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2.lecturelecture /ˈlektʃə(r)/ 词频4n. 讲座;讲课;教训. vi. (开)讲座;讲课. vt. 训斥派:lecturer 词频2 n.演讲者;(大学)讲师①高义频vi.&n.(尤指大学中的)讲座;讲课;演讲go to/attend a lecture 听讲座deliver/give a lecture做讲座a lecture on/about 关于……的讲课/训斥e.g. He lectures on literature at Manchester University. 他在曼彻斯特大学教文学。
②低义频vi.&n.教训;训斥lecture sb. about/on...因……训斥某人give sb. a lecture 给某人一个教训e.g. He’s always lecturing me about the way I dress. 他总是对我的穿着说三道四。
e.g. I know I should stop drinking-don’t give me a lecture about it.我知道我该戒酒,别教训我了。
1.单词拼写(1)I went to the ___(讲座) he gave in the hall.(lecture)(2)He learned a ___(教训)from this thing-he should stop smoking for his health.(lecture)(3)Professor Smith will give a l___ in Fudan University this evening about the history of English.(lecture)(4)She suffered a bad cold. As a result, she missed the ___(讲座) she liked very much.(lecture)(5)She preferred that we should have the discussion right after the ___(讲座).(lecture)(6)Please stop___(lecture) me! I know I should quit smoking.2.语法填空(1)The ___ (lecture) spoke very clearly so that we could hear every word.(lecturer) 3. 完成句子(1)He ___ ___ ___ ___time management to first-year students___ ___ ___ ___.他在报告厅给一年级学生做关于时间管理的讲座。
TPO-40托福听力题目文本——对话部分(Conversation)【附答案】托福TPO,英文名为TOEFL Practice Online,中文直译为托福线上练习,TPO都是历年托福真题,对托福备考是非常有帮助的,今天为大家分享的是TPO-40托福听力题目文本——对话部分(Conversation)【附答案】。
TPO-40托福听力题目文本——对话部分(Conversation)【附答案】QUESTIONS1. Why does the student go to see the professor?a. To find out all the requirements for a projectb. To discuss a service gap at a restaurantc. To get help understanding concepts relevant to his projectd. To get help with designing a business plan2. Why does the professor mention a student in another class?a. To describe an interesting topic for a projectb. To explain the cause of her initial confusionc. To point out that she has not received e-mails from all her students yetd. To indicate that she has several students doing projects about restaurans托福听力主旨题的答题技巧新托福听力考试总共有六大技巧的测试与考核。
与这六大技巧相对,ETS有六大题型的测试,分别是:主旨题、细节题、句子功能题、态度题、结构题和推论题。
2025年全国大学英语CET四级考试复习试题及解答参考一、写作(15分)Part I Writing (30 points)Directions: For this part, you are allowed 30 minutes to write a short essay on the topic “The Impact of Artificial Intelligence on Daily Life.” You should start your essay with a brief introduction to the topic, then give specific examples to illustrate your point, and finally, provide a conclusion with your personal view. Your essay should be about 120 to 150 words but no less than 100 words.Writing Sample:The advent of artificial intelligence (AI) has revolutionized our daily lives in numerous ways. From smart homes to advanced medical diagnosis, AI has become an integral part of modern society.In smart homes, AI systems like voice assistants and smart security cameras enhance our convenience and safety. These systems learn from our habits and preferences, making our homes more comfortable and efficient. Moreover, in the healthcare sector, AI algorithms are being used to analyze medical images and identify potential diseases at an early stage, which can significantly improvepatient outcomes.However, the rise of AI also brings challenges. For example, job displacement is a major concern, as AI can perform certain tasks more efficiently than humans. Additionally, there are ethical questions about privacy, data security, and the potential misuse of AI technology.In conclusion, while AI has brought substantial benefits to our daily lives, we must also address its challenges to ensure a balanced and ethical integration of AI into our society.Writing Analysis:•Introduction: The essay starts with a clear introduction to the topic of AI and its impact on daily life, providing a broad perspective.•Body Paragraphs: The body of the essay presents two distinct impacts of AI:•The positive impact of AI in smart homes and healthcare.•The negative impacts of job displacement and ethical concerns.•Conclusion: The essay concludes with a balanced view, acknowledging both the benefits and challenges of AI, and emphasizing the need for ethical considerations.•Structure and Coherence: The essay has a clear structure and is well-organized, making the flow of ideas easy to follow.•Length: The essay meets the required word count, with 120 words, demonstrating the writer’s ability to convey the main points concisely.二、听力理解-短篇新闻(选择题,共7分)第一题News:In recent years, global attention has been drawn to the rapid development of electric vehicles (EVs). According to a recent report by the International Energy Agency (IEA), the number of electric vehicles on the roads worldwide reached 13 million in 2021, up from just 2 million in 2015. The report also indicates that by 2030, the number of electric vehicles is expected to surpass 145 million.Question 1:What has the number of electric vehicles on the roads reached as of 2021 according to the recent report by the IEA?A) 1 millionB) 13 millionC) 2 millionAnswer: BQuestion 2:How many years is it mentioned from 2015 to 2021 in the report?A) 5 yearsB) 6 yearsC) 7 yearsAnswer: BQuestion 3:What is the expected number of electric vehicles by 2030 according to the report?A) 13 millionB) 2 millionC) 145 millionAnswer: C第二题News Item 1:A new study reveals that the global use of electric scooters has increased significantly in recent years. These scooters are becoming a popular form of transportation in cities around the world. However, the study also highlights the environmental and safety concerns associated with the rapid growth in electric scooter usage.Cities are faced with the challenge of managing the increased demand for parking spaces, as well as the potential risks of accidents involving these scooters. Improved infrastructure and regulations are being considered to address these issues.Questions:1、What is the primary topic of the news item?A. The decline of traditional scootersB. The environmental impact of electric scootersC. The safety concerns of using electric scootersD. The rise in global use of electric scooters2、“These scooters are becoming a popular form of transportation in cities around the world.” Which of the following is true regarding the use of electric scooters?A. They are only popular in developed countries.B. They have no environmental impact.C. They are causing a decrease in car usage.D. They have become a common mode of transportation globally.3、“Improved infrastructure and regulations are being considered to address these issues.” What is the implied issue that needs to be addressed?A. The overuse of public transportation.B. The need for more parking spaces for cars.C. The decline in bicycle usage.D. The potential safety risks and management challenges posed by electric scooters.Answers:1.D2.D3.D三、听力理解-长对话(选择题,共8分)First QuestionConversationA: Hey, Sarah! Did you finish listening to the podcast this morning?B: Yeah, I did. It was quite fascinating. Have you checked the transcript on their webpage?A: Not yet. I plan to review what we heard today after work. By the way, I was thinking it would be nice to form a study circle this semester.B: That sounds like a good idea. Could you host a meeting this weekend?A: Sure, I can. I’ll prepare some questio ns for us to discuss, and you can bring in your notes. It’ll make our learning more productive.B: Great! Should we stick to the topics in the podcast or choose something else?A: Let’s talk about the topics in the podcast first. That way, it’ll help us understand the context better.B: Sounds perfect. I have a couple of questions for you. How long have you been listening to podcasts?A: Since about a year now. I find it’s a great way to learn English while doing something productive.B: I agree. What’s your favorite podcast?A: Hmm, I really like “The Economist Briefing.” It covers current events and history, which are topics I find interesting.B: Nice choice. I’m a fan of “TED Talks Daily.” It’s a bit different from “The Economist Briefing” but still educational.A: That’s true. We can switch up the topics as we like. What are youstudying?B: I’m majoring in international relations. The podcast really helps me get more insights into what I’m studying.A: That’s awesome. What about yo ur plans for the future?B: I hope to travel around Europe for my study abroad program next year, so I’m trying to learn more European languages. It would be a great opportunity to practice my English as well.A: That sounds exciting! This weekend, let’s m eet for an hour at my place, okay?B: Sure, that works for me.Q1. What is one reason Sarah likes listening to this podcast?a)To practice her English.b)To pass CET-4.c)To prepare for a trip.d)To learn her major subject.Answer: aQ2. How long has the speaker been listening to podcasts?a)One yearb)Two yearsc)Three yearsd)Half a yearAnswer: aQ3. Who does the speaker admire for choosing “TED Talks Daily”?a)Sarahb) A friendc) A professord)Another studentAnswer: aQ4. What will they do this weekend?a)Meet for an hour at the speaker’s place.b)Join a club activity.c)Go to a coffee shop.d)Attend a lecture on English.Answer: aQuestion 2:Why does Liu feel a bit nervous about the exam?A) He is preparing for it for too long.B) He hasn’t studied hard enough.C) His friends are also enrolled in CET-4 course classes.D) He needs to take a break soon.Answer: AQuestion 3:What advice does Amy give to Liu?A) Enroll in a CET-4 course class.B) Review the past papers.C) Study every day.D) Take a break.Answer: BQuestion 4:What can be inferred about Liu from the conversation?A) He is confident about the exam.B) He has been preparing for the exam for a long time.C) He is ready for the upcoming exam.D) He doesn’t like studying hard.Answer: B四、听力理解-听力篇章(选择题,共20分)第一题Directions: In this section, you will hear a passage. Listen carefully and answer the questions that follow.Passage:In today’s fast-paced digital world, it has become increasingly important for businesses to adopt technologies that improve their efficiency and customer satisfaction. The rise of artificial intelligence (AI) and machine learning (ML) has led to significant advancements in the field of business operations. Companies are now exploring various ways to integrate these technologies to enhance their processes.1、What aspect of business operations has seen significant advancements dueto AI and ML integration?A) Customer serviceB) LogisticsC) Financial managementD) A2、Why is the adoption of AI and ML technologies regarded as important for businesses?A) To reduce operational costsB) To improve customer satisfactionC) To increase operational efficiencyD) C3、Which of the following is NOT an example of how businesses can integrate AI and ML?A) Enhancing predictive analyticsB) Automating routine tasksC) Increasing manual data entryD) C第二题Passage 1The globalization of the economy has brought about significant changes in the world, and one area that has been heavily affected is the sports industry. In this essay, we will explore how globalization has impacted the sports industry,focusing on the growth of international sports events and the role of sports in global culture.1、Why is globalization having a profound impact on the sports industry?A) Because it allows sports to be practiced anywhere in the world.B) Because it has led to the growth of international sports events.C) Because it has changed the way people culture around the world.D) Because it has increased the salaries of professional athletes.2、Which of the following is not mentioned as a change brought about by globalization in the sports industry?A) The increase in cross-cultural interactions.B) The decline in local sports teams.C) The rise of regional sports leagues.D) The increase in global fan bases for various sports.3、What is the main argument made by the essay about the role of sports in global culture?A) Sports have a单一 focus on winning and losing.B) Sports help to foster national pride and identity.C) Sports have become a way for countries to cooperatively compete.D) Sports have lost their relevance due to increased commercialization.Answer Key:1、B2、BThird Question: Listening Comprehension - Listening PassagePassage:Welcome to our final research trip to India. We are in a small village in the state of Kerala, known for its rich cultural heritage and scenic beauty. The village, named Paravoor, has a population of approximately 15,000. Today, we focus on the local economy, which is largely dependent on farming, tourism, and small-scale industries. Currently, the village is facing several challenges, including water scarcity and lack of proper infrastructure. The government plans to implement a new irrigation project, which will provide a significant boost to the agricultural sector. In addition, the village is promoting eco-tourism to diversify its economic base. However, these initiatives require support and investment from both the government and the local community.1、Which of the following is NOT a challenge facing Paravoor Village?A、Water scarcityB、Lack of proper infrastructureC、Dependence on large-scale industriesD、C、2、What is the villagers’ plan to diversify their economic base?A、Developing new industriesB、Promoting eco-tourismC、Increasing agricultural production3、Which of the following is a potential benefit of the new irrigation project?A、It will help diversify the local economy.B、It will improve the infrastructure.C、It will provide water to the entire state.D、C、五、阅读理解-词汇理解(填空题,共5分)第一题Reading PassageAlice, receiving a ring, was extremely pleased. Her father promptly asked, “Have you made up your mind, my dear?” “Not quite,” said Alice ominously, stepping out of her ring. “But I will do so directly,” she declared.With a faint shiver of delight, the father experienced her civil but firm decision and then together they went to bet {?1?} her little servant girl a seventeen-pound horse. While they were thus occupied, the children saw their disagreement. The richest and keenest-uprisinguchepest, perfectly struck their fancy, and though their(Game) competitive position was, by no means, satisfactory, they had no objection to feel very sorry for the seller.1、civil A. 非常高兴的B. 礼貌的;文明的C. 无数的;无休止的D. 非常出色的2、competititive A. 竞争性的;竞赛的B. 嫉妒的;充满敌意的C. 令人厌恶的;讨厌的D. 无能的;不称职的3、keen A. 苦涩的;尖利的B. 明锐的;敏锐的C. 高兴的;愉快的D. 枯燥的;乏味的4、Ominous A. 不吉利的;不祥的B. 温和的;文雅的C. 欢快的;愉快的D. 兴奋的;激动的5、shiver A. 战栗;发抖B. 淡水C. 快速降雨D. 柔软的动物答案:1、B2、A3、B4、A5、A第二题Directions: Read the following text and complete the sentences below. There is one word or phrase missing in each sentence. Choose the most appropriate word or phrase from the options given below each sentence.Reading Passage:The rapid growth of technology has profoundly transformed our social fabric. From the emergence of the internet to the advent of smartphones, our daily interactions and work routines have been fundamentally altered. These technological advancements have not only facilitated instant communication but also expanded our access to information. However, this shift comes with its own set of challenges. For instance, while the internet provides a vast array of resources, it also exposes us to misinformation and the need for digital literacy is increasingly important. Moreover, the reliance on technology in the workplace has raised concerns about job security, as automation and artificial intelligence continue to evolve and change the nature of work.1、The word “fabric” (Line 1) most closely r elates to the following word: _[Options: a) fabric b) structure c) society d) clothing_]•1、c) society2、The phrase “emergence of the internet” (Line 3) can be replaced with which of the following: _[Options: a) the start of the internet b) the appearance of the internet c) the deployment of the internet d) the invention of the internet_]•2、b) the appearance of the internet3、The word “instant” (Line 4) is synonymous with: _[Options: a) immediate b) brief c) quick d) rapid_]•3、a) immediate4、The challenge mentioned in the passage regarding the internet is: _[Options: a) accessing information b) exposure to misinformation c) maintaining digital literacy d) balancing physical and digital interactions_]•4、b) exposure to misinformation5、The phrase “nature of work” (Line 7) refers to: _[Options: a) the quality of work b) the purpose of work c) the essence of work d) the value of work_]•5、c) the essence of work六、阅读理解-长篇阅读(选择题,共10分)第一题Reading Passage OneIt is widely accepted that education is of great importance to all people. However, there are many arguments on its necessity. While some people believe it is important to receive an education, others argue that education is not essential in one’s life.One of the main arguments for education is that it offers opportunities for personal development. With a good education, individuals can acquire the knowledge and skills needed to succeed in life. They can also improve theircritical thinking abilities and make informed decisions. Furthermore, an education can help individuals become more adaptable and flexible, enabling them to thrive in a changing world.Opponents of education argue that people can succeed without it. They cite examples of successful individuals who dropped out of school, such as Steve Jobs and比尔·盖茨. They believe that talent and opportunities can compensate for a lack of formal education.In the following passage, there are some statements about education. Choose the most suitable answer for each of the following questions.Questions 1-51、Which of the following is the main issue discussed in the reading passage?A. The benefits of educationB. The drawbacks of educationC. The importance of personal developmentD. The relationship between education and success2、What do the proponents of education believe about the role of education in personal development?A. Education hinders personal growth.B. Education does not contribute to skill acquisition.C. Education improves critical thinking and decision-making skills.D. Education makes individuals less adaptable.3、What is the main argument against education mentioned in the passage?A. Education limits personal development.B. Successful individuals can compensate for a lack of education.C. Education stifles creativity and innovation.D. Education takes away opportunities for self-betterment.4、Which of the following does the reading passage NOT mention as a reason for supporting education?A. Increased opportunities for employment.B. Enhanced critical thinking abilities.C. Improved adaptability and flexibility.D. Theernenment in international cooperation.5、What is the author’s attitude towards the debate on education?A. The author believes that education is unnecessary.B. The author supports the idea that education is essential for personal development.C. The author prefers talent and opportunities over education.D. The author is neutral on the issue of education.Answer Key:1、A2、C3、B4、D5、B第二题Passage:The concept of cloud computing has been discussed for decades, but it has only recently become a practical solution for businesses and individuals. Itall began with the idea of using the Internet as a transmission medium for data and applications. As technology advanced, the costs of storage and bandwidth became more affordable, making cloud computing a viable option. Today, cloud services range from simple file storage to complex application delivery, and they are accessible via web browsers or special software applications.The benefits of cloud computing are numerous. First, there is no need for costly hardware or maintenance. Cloud providers handle all the backend operations, ensuring that the service runs smoothly without requiring any intervention from users. Second, cloud services are highly scalable, meaning they can handle sudden increases in demand without additional investment. Third, cloud computing encourages collaboration and mobility, as users can access data and applications from anywhere with an internet connection. Finally, cloud services often come with robust security features, which are continuously updated, minimizing the risk of data breaches.However, cloud computing also comes with challenges. Security remains a significant concern, as data is stored remotely and vulnerable to cyberattacks. Additionally, there is the issue of data sovereignty, where data stored outside a country’s borders may be subject to the laws of that country. Furthermore, some companies may be hesitant to switch to cloud services due to the lack of control over their data, a common concern known as “control issues.”Questions:1、What is the main idea of the passage?a) The history of cloud computing.b) The benefits and challenges of cloud computing.c) The security concerns of cloud computing.d) The scalability of cloud computing.2、Why did cloud computing become practical recently?a) Because of the decreased costs of storage and bandwidth.b) Because of the widespread availability of the Internet.c) Because of the advancement in technology.d) Because of the decreasing demand for hardware.3、What are the benefits of cloud computing mentioned in the passage?a) No need for costly hardware, scalability, collaboration and mobility, and robust security features.b) High scalability, easy maintenance, and data sovereignty.c) Low costs, easy access, and increased data security.d) Remote access, data availability, and decreased bandwidth requirements.4、Which of the following is a challenge of cloud computing?a) The lack of mobility.b) The high costs of hardware.c) The security risks associated with remote data storage.d) The limited availability of web browsers.5、What is the common concern known as “control issues” mentioned in the passage?a) Users have no control over their data.b) Users have control over their data, but it is stored remotely.c) Data stored outside a country’s borders may be subject to the laws of that country.d) Users can choose to control their data through special software applications.Answers:1、b) The benefits and challenges of cloud computing.2、a) Because of the decreased costs of storage and bandwidth.3、a) No need for costly hardware, scalability, collaboration and mobility, and robust security features.4、c) The security risks associated with remote data storage.5、a) Users have no control over their data.七、阅读理解-仔细阅读(选择题,共20分)First Reading Comprehension Part AReading PassageThe following is a passage about the importance of exercise for mental health and productivity. This passage is followed by some questions to which the answers can be found in the passage.In today’s fast-paced world, stress has become an integral part of our lives. It’s essential to find ways to manage and reduce stress to maintain both our mental and physical health. One effective way to combat stress is through regularexercise. Research has consistently shown that physical activity can have a profound impact on our mental well-being and productivity.1.Physical activity has been found to:A) improve mental healthB) enhance productivityC) both improve mental health and enhance productivityD) have no effect on mental health2.The passage primarily discusses:A) the negative impact of stress on mental healthB) the benefits of exercise in reducing stressC) the effectiveness of various stress management techniquesD) the effects of different types of stress on the body3.It is mentioned that physical activity can have a “profound impact” on our:A) attention spanB) moodC) ability to sleepD) All of the above4.The word “integral” in the first paragraph most closely means:A) essentialB) foundationC) simpleD) occasional5.According to the passage, what is one effective way to combat stress?A) Avoiding situations that cause stressB) Seeking professional helpC) Regular physical activityD) Meditating for a few minutes dailyOptions:1、C2、B3、D4、A5、C第二题阅读下面的文章,然后回答问题。
第五节:五单元复相系的热力学平衡条件和稳定条件 平衡的稳定条件举例:利用内能的判据(其它判据也可以导出来相应的公式!):20,0,U U δδ=>i i i i i i iiiU U T S P V N δδδδμδ==-+∑∑2222i i i i i i i i i i i iiU T S P V N T S P V N δδδμδδδδδδμδ=-++-+∑0V S N δδδ===约束条件120V V V δδδ=+=利用等约束条件0,,i i i U T T P P δμμ=→===222121200V V V V V V δδδδδδ=+=⇒=+=()()()2221211211210;T T S P P V N δδμμδ⇒---+-=2;i i i i i i iU T S P V N δδδδδδμδ⇒=-+∑,;,.i i i i i i i i i i i i i i i i S N s S N s N s V N v V N v N v δδδδδδ==+==+()()2i i i i i i i i i i iiiU N T s P v s T v P N δδδδδδδδμδ⇓=-+-+∑∑0i i i i i s T v P δδδμ-+=热力学基本方程()2i i i i i iU N T s P v δδδδδ⇒=-∑i i i i T s P v δδδδ->故对任意指数i, 0T s P v δδδδ->简写为用T,v 做独力变量来表达上式:;;v v T vv Ts s c P s T v T v T v T T P P P T v T v δδδδδδδδ∂∂∂⎛⎫⎛⎫⎛⎫=+=+ ⎪ ⎪ ⎪∂∂∂⎝⎭⎝⎭⎝⎭∂∂⎛⎫⎛⎫=+ ⎪ ⎪∂∂⎝⎭⎝⎭()()22v Tc P T s P v T v T v δδδδδδ∂⎛⎫-=- ⎪∂⎝⎭0,0v TP c v ∂⎛⎫⇒>< ⎪∂⎝⎭0T s P v δδδδ->可以证明其它稳定条件(选择不同独立变量),并证明这些条件是等价的. 如0,0P sv c P ∂⎛⎫>< ⎪∂⎝⎭20,0,0U U V S N δδδδδ=>===Remark:只能确定能量是不是极小, 不能确定是不是最小. 如果是极小,不是最小, 这些态是亚稳态.在系统涨落较小的情况下, 亚稳态也是稳定的. 如果系统涨落比较大, 亚稳态是有有限的寿命.课外思考:磁性系统的稳定性的讨论M. Plischke and B. Bergersen, Equilibrium Statistical Physics参考此书第一章第七节单元复相系平衡条件过去我们是研究物质处于一种物态, 我们称之为单相. 系统也可以同时处于多种物态(多种物态共存,比如冰和水),称为多相或复相.化学纯物质(只有一个组元或一种分子),只含有一个化学纯物质情况下称为单元系.考虑单元系系统处于复相. 相i 的内能,体积,粒子数为 ,,i i iU V N20,0;0;,,.i i i iiiS S U V N U U V V N N δδδδδ=<======∑∑∑我们下面利用熵判据得到系统的平衡条件:()1i i i i i i i i iS U P V N T δδδμδ=+-∑∑代入可以用拉氏乘子法考虑约束条件()1231230;i i i i iS U V N S U V N δλλλδλδλδλδ---=---=∑1231,,P T T Tμλλλ⇒===,,.i i i T T P P μμ⇒===,-00.i j i j i T T U U dS U dUδδδ>=<⇒>=如果虚过程变为实过程第六节:相变热力学平衡相变相:在不同温度和压强范围,一个单元系可以分别处在气相,液相,固相.不同物态或者相(phase):同一金属低温下铁磁体,高温是顺磁体.金属与合金在高温是正常态金属,低温是超导体.固相也可以有不同的晶体结构。
这些不同的晶体结构也是不同相。
如高压冰,迄今为止发现16种晶格态冰和三种非晶格态冰(/water/phase.html).水的简单相图C O相图2各种神奇形状的雪花水的p,v,T 面.P,T相图p,v相图T,V相图系统中物理性质均匀部分叫做相。
相是按物理性质不同来划分的.在不同的外界条件下, 物态呈现不同的相.热力学不能解释这些现象,这是统计力学要解决的问题.一般物态在低温下是有序态,比如晶格态.高温下是无序态, 比如气态和液态.在更加低温情况下, 有些系统会有超导现象发生.对简单PV 系统,不同相达到平衡时(既单元系2相共存).压强温度满足两相平衡方程:()();;,,i j i j i j T T P P T P T P μμ===水的相图, 存在固液(溶解线)共存线,气液(气化线)共存线,固气(升华线) 共存线,及其三条线的交点(三相点).1.在平衡曲线上,温度和压强两个参量只有一个可以独立改变.2.曲线上两相的化学势相等. 两相可按任意比例共存. 整个系统的吉布斯函数是相等的.水的p,v 相图平衡相变:当系统缓慢地从外界吸收或者放出热量时,物质将从一个相转变到另外一个相而始终保持平衡态。
故称为平衡相变.平衡相变潜热(一级相变.相变级数定义下面会讲到)一级相变的特点:1.相变过程中系统与外界有热交换. 1摩尔物质从i 相转变为j 相所吸收的热量. 由于过程是等温可逆, 故吸收的热量为:()j i L T s s =-L 称为潜热. 潜热的存在表明, 两相的摩尔熵不等. 2.从一个相转变为另外一个相时,物质的摩尔体积也发生变化。
如水100C,气压1.013×105Pℎ下变成蒸汽时,体积增加1600多倍. 克拉珀龙方程在两相平衡曲线的热上,相变平衡条件:()()()()()(),,,,,,,i j i j T P T dT P dP T P T P T dT P dP T dT P dT μμμμ++⇓=++=++如在相变曲线上()()()()()(),,,,,,i i i j j j T dT P dP T P d T P d T P T dT P dP d T P μμμμμμ++-===++-()(),,i i i j j j d T P s dT v dP d T P s dT v dPμμ=-+==-+⇓热力学方程()j i j i j i s s dP L dT v v T v v -==-- 克拉珀龙方程克拉珀龙方程适用于一级相变. 二级相变有类似方程(以后会再提到)。
克拉珀龙(Benoit Pierre Emile Clapeyron,1799~1864)法国物理学家和土木工程师。
主要从事热学、蒸汽机设计和理论、铁路工程技术方面研究。
他设计了法国第一条铁路线。
在设计计算中发明了以他命名的支撑力矩计算法。
1799年1月26日生于巴黎。
1818年毕业于巴黎工艺学院。
1820~1830年在俄国彼得堡交通工程部门担任工程师,在铁路部门有较大贡献。
回到法国后,1844年起任巴黎桥梁道路学校教授。
1848年被选为巴黎科学院院士。
1834年赋予卡诺理论以易懂的数学形式,使卡诺理论显出巨大意义。
1834年克拉珀龙还由气体的实验定律归纳出了理想气体的状态方程,这个方程1874年被门捷列夫推广,故称为克拉珀龙-门捷列夫方程。
相变级数的定义:在相变平衡曲线上各相化学势相等,但摩尔熵不等,摩尔体积也不等,;;.i j j i i j P P j i i j T Ts s T T v v P P μμμμμμ=∂⎛⎫∂⎛⎫≠⇒≠⎪ ⎪∂∂⎝⎭⎝⎭∂⎛⎫∂⎛⎫≠⇒≠⎪ ⎪∂∂⎝⎭⎝⎭即相变时,化学势相等,但其一级导数不连续.这种相变称为一级相变. 如果一级导数连续, 二级导数不连续,则称为二级相变, 等等.克拉珀龙方程应用举例 潜热沿相变曲线的变化(){}j i j i j i j j i i j i P T P T d T s s ds dL ds s s T dT dT dT dT s s dP s s dP s s T T P dT T P dT -⎛⎫==-+- ⎪⎝⎭⎛⎫∂∂⎡⎤⎛⎫⎛⎫∂∂⎛⎫⎛⎫=-++-+ ⎪ ⎪ ⎪ ⎪ ⎪⎢⎥∂∂∂∂⎝⎭⎝⎭⎝⎭⎝⎭⎣⎦⎝⎭饱和蒸汽j j ii P P T T j j ii P P P P j j ii P P P j iP s dL L s dP c c T dT T P P dT v L v dP c c T T T T dT v L v L c c T T T v v ⎛⎫∂⎛⎫∂⎛⎫=+-+- ⎪ ⎪ ⎪∂∂⎝⎭⎝⎭⎝⎭⎛⎫∂⎛⎫∂⎛⎫=+--- ⎪ ⎪ ⎪∂∂⎝⎭⎝⎭⎝⎭⎛⎫∂⎛⎫∂⎛⎫=+--- ⎪ ⎪ ⎪∂∂-⎝⎭⎝⎭⎝⎭导出的方程可用在饱和蒸汽:现在应用这些方程来研究饱和蒸汽. 饱和蒸汽是指和凝聚相(液相或者固相)达到平衡的蒸汽. 设蒸汽相为相1,凝聚相为相2. 由于v 1≫v 2, 我们可以忽略上式中含v 2项的公式.()1211121,=P P P dL L v L c c dT T T v dP L LdT T v v Tv ∂⎛⎫≈+-- ⎪∂⎝⎭≈-如果把水蒸汽近试为理想气体1121211;P P P P P RT v Pv dL L L c c c c dT T T v =⇒∂⎛⎫=+--=- ⎪∂⎝⎭()012120;TP P P P T dL c c L c c dT L dT =-⇒=-+⎰对上式积分:如果蒸汽压变化不大, 并且加上凝聚相c p 2对压强依赖不大, 可以认为只是温度的函数:()012222TPPT c c dT L dP L LP dP L dT dTdT Tv RT P RTRT-+≈≈→≈=⎰(上步用了理想气体方程)()0012002ln .T TP P T T L dT P c c dT A RT RT ⇒=-+-+⎰⎰如果温度也变化不大,则c p 1,c p2可以看成常数,上式可以积分为 ln ln .BP A C T T=-+,,A B C可以实验测定,从而得到相变曲线超导相变对正常态和超导态(Meissner 态, 不考虑二类超导体 )的吉布斯函数满足下列方程,.N N N S S S dG s dT B dH dG s dT B dH =--=--在正常态和超导态 平衡线上有:();.N S N S c N SN SG G dG dG dH T s s dT B B =→=⇓-=--超导体排斥磁场, 故B s =0, 而且B N ≈0H c (T)。