洗）. ※ The downwash velocity combines with the freestream velocity to produce a local relative wind which is canted downward in the vicinity of each airfoil section of the wing. ※ definition of induced angle of attack
a wing-tip vortices destroy the net pressure balance
b the wing-tip vortices contain large amount of translational and rotational energy, and this energy serves no useful purpose. In effect, the extra power should be provided by the engine to overcome the the induced drag.
5.3 Prandtl’s Classical Lifting-line Theory
Importance of the Prandtl’s lifting-line theory
bound vortex and free vortex
Replacement of the finite wing with a bound vortex
第5章稀溶液(新)
适用范围：难挥发性、非电解质、 稀溶液（xB< 0.02）
5-2 溶液的沸点升高 5-2-1 液体的沸点 5-2-2 溶液的沸点升高
5-2 溶液的沸点升高 5-2-1液体的沸点（boiling point）（Tb）
1.液体蒸发的特点 T < Tb ，表面蒸发 T = Tb ， 内 部 形 成 气 泡 ， 内 、 表 蒸 发 （气泡内压=外压） 2.定义：液体蒸气压和外界压力相等时的温度。
（2）不同的物质温度相同，蒸气压不同(0℃时)
乙醚 乙醇 苯 水 汞 65 5.8 9.9 2.3 1.6×10-4 kPa kPa kPa kPa kPa
（3）不同的物质，沸点不同 乙醚 34.6℃ 101.3kPa 乙醇 78.5℃ 101.3kPa 水 100℃ 101.3kPa
影响蒸气压的因素 乙醚 乙醇 水
②第二表达式
xA+ xB =1
xA=1-xB Δp = pºxB
p = pº （1- xB）
Δp = pº = pº （1- xB）= pºxB -p -pº 浓度越大，蒸气压下降越多.
③第三表达式
Raoult定律仅适合于稀溶液 在稀溶液中nA>>nB
nA+nB≈ nA
nB nB nB nB M A xB nA nB nA mA / M A mA
测ΔTb，ΔTf →测Mr，哪种方法更好 ? ΔTf
①大多数溶剂Kf > Kb，测定ΔTf比ΔTb误差小; ②生物样品温度高时易变性，而测定ΔTf是在低温 下进行的，反复多次也不会变性，故选择ΔTf 。
例5-2：将0.200g葡萄糖溶于10.0g水中，溶液的凝 固点降低为0.207℃，试求葡萄糖的相对分子质量。 解：水的Kf=1.86(K· mol-1)， mB= 0.200g ； kg·
小学上册F卷英语第5单元寒假试卷
小学上册英语第5单元寒假试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.What is the name of the famous ancient city in Egypt?A. CairoB. AlexandriaC. LuxorD. GizaD2.The ______ (小鸟) builds a nest for its eggs.3.Chemical properties can be observed during a _____ reaction.4. A polymer is a large molecule made up of many ______ units.5.We enjoy visiting the ___. (zoo)6.The chemical symbol for bromine is _____.7.What is the term for a young monkey?A. KidB. PupC. InfantD. BabyD Baby8.What do you call the outer layer of the Earth?A. CoreB. MantleC. CrustD. LayerC9.What is the name of the famous English playwright known for his tragic plays?A. Charles DickensB. William ShakespeareC. George OrwellD. J.K. RowlingB10.Which of these is a mode of transportation?A. PencilB. BicycleC. BookD. Chair11.I enjoy making _______ (手工艺品). It lets me be _______ (形容词) and creative.12.The _____ (花卉香气) enhances the atmosphere.13.I saw a _______ (小鹿) in my yard.14. A solution can be ______ or colored.15.The teacher assigns creative _____ (项目).16. A __________ is shaped by the action of water and erosion.17.The _______ (蛇) slithers on the ground.18.The __________ (历史的参与性) enhances engagement.19.The ________ is known for its bright and cheerful presence.20.I have a ___ (pet/animal) at home.21.What is the name of the story about a girl who befriends seven dwarfs?A. CinderellaB. Snow WhiteC. RapunzelD. AladdinB22.What is the tallest mountain in the world?A. K2B. EverestC. KilimanjaroD. DenaliB23. A natural resource that is not renewable is _____ (fossil fuels).24.What do you call a sweet, baked treat made from chocolate?A. CakeB. BrownieC. CookieD. All of the aboveD25.The process of making glass involves heating sand to a high _____.26.The chemical formula for acetic acid is ________.27.What is the name of the famous American holiday celebrated on the last Thursday in November?A. Independence DayB. ThanksgivingC. HalloweenD. ChristmasB Thanksgiving28.What is the term for a human's outer covering?A. SkinB. MuscleC. BoneD. FatA29.The process of heat being absorbed is called _______.30.How many players are there in a soccer team?A. SevenB. EightC. NineD. ElevenD31.What do you need to draw?A. PencilB. SpoonC. ForkD. PlateA32.What is the capital city of Hungary?A. BudapestB. DebrecenC. SzegedD. Pécs33.The turtle is very ______.34.The __________ is a large area of dry land.35.The train is ______ (fast) and convenient.36.My grandma has a wealth of __________ (历史) to share.37.What is the capital of Belgium?A. AmsterdamB. BrusselsC. LuxembourgD. Paris38. A ________ is a large area of land that is covered in snow.39.What do we call a large area of trees?A. DesertB. ForestC. MountainD. Field40.The __________ (历史的遗址) reveal clues about our ancestors.41.What is the capital city of Argentina?A. Buenos AiresB. SantiagoC. LimaD. BogotáA42.The beach is _______ (sandy).43.He plays the _______ (吉他) very well.44.The _____ (sky) is clear.45.My teacher helps us _______ (动词) better. 她很 _______ (形容词).46.Which vegetable is orange and long?A. PotatoB. CarrotC. BroccoliD. Cucumber47.My brother enjoys __________ (参加) local sports events.48.The weather is ________ (晴天).49.The stars are _____ (twinkling/shining) in the sky.50.The process of burning is a type of ______ reaction.51.The kitty loves to chase a _________. (光点)52.What is the name of the largest land animal?A. ElephantB. GiraffeC. HippopotamusD. RhinoA53.We are going to ___ a field trip. (have)54.The boys are ___ in the yard. (running)55. A __________ solution has less solute than it can dissolve.56.The _____ (rainbow) appears after rain.57.The ____ loves to chase butterflies in the garden.58.What is the smallest continent?A. AsiaB. AntarcticaC. AustraliaD. EuropeC Australia59.The chemical symbol for cobalt is ______.60.The tree is ___ (bushing/barren).61.Gardening can help promote ______ (身心健康).62.The weather can affect our ______ (心情).63.The chemical symbol for lithium is ______.64.What is the main ingredient in tacos?A. BreadB. TortillaC. RiceD. NoodlesB65.The ________ (camera) takes good pictures.66.The first successful flight of a powered aircraft was in _______.67.Metals tend to lose ______ in reactions.68.What is the name of the fairy in "Peter Pan"?A. Tinker BellB. CinderellaC. Snow WhiteD. ArielA69.What is the fastest land animal?A. CheetahB. HorseC. LionD. Gazelle70.What is the name of the famous painting by Leonardo da Vinci?A. The Starry NightB. The Last SupperC. The Girl with a Pearl EarringD. Mona LisaD71.Which month comes before January?A. DecemberB. NovemberC. OctoberD. February72.The chemical symbol for erbium is ______.73.What is the main ingredient in potato chips?A. RiceB. PotatoC. CornD. WheatB74.Oxygen is necessary for _______.75.What do you wear on your feet?A. HatB. ShoesC. GlovesD. ScarfB76.What is the capital of Bhutan?A. ThimphuB. ParoC. PunakhaD. Phuentsholing77.The ________ (地形) can be very rugged.78.The train is _______ (准时到达).79.What do we call a place where animals are kept for public viewing?A. AquariumB. ZooC. FarmD. Circus80.What is the primary reason for seasons on Earth?A. Earth's distance from the SunB. The tilt of Earth's axisC. The phase of the MoonD. Solar flares81.What is the primary ingredient in hummus?A. LentilsB. ChickpeasC. PeasD. Beans82.What is the currency used in the United States?A. EuroB. YenC. DollarD. Peso83.What is the capital city of Libya?A. TripoliB. BenghaziC. MisrataD. Tobruk84.The cake is ______ with colorful sprinkles. (topped)85.My sister loves __________ (动物) and wants to volunteer at shelters.86. A ______ (田野) can be colorful with wildflowers.87.Planting in pots allows for ______ in small spaces. (在花盆中种植可以在小空间中进行种植。
材料科学与工程基础英文版第五版课后习题
Homework 11.1 What are materials? List eight commonly encountered engineering materials. Answer1.1: Materials are substances of which something is composed or made. Steels, aluminum alloys, concrete, wood, glass, plastics, ceramics and electronic materials.1.2 What are the main classes of engineering materials?Answer1.2: Metallic, polymeric, ceramic, composite, and electronic materials are the five main classes.1.3 What are some of the important properties of each of the five main classes of engineering materials?Answer1.3:Metallic Materials• many are relatively strong and ductile at room temperature• some have good strength at high temperature• most have relatively high electrical and thermal conductivitiesPolymeric Materials• generally are poor electrical and thermal conductors• most have low to medium strengths• most have low densities• most are relatively easy to process into final shape• some are transparentCeramic Materials• generally have high hardnes s and are mechanically brittle• some have useful high temperature strength• most have poor electrical and thermal conductivitiesComposite Materials• have a wide range of strength from low to very high• some have very high strength-to-weight ratios (e.g. carbon-fiber epoxy materials)• some have medium strength and are able to be cast or formed into a variety of sha (e.g. fiberglass-polyester materials)• some have useable strengths at very low cost (e.g. wood and concrete)Electronic Materials• able to detect, amplify and transmit electrical signals in a complex manner• are light weight, compact and energy efficient1.8 What are nanomaterials? What are some proposed advantages of using nanomaterials over their conventional counterparts?Answer1.8: Are defined as materials with a characteristic length scale smaller than 100 nm. The length scale could be particle diameter, grain size in a material, layer thicknessin a sensor, etc. These materials have properties different than that at bulk scale or at themolecular scale. These materials have often enhanced properties and characteristics because of their nano-features in comparison to their micro-featured counterparts. The structural, chemical, electronic, and thermal properties (among other characteristics) are often enhanced at the nano-scale.Homework 2Chapter 3, Problem 4What are the three most common metal crystal structures? List five metals that have each of these crystal structures. Chapter 3, Solution 4The three most common crystal structures found in metals are: body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP). Examples of metals having these structures include the following. BCC:iron,α-vanadium, tungsten, niobium, and chromium.FCC: copper, aluminum, lead, nickel, and silver. HCP: magnesium, titanium,α-zinc, beryllium, and cadmium.Chapter 3, Problem 5For a BCC unit cell, (a) how many atoms are there inside the unit cell, (b) what is the coordination number for the atoms, (c) what is the relationship between the length of the side a of the BCC unit cell and the radius of its atoms, and (d) APF = 0.68 or 68%Chapter 3, Solution 5(a) A BCC crystal structure has two atoms in each unit cell. (b) A BCC crystal structure has a coordination number of eight . (c) In a BCC unit cell, one complete atom and two atom eighths toucheach other along the cube diagonal. This geometry translates into the relationship 4.R =Chapter 3, Problem 6For an FCC unit cell, (a) how many atoms are there inside the unit cell, (b) What is the coordination number for the atoms, (c) 24R a =, and (d) what is the atomic packing factor?Chapter 3, Solution 6(a) Each unit cell of the FCC crystal structure contains four atoms. (b) The FCC crystal structure has acoordination number of twelve . (d) By definition, the atomic packing factor is given as:volume of atoms in FCC unit cellAtomic packing factor volume of the FCC unit cell=These volumes, associated with the four-atom FCC unit cell, are33416433atoms V R R ππ⎡⎤==⎢⎥⎣⎦and 3unit cellV a =where a represents the lattice constant. Substitutinga =, 33unit cellV a ==The atomic packing factor then becomes,316APF (FCC unit cell)332R R π⎛⎫== ⎪⎝⎭⎝⎭=0.74 Chapter 3, Problem 7For an HCP unit cell (consider the primitive cell), (a) how many atoms are there inside the unit cell, (b) What is the coordination number for the atoms, (c) what is the atomic packing factor, (d) what is the ideal c/a ratio for HCP metals, and (e) repeat a through c considering the “larger 〞 cell.Chapter 3, Solution 7The primitive cell has (a) two atoms/unit cell; (b) The coordination number associated with the HCP crystal structure is twelve . (c)the APF is 0.74 or 74%; (d) The ideal c/a ratio for HCP metals is ; (e) all answers remain the same except for (a) where the new answer is 6.Homework 3 Chapter 3, Problem 25Lithium at 20︒C is BCC and has a lattice constant of 0.35092 nm. Calculate a value for the atomic radius of a lithium atom in nanometers.Chapter 3, Solution 25For the lithium BCC structure, which has a lattice constant of a = 0.35092 nm, the atomic radius is,R ===0.152 nmPalladium is FCC and has an atomic radius of 0.137 nm. Calculate a value for its lattice constant a in nanometers.Chapter 3, Solution 27Letting a represent the FCC unit cell edge length and R the palladium atomic radius,4 orR a ====0.387 nmChapter 3, Problem 31 Draw the following directions in a BCC unit cell and list the position coordinates of the atoms whose centers are intersected by the direction vector: (a ) [100] (b ) [110] (c ) [111]Chapter 3, Solution 31Chapter 3, Solution 32(1, 0, 0)yxzyxz[111]x = +1y = -1 z = -1 x = +1 y = -1 z = 0(a) (b)[110](c)(d)A cubic plane has the following axial intercepts: 121332, , a b c ==-=. What are the Miller indicesof this plane?Chapter 3, Solution 46Given the axial intercepts of (⅓, -⅔, ½), the reciprocal intercepts are:11313,, 2.2x y z ==-=Multiplying by 2 to clear the fraction, the Miller indices are .(634)Chapter 3, Problem 50Determine the Miller indices of the cubic crystal plane that intersects the following positioncoordinates:1122(, 0, ); (0,0,1); (1,1,1).Chapter 3, Solution 50First locate the three position coordinates as shown. Next, connect points a and b and extend the line to point d . Complete the plane by connecting point d to c and point c to b . Using (1, 0, 1) as the plane origin, x = -1, y = 1 and z = –1. The intercept reciprocals are thus1111,1, 1.x y z =-==- The Miller indices are .(111)你的好评和关注，我们将会做得更好】a(½, 0, ½ )。
FEKO中文手册第五章
5 在CADFEKO中定义求解配置。
利用CADFEKO 2,我们可以建立模型并且得到其在CADFEKO中的完全解。
对于高级用户而言，EDITFIKO 提供了关于求解的更多控制（见5.12节）。
但是，需要注意的是，我们不能在CADFEKO和EDITFEKO中同时控制求解。
一旦*.pre文件在CADFEKO之外定义或编辑，那么在CADFEKO中的求解配置选项就不能再使用了。
通过选择主菜单中Solution →Enable solution configuration，可以重新使用CADFEKO设置，只是在*.pre文件中的用户设置将会被忽略。
5.1使用绝缘耗散媒质在模型中，须要在使用媒质之前定义它们。
模型中的绝缘体由在相应几何体区域中设置Dielectric媒质来确定。
传导损耗是由传导表面是用户定义的金属媒质构成造成的。
表面覆盖层和薄的绝缘层由用户定义的Layered dielectrics在模型表面确定。
Layered dielectrics是由多个单一绝缘层构成的。
在某些情况下我们只知道表面的平均表面阻抗，这时表面可以被看作是一个阻抗层（Impedance sheet）。
用户定义的媒质列举在目录树的Media下。
每种类型都被单独列出来，只是须要使得媒质名称是全局唯一的并且不超过43个字符。
每个选项旁边的颜色标志表明了使用哪种颜色来表示在3D视图和明细树形结构中的媒质（见3.4.2节）。
我们可以通过每种媒质的弹出菜单中Change display color项来修改颜色设置。
（选择的颜色设置保存在*.cfs 文件中）前三个选项分别是良电导体，良磁导体（目前只在设置导磁地平面时使用）和自由空间。
自由空间不能编辑也不能删除。
虽然单一阻抗层严格来说不能看作是一种介质，但是用户定义的阻抗层也在树形结构的Media项下列举了出来。
这时可以像其他介质那样定义、应用和显示阻抗层。
绝缘介质可以在树形结构中重命名，也可以在其相应的属性对话框中修改。
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还可以直接得到下面的重要关系式。 If
B b(T , P , x1 , , xk 1 , xk 1 , , x K )
Bi xi 0 x i 1 j T , P , x[ j , k ]
K
21
Gibbs-Duhemn 方程的应用： 1、判断溶液热力学性质表达式的正确性(原理：由溶液热力 学性质计算得到的偏摩尔性质必须满足Gibbs-Duhem方程， 如果不满足，说明溶液热力学性质的表达式不正确。)。 2、已知一个组分的偏摩尔性质，求另外一个组分的偏摩尔 性质。
特别注意的是： i G i
10
如果溶液的组成不用 ni 表示，而是用 xi 表示，由于 xi 之 间存在关系式
i 1
K
xi 1
K 1 i 1
xK 1
溶液的摩尔性质可以表示成
xi
B b(T , P , x1 , , xK 1 )
K 1 B B B dB dxi dT dP x i 1 T P , x P T , x i T , P , x[ i , K ]
Chapter 5 溶液热力学性质
Solution Thermodynamics
1
Why should we study Solution Thermodynamics?
Chapter 4 treats the thermodynamic properties of pure substances or constant-composition fluids. However applications of Chemical Engineering Thermodynamics are often to systems wherein composition is a primary variable. In the chemical, petroleum, and pharmaceutical industries multicomponent gases or liquids commonly undergo composition changes as the result of mixing and separation processes, or chemical reaction.
K 1 i 1
( B i B K )dxi
K 1 i 1
B i dxi B K
K 1 i 1
dxi
K
K 1 i 1
B i dxi B K dxK
i 1
B i dxi
K B B dB dT dP B i dxi i 1 T P , x P T , x
3
对于单相敞开系统，系统与环境(surrounding)之间有物 质的交换，系统的组成要发生变化。此时，系统总的Gibbs 能是温度、压力和组成的函数。即
nG g ( P , T , n1 , n2 , , ni , , nK )
当系统的T, P, 和ni 都发生变化时，nG 的变化量是
K ( nG ) ( nG ) ( nG ) d ( nG ) dni dP T dT i1 n P T , n P ,n i T , P ,n[ i ]
右边第一项和第二项偏导数表示在恒组成条件下温度、压力 对溶液热力学性质的影响。
9
上式最后一项偏导数是一种新的物理量，定义为溶液中 组分的偏摩尔性质：
( nB ) Bi ni T , P ,n[ i ]
K ( nB ) ( nB ) d ( nB ) dP T dT i1B i dni P T , n P ,n
B B ndB Bdn n dP n dT B i ( xi dn ndxi ) i P T , n T P , n
17
B B dT B i dxi n dB dP i P T , x T P , x
B Bi B K x i T , P , x[ i , K ]
K 1 B B dB dT dP ( B i B K )dxi i 1 T P , x P T , x
13
Since
B xi B i dn 0 i
Since
B B dB dP dT B i dxi i P T , x T P , x
Thus
B xi B i
i
or
nB ni B i
i
18
Gibbs-Duhem 方程 Question：溶液中组分的偏摩尔性质是独立变化还是相互 制约？如果是相互制约，它们之间存在什么样的关系式？ 因为
2
5.1 变组成体系热力学性质关系式
对于组成不变的封闭系统（没有化学反应发生，没有 相变发生），
d (nG) (nV )dP (nS )dT
因此，
( nG ) nV P T ,n ( nG ) nS T P ,n
偏导数的下标n 表示体系组成不 变。
对于给定的敞开体系，其总的热力学性质是温度、压力 和组成的函数 nB b(T , P , n1 , n2 , , ni , , nK ) 当系统的温度、压力和组成都发生变化时，溶液热力学性质 变化量为
K ( nB ) ( nB ) ( nB ) d ( nB ) dni dP T dT i1 n P T , n P ,n i T , P ,n[ i ]
根据
nU nH P(nV )
d ( nU ) Td ( nS ) Pd ( nV )
i 1
K
i dni
由该公式也可以写出化学位的另一个定义式
( nU ) i ni nS ,nV ,n[ i ]
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根据
nA = nU- T(nS)
d ( nA) ( nS )dT Pd ( nV )
d ( nG ) ( nV )dP ( nS )dT
根据
K
i dni
nH nG T (nS )
d ( nH ) Td ( nS ) ( nV )dP
i 1
K
i dni
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由上述公式可以写出化学位的另一个定义式
( nH ) i ni nS , P ,n[ i ]
K
i 1
K
i dni
i 1
i dni
K
d ( nA) ( nS )dT Pd ( nV )
i 1
i dni
d ( nG ) ( nV )dP ( nS )dT
称为变组成体系的热力学基本方程。
i 1
K
i dni
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5.2 偏摩尔性质（Partial molar Properties）
Since
ni x i n
ni xi n x x j T , P , x[ j , K ] j T , P , x[ j , K ]
0 i , K
1 i=j -1 i = K n
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Thus
( nB ) n( B j B K ) x j T , P , x[ j , K ] B B j BK x j T , P , x[ j , K ]
下标n[i]表示除 i 组分外其它组分的摩尔数不变。
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定义
( nG ) i ni T , P ,n[ i ]
( nG ) nV P T ,n ( nG ) nS T P ,n
i 1
为化学位，同时有，
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Example
For a binary of components 1 and 2, if the partial molar enthalpy H 1 were available as a function of mole fraction x1, show how H 2 and the mixture enthalpy can be determined. The data H 1 f ( x1 ) are at constant T and P.
i 1
K
i dni
由该公式可以写出化学位的另一个定义式
( nA ) i ni T ,nV ,n[ i ]
化学位有4个定义式，它们都是等价的。
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方程组
d ( nU ) Td ( nS ) Pd ( nV )
d ( nH ) Td ( nS ) ( nV )dP
该公式就是著名的Gibbs-Duhemn方程，它在溶液热力学领 域具有非常重要的作用。
如果溶液温度和压力不变，只是组成发生变化，GibbsDuhemn方程简化成
xi d B i
i
0
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由Gibbs – Duhemn方程
xi d B i
i
B B dP dT P T , x T P , x
B xi B i
i
dB xi d B i B i dxi
i i
(A)
又因为
B B dB dP dT B i dxi i P T , x T P , x