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One dimensional element details

One dimensional element details
One dimensional element details

One Dimensional Elements

In the finite element method elements are grouped as 1D, 2D and 3D elements. Beams and plates are grouped as structural elements. One dimensional elements are the line segments which are used to model bars and truss. Higher order elements like linear, quadratic and cubic are also available. These elements are used when one of the dimension is very large compared to other two. 2D and 3D elements will be discussed in later chapters.

Seven basic steps in Finite Element Method

These seven steps include

?Modeling

?Discretization

?Stiffness Matrix

?Assembly

?Application of BC’s

?Solution

?Results

Let’s consider a bar subjected to the forces as shown

First step is the modeling lets us model it as a stepped shaft consisting of discrete number of elements each having a uniform cross section. Say using three finite elements as shown. Average c/s area within each region is evaluated and used to define elemental area with uniform cross-section.

A1= A1’+ A2’/ 2 similarly A2 and A 3 are evaluated Second step is the Discretization that includes both node and element numbering, in this model every element connects two nodes, so to distinguish between node numbering and element numbering elements numbers are encircled as shown.

Above system can also be represented as a line segment as shown below.

Here in 1D every node is allowed to move only in one direction, hence each node as one degree of freedom. In the present case the model as four nodes it means four dof. Let Q1, Q2, Q3 and Q4 be the nodal displacements at node 1 to node 4 respectively, similarly F1, F2, F3, F4 be the nodal force vector from node 1 to node 4 as shown. When these parameters are represented for a entire structure use capitals which is called global numbering and for representing individual elements use small letters that is called local numbering as shown.

This local and global numbering correspondence is established using element connectivity element as shown

Now let’s consid er a single element in a natural coordinate system that varies in ξand η, x1be the x coordinate of node 1 and x2be the x coordinate of node 2 as shown below.

Let us assume a polynomial

Now

After applying these conditions and solving for constants we have

a0=x1+x2/2 a1= x2-x1/2

Substituting these constants in above equation we get

Where N1 and N2 are called shape functions also called as interpolation functions.

These shape functions can also be derived using nodal displacements say q1 and q2 which are nodal displacements at node1 and node 2 respectively, now assuming the displacement function and following the same procedure as that of nodal coordinate we get

U = Nq

U = Nq

Where N is the shape function matrix and q is displacement matrix. Once the displacement is known its derivative gives strain and corresponding stress can be determined as follows.

element strain displacement matrix

From the potential approach we have the expression of as

Third step in FEM is finding out stiffness matrix from the above equation we have the value of K as

But

Therefore now substituting the limits as -1 to +1 because the value of varies between -1 & 1 we have

Integration of above equations gives K which is given as

Fourth step is assembly and the size of the assembly matrix is given by number of nodes X degrees of freedom, for the present example that has four nodes and one degree of freedom at each node hence size of the assembly matrix is 4 X 4. At first determine the stiffness matrix of each element say k1, k2 and k3 as

Similarly determine k2 and k3

The given system is modeled as three elements and four nodes we have three stiffness matrices.

Since node 2 is connected between element 1 and element 2, the elements of second stiffness matrix (k2) gets added to second row second element as shown below similarly for node 3 it gets added to third row third element

Fifth step is applying the boundary conditions for a given system. We have the equation of equilibrium KQ=F

K = global stiffness matrix

Q = displacement matrix

F= global force vector

Let Q1, Q2, Q3, and Q4 be the nodal displacements at node 1 to node 4 respectively. And F1, F2, F3, F4 be the nodal load vector acting at node 1 to node 4 respectively.

Given system is fixed at one end and force is applied at other end. Since node 1 is fixed displacement at node 1 will be zero, so set q1 =0. And node 2, node 3 and node 4 are free to move hence there will be displacement that has to be determined. But in the load vector because of fixed node 1 there will reaction force say R1. Now replace F1 to R1 and also at node 3 force P is applied hence replace F3 to P. Rest of the terms are zero.

Sixth step is solving the above matrix to determine the displacements which can be solved either by

?Elimination method

?Penalty approach method

Details of these two methods will be seen in later sections.

Last step is the presentation of results, finding the parameters like displacements, stresses and other required parameters.

Body force distribution for 2 noded bar element

We derived shape functions for 1D bar, variation of these shape functions is shown below .As a property of shape function the value of N1 should be equal to 1 at node 1 and zero at rest other nodes (node 2).

From the potential energy of an elastic body we have the expression of work done by body force as

Where f b is the body acting on the system. We know the displacement function U = N1q1 + N2q2 substitute this U in the above equation we get

This amount of body force will be distributed at 2 nodes hence the expression as 2 in the denominator.

Surface force distribution for 2 noded bar element

Now again taking the expression of work done by surface force from potential energy concept and following the same procedure as that of body we can derive the expression of surface force as

Where T e is element surface force distribution.

Methods of handling boundary conditions

We have two methods of handling boundary conditions namely Elimination method and penalty approach method. Applying BC’s is one of the vital role in FEM improper specification of boundary conditions leads to erroneous results. Hence BC’s need to be accurately modeled.

Elimination Method: let us consider the single boundary conditions say Q1 = a1.Extremising results in equilibrium equation.

Q = [Q1, Q2, Q3……….Q N]T be the displacement vector and

F = [F1, F2, F3…………F N]T be load vector

Say we have a global stiffness matrix as

K11K12 (1)

K21 K22 (2)

.

K =

.

.

K N1 K N2…………..K NN

Now potential energy of the form ∏ = ? Q T KQ-Q T F can written as ∏ = ? (Q1K11Q1 +Q1K12Q2+…..+ Q1K1N Q N

+ Q2K21Q1+Q2K22Q2+………. + Q2K2N Q N

…………………………………………

……………………………………… ..

+ Q N K N1Q1+Q N K N2Q2+……. +Q N K NN Q N)

-(Q1F1 + Q2F2+…………………+Q N F N) Substituting Q1 = a1 we have

∏ = ? (a1K11a1 +a1K12Q2+…..+ a1K1N Q N

+ Q2K21a1+Q2K22Q2+………. + Q2K2N Q N

…………………………………………

……………………………………… ..

+ Q N K N1a1+Q N K N2Q2+……. +Q N K NN Q N)

-(a1F1 + Q2F2+…………………+Q N F N) Extremizing the potential energy

ie d∏/dQi = 0 gives

Where i = 2, 3...N

K22Q2+K23Q3+………. + K2N Q N = F2– K21a1

K32Q2+K33Q3+………. + K3N Q N = F3– K31a1

………………………………………………

K N2Q2+K N3Q3+………. + K NN Q N = F N– K N1a1 Writing the above equation in the matrix form we get

K22K23…………K2N Q2 F2-K21a1

K32 K33………….K2N Q3 F3-K31a1

. .

=

. .

.

K N2 K N3…………..K NN Q N F N-K N1a1

Now the N X N matrix reduces to N-1 x N-1 matrix as we know Q1=a1 ie first row and first column are eliminated because of known Q1. Solving above matrix gives displacement components. Knowing the displacement field corresponding stress can be calculated using the relation σ = εBq.

Reaction forces at fixed end say at node1 is evaluated using the relation R1= K11Q1+K12Q2+……………+K1N Q N-F1

Penalty approach method: let us consider a system that is fixed at both the ends as shown

In penalty approach method the same system is modeled as a spring wherever there is a support and that spring has large stiffness value as shown.

Let a1 be the displacement of one end of the spring at node 1 and a3 be displacement at node 3. The displacement Q1at node 1 will be approximately equal to a1, owing to the relatively small resistance offered by the structure. Because of the spring addition at the support the strain energy also comes into the picture of ∏ equation .Therefore equation ∏ becomes

∏ = ? Q T KQ+ ? C (Q1–a1)2 - Q T F

The choice of C can be done from stiffness matrix as

We may also choose 105 &106 but 104 found more satisfactory on most of the computers.

Because of the spring the stiffness matrix has to be modified ie the large number c gets added to the first diagonal element of K and Ca1 gets added to F1 term on load vector. That results in.

A reaction force at node 1 equals the force exerted by the spring on the system which is given by

To solve the system again the seven steps of FEM has to be followed, first 2 steps contain modeling and discretization. this result in

Third step is finding stiffness matrix of individual elements

Similarly

Next step is assembly which gives global stiffness matrix

Now determine global load vector

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Hey Jude, don't make it bad. 嘿!Jude,不要这样沮丧 Take a sad song and make it better 唱首悲伤的歌曲让事情好转Remember to let her into your heart 将她牢记在心底 Then you can start to make it better. 然后开始让事情好转 Hey Jude, don't be afraid 嘿Jude,不要害怕 You were made to go out and get her. 你生来就是要得到她 The minute you let her under your skin, 在你将她放在心上的时候

Then you begin to make it better. 你就开始做的更好 And anytime you feel the pain, 无论何时,当你感到痛苦 hey Jude, refrain, 嘿Jude 停下来 Don't carry the world upon your shoulders. 不要把全世界都扛在你肩膀上 For well you know that it's a fool who plays it cool 你应该很清楚谁耍酷谁就是笨蛋 By making his world a little colder. 这会使他世界更加冰冷 Hey Jude don't let me down 嘿Jude 不要让我失望 You have found her, now go and get her. 你已遇见她现在去赢的她芳心 Remember to let her into your heart, 记住将她牢记在你心中 Then you can start to make it better. 然后你就可以开始做的更好 So let it out and let it in, hey Jude, begin, 所以遇事要拿得起放得下嘿!jude ,振作起来 You're waiting for someone to perform with. 你一直期待的那个和你一起表演的人 And don't you know that it's just you, hey Jude, you''ll do 你不知道那个人就是你自己吗?嘿jude 你办得到的The movement you need is on your shoulder 下一步该怎么做就全看你自己 Hey Jude, don't make it bad. 嘿Jude 不要这样消沉 Take a sad song and make it better 唱首伤感的歌曲会使你振作一些 Remember to let her under your skin 记得心中常怀有她 Then you'll begin to make it better 然后你就会使它变得更好 Better better better better better better, Oh. 更好、更好、更好、更好、更好 Na na na, na na na na, na na na

美国英文简介-An Introduction to U.S.

The United States of America (also referred to as the United States, the U.S., the USA, or America) is a federal constitutional republic comprising fifty states and a federal district. The country is situated mostly in central North America, where its forty-eight contiguous states and Washington, D.C., the capital district, lie between the Pacific and Atlantic Oceans, bordered by Canada to the north and Mexico to the south. The state of Alaska is in the northwest of the continent, with Canada to the east and Russia to the west across the Bering Strait. The state of Hawaii is an archipelago in the mid-Pacific. The country also possesses several territories in the Caribbean and Pacific. At 3.79 million square miles and with over 310 million people, the United States is the third or fourth largest country by total area. It is one of the world's most ethnically diverse and multicultural nations, the product of large-scale immigration from many countries. The

化学常用英文单词

Bunsen burner 本生灯 product 化学反应产物 flask 烧瓶 apparatus 设备 PH indicator PH值指示剂,氢离子(浓度的)负指数指示剂 matrass 卵形瓶 litmus 石蕊 litmus paper 石蕊试纸 graduate, graduated flask 量筒,量杯 reagent 试剂 test tube 试管 burette 滴定管 retort 曲颈甑 still 蒸馏釜 cupel 烤钵 crucible pot, melting pot 坩埚 pipette 吸液管 filter 滤管 stirring rod 搅拌棒 element 元素 body 物体 compound 化合物 atom 原子 gram atom 克原子 atomic weight 原子量 atomic number 原子数 atomic mass 原子质量 molecule 分子 electrolyte 电解质 ion 离子 anion 阴离子 cation 阳离子 electron 电子 isotope 同位素 isomer 同分异物现象 polymer 聚合物 symbol 复合 radical 基 structural formula 分子式 valence, valency 价 monovalent 单价 bivalent 二价 halogen 成盐元素bond 原子的聚合mixture 混合combination 合成作用compound 合成物alloy 合金 metal 金属metalloid 非金属Actinium(Ac) 锕Aluminium(Al) 铝Americium(Am) 镅Antimony(Sb) 锑Argon(Ar) 氩Arsenic(As) 砷Astatine(At) 砹Barium(Ba) 钡Berkelium(Bk) 锫Beryllium(Be) 铍Bismuth(Bi) 铋Boron(B) 硼Bromine(Br) 溴Cadmium(Cd) 镉Caesium(Cs) 铯Calcium(Ca) 钙Californium(Cf) 锎Carbon(C) 碳Cerium(Ce) 铈Chlorine(Cl) 氯Chromium(Cr) 铬Cobalt(Co) 钴Copper(Cu) 铜Curium(Cm) 锔Dysprosium(Dy) 镝Einsteinium(Es) 锿Erbium(Er) 铒Europium(Eu) 铕Fermium(Fm) 镄Fluorine(F) 氟Francium(Fr) 钫Gadolinium(Gd) 钆Gallium(Ga) 镓Germanium(Ge) 锗Gold(Au) 金Hafnium(Hf) 铪Helium(He) 氦

九年级下科学物质的转化和元素的循环复习

物质的转化和元素的循环 (一)金属的氧化和金属氧化物的还原 1、铜与氧化铜之间的相互转化实验 (1)实验步骤和实验现象: ①用坩埚钳夹着铜片在酒精灯的外焰上加热。现象:发现紫红色铜片变成了黑色。铜的表面生成了氧化铜。 ②把在酒精灯外焰上加热后的铜片,马上插入酒精(乙醇)中。现象:铜片表面又由黑色变成了紫红色。 (2)实验结论: 在这个过程中,铜在加热的条件下能和空气中的氧气结合形成黑色的氧化铜,铜片表面生成的黑色氧化铜马上和酒精(乙醇)反应又转化成了铜。 (3)注意事项: 铜一定要在酒精灯的外外焰上加热,不要使铜碰到酒精灯的灯芯。因为在铜的表面生成的氧化铜与酒精灯的内焰或灯芯接触,实质上是和还没有燃烧的酒精(乙醇)蒸气接触,会使已经生成的氧化铜又被酒精还原成铜。 (4)实验小结: ①氧气在加热的条件下能和铜结合生成氧化铜。金属获得氧的过程被称为金属的氧化(oxidation)。 ②酒精能与灼热的氧化铜反应从氧化铜中夺取氧,使氧化铜转化为铜。金属氧化物失去氧的过程被称为金属氧化物的还原(deoxidation)。 2、使铁的表面形成氧化层保护膜实验

铁片放在浓硝酸、浓硫酸中,没有气体放出,这是因为铁在浓硝酸、浓硫酸中生成了铁的氧化物,正是这层致密的氧化膜保护了铁,使铁不能与酸反应生成氢气。但将铁片放在稀硫酸中,则有气体放出,即生成了氢气。 绝大部分金属都能在一定条件下与氧气化合生成金属的氧化物,但一些不活泼的金属如:金、铂等,很难和氧化合生成氧化物。金属还能和某些能提供氧的物质如:硝酸、浓硫酸等反应,生成金属氧化物。 3、氢气还原氧化铜实验 (1)实验步骤: 在干燥的硬质试管里铺一薄层黑色氧化铜粉末,固定在铁架台上,通入氢气,待空气排尽后,加热氧化铜。反应完成后停止加热,再继续通入一会儿氢气,直到试管冷却。 (2)实验装置: (3)实验现象: 黑色的氧化铜变成紫红色,试管口有水珠生成。 (4)注意事项: ①试管口应略向下倾斜,防止反应过程中生成的水流到试管底部使试管破裂; ②氢气的导入管要伸到试管的底部; ③反应开始前要先通入氢气,以排尽试管中的空气;当反应完成时,要先停止加热,继续通入氢气,直到试管冷却,再停止通入氢气,以防止生成的灼热的铜又被空气中的氧气氧化成氧化铜。

hey,jude含义解析

Hey Jude The Beatles

?这首歌就是英国的难忘今宵!!!伦敦奥运会的压轴歌曲,我觉得很适合大合唱由麦卡特尼创作的,鼓励列农的儿子朱利安勇敢面对现实,在约翰列侬离婚后希望朱利安不要消沉其实这首歌的原名是Hey Julian,后来改为Hey Jules, 最终变成Hey Jude

?《Hey Jude》是Paul McCartney(保罗·麦卡特尼,The Beatles(披头士乐队,又称甲壳虫乐队)成员之一)为一个五岁的孩子写下的一首歌。这个男孩叫Julian,是John Lennon(约翰·列侬)与前妻Cynthia 的儿子。1968年夏天,John Lennon开始和Yoko Ono(小野洋子)同居了,他与前妻Cynthia的婚姻也到了崩溃的边缘

?Paul一直非常喜爱John Lennon的儿子Julian,他担心大人之间的婚姻变故会对一个小孩子带来心理上的阴影。(不过,当时Paul也正和相恋5年的未婚妻Jane Asher分手,开始与Linda Eastman 的感情)他曾说:“我总是为父母离异的孩子感到难过。大人们也许没什么,但是孩子……”同时,他也想要安慰一下Cynthia。于是有一天,他去了Cynthia的家里,还给她带了一枝红玫瑰,开玩笑的对她说:“Cyn,你说咱俩结婚怎么样?”说完两人同时大笑起来,Cynthia从他的玩笑中感受到了温暖和关心。

?Paul在车里为Julian写下了这首Hey Jude (Hey,Julian),可当时的Julian并不知道。直到二十年后,Julian才明白这首歌是写给自己的。他一直很喜爱爸爸的这个朋友,像一个叔叔一样的Paul。John Lennon也非常喜爱这一首歌。自从第一次 听到,他就觉得,“噢,这首歌是写给我 的!”Paul 说“Hey,John!去吧,离开我们和Yoko在一起吧。”他似乎又在说:“Hey,John!不要离开!来 自:”https://www.doczj.com/doc/859098584.html,/view/965993.htm

化学专业词汇

普通化学术语中英文对照表原子atom 原子核nucleus 质子proton 中子neutron 电子electron(abbr.e) 离子ion[an] 阳离子cation 阴离子anion 分子molecular[mlekjl] 单质element 化合物compound 纯净物puresubstance/chemicalsubstance 混合物mixture 相对原子质量relativeatomicmass(abbr.Ar) 相对分子质量relativemolecularmass(abbr.Mr) 化学式量relativeformulamass 物质的量amountofsubstance 阿伏加德罗常数Avogadroconstant(abbr.NA) 摩尔mole 摩尔质量molarmass 实验式/最简式/经验式empiricalformula 气体摩尔体积molarvolume 阿伏加德罗定律Avogadro’sLaw 溶液solution 溶解dissolve 浓度concentration 质量/体积分数mass/volumeconcentration 浓缩concentrate 稀释dilute 蒸馏distillation 萃取extraction 化学反应方程式chemicalequation 反应物reactant 生成物product 固体solid 液体liquid 气体gaseous

溶液aqueous 配平balance 化学计量学stoichiometry 酸acid 碱 base/alkali(referstosolublebases)盐salt 酸式盐acidsalt 离子方程式ionicequation 结晶水waterofcrystallisation 水合的hydrated 无水的anhydrous 滴定titration 指示剂indicator 氧化数oxidationnumber 氧化还原反应redoxreaction 氧化反应oxidationreaction 还原反应reductionreaction 歧化反应disproportionationreaction 归中反应 comproportionation(symproportiona tion) reaction 氧化剂oxidisingagent 还原剂reducingagent 电子层(壳)(electron)shell 电离能ionisationenergy(abbr..) 第一,第二,第三等电离能 first,second,third,etc.ionisation energy(abbr.1st,2nd,3rd,etc..) 电子亲和能 electronaffinityenergy(abbr..) 屏蔽效应electronicshielding(screening) 原子轨道atomicorbital 电子云electroncloud 电子亚层sub-shell 能层layer 能级energylevel 电子排布electronconfiguration 电子云重叠shelloverlap 洪特规则Hund’srule 泡利原理Pauliexclusionprinciple

无机化学实验习题答案新整理

无机化学实验题答案 实验习题p 区非金属元素( 卤素、氧、硫)1. 氯能从含碘离子的溶液中取代碘,碘又能从氯酸钾溶液中取代氯,这两个反应有无矛盾?为什么?答:这两个反应无 矛盾。因为氯的氧化性强于碘,而碘的氧化性又强于氯酸钾。 2. 根据实验结果比较:① S2O82-与MnO4-氧化性的强弱;② S2O32-与I- 还原性的强弱。答:因为S2O82-可以将Mn2+氧化为MnO4-,所以S2O82-的氧化性强于MnO4-,S2O32-能将I2 还原为 I- ,S2O32-和还原性强于I- 。3. 硫代硫酸钠溶液与硝酸银溶液反应时,为何有时为硫化银沉淀,有时又为[Ag(S2O3)2]3- 配离子?答:这与溶液的浓度和酸碱性有关,当酸性强时,会生成硫化银沉淀,而在中性条件下就会生成[Ag(S2O3)2]3- 配离子。 4. 如何区别:①次氯酸钠和氯酸钠;②三种酸性气体:氯化氢、二氧化硫、硫化氢;③硫酸钠、亚硫酸钠、硫代硫酸钠、硫化钠。答:① 分别取少量两种固体,放入试管中,然后分别往试管中加入适量水,使固体全部溶解,再分别向两支试管中滴入两滴品红溶液,使品红溶液褪色的试管中放入的固体为次氯酸钠,剩下的一种为氯酸钠。②将三种气体分别通入品红溶液中,使品红褪色的是二氧化硫,然后将剩余的两种气体分别通入盛有 KMnO4溶液的试管中,产生淡蓝色沉淀的是H2S,剩下的一种气体是氯化氢。③分别取四种溶液放入四支试管中,然后向四支试管中分别加入适量等量的H2SO4溶液,有刺激性气味 气体产生的是亚硫酸钠,产生臭鸡蛋气味气体是的硫化钠,既有刺激性气味气体产生,又有黄色沉淀产生的是硫代硫酸钠,无明显现象的是硫酸钠。 5. 设计一张硫的各种氧化态转化关系图。 6. 在氯酸钾和次氯酸钠的制备实验中,如果没有二氧化锰,可改用哪些药品代替地二氧化锰?答:可用高锰酸钾代替二氧化锰。7. 用碘化钾淀粉试纸检验氯气时,试纸先呈蓝色,当在氯气中放置时间较长时,蓝色褪去,为什么?答:因为2KI+Cl2=2KCl+I2,I2 遇淀粉变蓝,因此试纸呈蓝色,但氯气有氧化性,可生成HClO,可以将蓝色漂白,所以在氯气中放置时间较长时,蓝色褪去。8. 长久放置的硫化氢、硫化钠、亚硫酸钠水溶液会发生什么变化?如何

HI jude

《Hey Jude》歌词中英文... Hey jude, don't make it bad 嗨,jude,不要如此消沉 Take a sad song and make it better 唱一首感伤的歌,振作一些 Remember to let her into your heart 记得要真心爱她 Then you can start to make it better 生活会开始好起来 Hey jude, don't be afraid 嗨,jude,不要害怕 You were made to go out and get her 去追她,留住他 The minute you let her under your skin 当你深爱上她的那一刻 Then you begin to make it better 生活变得美好起来 And anytime you feel the pain, hey jude, refrain 嗨,jude,不管何时你感到痛苦,要忍耐 Don't carry the world upon your shoulders 别把整个世界压在心头 For well you know that it's a fool who plays it cool 你知道愚蠢的人总是装做什么都不在乎 By making his world a little colder 把他的世界伪装得有些冷酷 Hey jude, don't let me down 嗨,jude,不要让我失望 You have found her, now go and get her 既然找到所爱的人,就要勇敢追求 Remember to let her into your heart 记住要真心爱她 Then you can start to make it better

无机化学实验习题答案新

转无机化学实验习题答案 实验习题p区非金属元素(卤素、氧、硫)1.氯能从含碘离子的溶液中取代碘,碘又能从氯酸钾溶液中取代氯,这两个反应有无矛盾?为什么?答:这两个反应无 矛盾。因为氯的氧化性强于碘,而碘的氧化性又强于氯酸钾。2.根据实验结果比较:①S2O82-与MnO4-氧化性的强弱;②S2O32-与I-还原性的强弱。答:因为 S2O82-可以将Mn2+氧化为MnO4-,所以S2O82-的氧化性强于MnO4-,S2O32-能将I2还原为I-,S2O32-和还原性强于I-。3.硫代硫酸钠溶液与硝酸银溶液反应时,为 何有时为硫化银沉淀,有时又为[Ag(S2O3)2]3-配离子?答:这与溶液的浓度和酸 碱性有关,当酸性强时,会生成硫化银沉淀,而在中性条件下就会生成 [Ag(S2O3)2]3-配离子。4.如何区别:①次氯酸钠和氯酸钠;②三种酸性气体:氯 化氢、二氧化硫、硫化氢;③硫酸钠、亚硫酸钠、硫代硫酸钠、硫化钠。答:① 分别取少量两种固体,放入试管中,然后分别往试管中加入适量水,使固体全部 溶解,再分别向两支试管中滴入两滴品红溶液,使品红溶液褪色的试管中放入的 固体为次氯酸钠,剩下的一种为氯酸钠。②将三种气体分别通入品红溶液中,使 品红褪色的是二氧化硫,然后将剩余的两种气体分别通入盛有KMnO4溶液的试管中,产生淡蓝色沉淀的是H2S,剩下的一种气体是氯化氢。③分别取四种溶液放入四支试管中,然后向四支试管中分别加入适量等量的H2SO4溶液,有刺激性气味 气体产生的是亚硫酸钠,产生臭鸡蛋气味气体是的硫化钠,既有刺激性气味气体 产生,又有黄色沉淀产生的是硫代硫酸钠,无明显现象的是硫酸钠。5.设计一张 硫的各种氧化态转化关系图。6.在氯酸钾和次氯酸钠的制备实验中,如果没有二 氧化锰,可改用哪些药品代替地二氧化锰?答:可用高锰酸钾代替二氧化锰。7.用 碘化钾淀粉试纸检验氯气时,试纸先呈蓝色,当在氯气中放置时间较长时,蓝色 褪去,为什么?答:因为2KI+Cl2=2KCl+I2,I2遇淀粉变蓝,因此试纸呈蓝色,但 氯气有氧化性,可生成HClO,可以将蓝色漂白,所以在氯气中放置时间较长时, 蓝色褪去。8.长久放置的硫化氢、硫化钠、亚硫酸钠水溶液会发生什么变化?如何

中英双语歌词

中英双语歌词 Hey Jude, don't make it bad. 嘿 Jude 不要这样消沉 Take a sad song and make it better. 唱首伤感的歌曲会使你振作一些Remember to let her into your heart, 记住要永远爱她 Then you can start to make it better. 开始新的生活 Hey Jude, don't be afraid. 嘿 Jude 不要担心 You were made to go out and get her. 去追她,留下她

The minute you let her under your skin, 拥抱她的时候 Then you begin to make it better. 将开始新的生活 And anytime you feel the pain, 无论何时,当你感到痛苦的时候 hey Jude, refrain, 嘿 Jude 放松一下自己 Don't carry the world upon your shoulders. 不要去担负太多自己能力以外的事 For well you know that it's a fool who plays it cool 要知道扮酷是很愚蠢的 Hey Jude, don't make it bad. 嘿 Jude 不要这样消沉

Take a sad song and make it better. 唱首伤感的歌曲会使你振作一些Remember to let her into your heart, 记住要永远爱她 Then you can start to make it better. 开始新的生活 Hey Jude, don't be afraid. 嘿 Jude 不要担心 You were made to go out and get her. 去追她,留下她 The minute you let her under your skin, 拥抱她的时候 Then you begin to make it better. 将开始新的生活 And anytime you feel the pain,

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