Investigative Science Class Nine PDF

Class Nine Developed by the National Curriculum and Textbook Board as a textbook according to the National Curriculum 2022 for Class Nine from the academic year 2024 Investigative Science Study...

Class Nine Developed by the National Curriculum and Textbook Board as a textbook according to the National Curriculum 2022 for Class Nine from the academic year 2024 Investigative Science Study Class Nine (Experimental Version) Writers Dr. Muhammed Zafar Iqbal Nasreen Sultana Mitu Dr. Mohammad Mizanur Rahman Khan Shihab Shahriyar Nirjhor Rony Basak Md. Rokonuzzaman Sikder Dr. Tahmina Islam Dr. Manash Kanti Biswas Md. Ishhad Sadeque Dr. Md. Iqbal Hossain Saifa Sultana Editor Dr. Muhammed Zafar Iqbal Translated by Dr. Md. Zulfeqar Haider Ahmed Karim Hasnain Ramij Ahmad Muhammad Ali Medha Roshnan Sarwar Zakia Sultana National Curriculum and Textbook Board, Bangladesh  Published by National Curriculum and Textbook Board 69-70 Motijheel Commercial Area, Dhaka-1000 [All rights reserved by National Curriculum and Textbook Board, Bangladesh] First Published: December, 2023 Art Direction Monjur Ahmed Nasreen Sultana Mitu Illustration Sabyasachi Chakma Mehedi Haque Cover Illustration Mehedi Haque Graphics Design Nasreen Sultana Mitu For Free Distribution by the Government of the People’s Republic of Bangladesh Printed by:  PREFACE In this ever-changing world, the concept of life and livelihood is changing every moment. This process of change has been accelerated due to the advancement of technology. There is no alternative to adapting to this fast changing world as technology is changing rapidly ever than before. In the era of fourth industrial revolution, the advancement of artificial intelligence has brought about drastic changes in our employment and lifestyles that will make the relationship among people more and more intimate. Various employment opportunities will be created in near future which we cannot even predict at this moment. We need to take preparation right now so that we can adapt ourselves to that coming future. Although a huge economic development has taken place throughout the world, problems like climate change, air pollution, migrations and ethnic violence have become much more intense nowadays. The breakouts of pandemics like COVID 19 have crippled the normal lifestyle and economic growth of the world. Thus, different challenges as well as opportunities, have been added to our daily life. Standing amid the array of challenges and potentials, sustainable and effective solutions are required to transform our large population into a resource. It entails global citizens with knowledge, skill, values, vision, positive attitude, sensitivity, adaptability, humanism and patriotism. Amidst all these, Bangladesh has graduated into a developing nation from the underdeveloped periphery and is continuously trying to achieve the desired goals in order to become a developed country by 2041. Education is one of the most crucial instruments to attain the goals. Hence, there is no alternative to the transformation of our education system. This transformation calls for developing an effective and updated curriculum. Developing and updating the curriculum is a routine and important activity of National Curriculum and Textbook Board. The curriculum was last revised in 2012. Since then, more than a decade has elapsed. Therefore, there was a need for curriculum revision and development. With this view, various research and technical studies were conducted under NCTB from 2017 to 2019 to analyze the current state of education and identify the learning needs. Based on the researches and technical studies, a competency-based and seamless curriculum from K−12 has been developed to create a competent generation capable of surviving in the new world situation. Under the framework of this competency based curriculum, the textbooks have been prepared for all streams (General, Madrasah and Vocational) of learners for Class Nine. The authentic experience- driven contents of this textbook were developed with a view to making learning comprehensible and enjoyable. This will connect the textbooks with various life related phenomenon and events that are constantly taking place around us. It is expected that, through this, learning will be much more insightful and lifelong. In developing the textbooks, due importance has been given to all − irrespective of gender, ethnicity, religion and caste while the needs of the disadvantaged and special children are taken into special considerations. I would like to thank all who have put their best efforts in writing, editing, revising, illustrating and publishing the textbook. If any errors or inconsistencies in this experimental version are found or if there is any suggestions for further improvement of this textbook, you are requested to let us know. Professor Md. Farhadul Islam Chairman National Curriculum and Textbook Board, Bangladesh  Index Page Chapter 1 : Force, Pressure & Energy 01 Chapter 2 : Temperature and Heat 28 Chapter 3 : Modern Physics 50 Chapter 4 : States of Matter 68 Chapter 5 : Structure of Matter 77 Chapter 6 : Periodic Table 95 Chapter 7 : Chemical Bonds 110 Chapter 8 : Genetics and Heredity 124  Index Page Chapter 9 : Biomolecules 134 Chapter 10 : Photosynthesis 147 Chapter 11 : Human Body Systems 155 Chapter 12 : Ecosystem 182 Chapter 13 : Earth and Universe 206 Chapter 14 : The Environment and Landform 218 A few words for the students- Students, how are you all? Welcome to the Science subject of Class Nine. You can see, there is going to be a big change in the way you have been studying for so long! Your books on all subjects are also a little different this time. You must have got two books on Science! Along with this ‘Investigative Study’ book you are given another ‘Exercise Book’. If you have a look, you will realize that there is a big difference between this book and the Exercise book. Honestly speaking, the way you used to try to learn science by reading different chapters of textbooks, now this way of learning is completely changing. Throughout the year, you will go through several new experiences, solve some new problems. These new experiences and problem solving steps are detailed in your work book. In solving these problems, you will need to know different aspects of science at different stages. This ‘Investigative Study’ book will help you in this regard. At school or at home, wherever you are, you can use this book to solve problems yourself if needed! This book covers the topics of Science that you will need to know in Class Nine. The topics are organized in Fourteen chapters. Many of these things will be useful to you at different times in the experiences that you will go through throughout the year. So let us start, what do you say?  Chapter 1 Force, Pressure and Energy 1  Science Chapter 1 Force, Pressure and Energy This chapter discusses the following topics: 5 Newton’s First Law 5 Newton’s Second Law 5 Force 5 Four Kinds of Force 5 Newton’s Third Law 5 Gravitational Force and the law of Gravity 5 Pressure, Archimedes' principle and Buoyancy 5 Energy: Kinetic and Potential In the previous grade, you learned a bit about motion-related terms and also came to know how to express, with some simple mathematical equations, the changes in these quantities over time. That is, you learned about the definitions of terms such as displacement, velocity, and acceleration, and the equations that relate them. But the science behind where that motion comes from is only hinted at, but not explained. In this chapter, for the first time, you will be told where that motion comes from and how it relates to force. You will see how Newton's three groundbreaking laws can be used to analyze the motion of everything from Academic year 2024 planets and satellites to rockets and cars, to even cricket balls. 2  Force, pressure and energy Philosophiae Naturalis Principia Mathematica Isaac Newton was a British physicist who made significant contributions to many subjects such as motion, gravity, and light almost three centuries ago. Newton was also an extremely expert mathematician. He was considered the inventor of calculus along with German mathematician Leibniz. Newton was both a theoretical and practical scientist. His ideas about motion and gravitation were purely theoretical, but he proved much by direct experiment in many matters relating to light. As scientists' works are now published through scientific journals, this was not the case three centuries ago. Then some people wrote books and published their work. Newton wrote a book called 'Philosophiæ Naturalis Principia Mathematica'. This masterpiece written in Latin is known as “Mathematica”. 1.1 Newton’s First Law Newton’s first law of motion is often referred to as the law of inertia. This law explains how an object’s motion remains unchanged if no force is applied to it. Before understanding this law, it is necessary to understand the concepts of Static Inertia and Dynamic Inertia. 1.1.1 Static Inertia and Dynamic Inertia If you are standing in a bus or train, and suddenly the bus or train starts moving, you will notice that you want to fall backwards. As your lower body, touching the floor of Academic year 2024 the bus or train, begins to move forward, but your upper body wants to remain in its previous position, your upper body leans back, and you tend to fall. If you put a coin on a piece of paper or cardboard on top of a glass and pull the paper away, you will see that the coin falls inside the glass instead of with the paper (Figure 1.1). That is, the coin tries 3  Science to stay in its previous position even as the paper moves. The fact that a stationary object wants to remain stationary is called Static Inertia. You must have noticed that when a moving car is stopped suddenly, our body jerks and Figure 1.1: If the cardboard is moved away, the coin will leans forward. Braking causes fall into the glass because of static inertia. the lower body to stop with the car but our upper body is still in motion, causing it to lean forward. Have you ever seen someone getting off a moving bus or train? Those who are experienced in this matter run a short distance with their feet on the ground but do not stop. They know that if they land Figure 1.2: When a moving car is stopped suddenly, our body on the ground their feet will jerks and leans forward because of dynamic inertia. stop but the rest of the body will still remain in motion, so if the lower part of the body is not released at the same speed, it will fall down. Figure 1.2). The fact that an object in motion wants to maintain its previous speed is called 'Dynamic Inertia'. ୗ Food for thought: » Dust can be removed by beating a kantha or a blanket with a stick, why? » Spin bowlers bowl from almost a standing position, but pace bowlers Academic year 2024 run from a distance. Why? 4  Force, pressure and energy 1.1.2 Newton's First Law: Definition and Explanation Static inertia and Dynamic inertia together are called inertia. That is, the tendency of stationary objects to remain stationary and moving objects to remain in motion is inertia. Newton stated this inertia in his first law of motion. » Newton’s First Law: An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an external force. We don't have a problem with the first part of this law. We see it all the time in everyday life that if a stationary object is not pushed, it stays still, not moving on its own. But we may have a little trouble understanding the latter part from everyday experience, because we do not see any object in motion going on forever. But the answer to this problem is given at the beginning of Newton's first law, which speaks of 'external force'. Whenever you set an object in motion, forces such as friction or air resistance act in the opposite direction to slow down the motion. Since there is no air in space, there is no air friction, so if an object could be pushed out there, it would continue at the same speed forever. ୗ Food for thought: B The adjacent figure shows a heavy object hanging by a string, and another string hanging A below the object. A jerky pull on the lower thread will tear the A thread and a slow pull will tear the B thread (Figure 1.3). Why? Figure 1.3: A jerky pull will tear the A thread and a slow pull will tear the B thread. 1.2 Newton’s Second Law Academic year 2024 Newton's first law states how an object moves when no force is applied to it. You will see that Newton's second law explains how an object moves when force is applied to it. In the previous grade you learned that force must be applied to change velocity, Newton's first law reaffirmed that fact. The first formula, 5  Science however, does not say anything about the scientific definition of force or how to measure force. The method of measuring force is derived from Newton's second law. Before learning Newton's second law, you need to be familiar with a new term, momentum. 1.2.1 Concept of Momentum If someone comes towards you on a bicycle with a speed of 1 ms-1, you can stop him by putting your hand on the handle of his bicycle. But if someone drives a car with a speed of 1 ms-1, you cannot stop the car by holding it with your hand, even though both the bike and the car were moving at the same speed. The difference between the two is actually the mass. A bicycle is a low-mass or light object, a car is not at all, it is an object of high mass. That is, there is a matter of mass being less or more besides the velocity while changing the speed by applying force. If someone throws a small stone at you with a velocity of 1 ms-1, you can easily catch the stone. Now if he throws the same stone at you with a slingshot at 100 ms-1, you will not dare to catch it. Although the two stones are the same, i.e. they have the same mass, in both cases, the stone is not moving at the same speed. It is understood that the difference in this case is the velocity. That is, in addition to mass, there is also a matter of increasing or decreasing velocity while applying force to change motion. From these two examples, you can understand that the change in motion of an object by applying a force depends on both the mass of the object and the velocity of the object. That is why a new quantity is needed to combine mass and velocity, called momentum. It is actually the product of mass and velocity. You might think that since there are two quantities, mass, and velocity, there was no need to create a new quantity by multiplying them. Your idea is true in our daily familiar life, but you will be surprised to know that when the speed of an object approaches the speed of light, momentum is no longer just the product of mass and velocity. Not only that, light particles (photons) have zero mass but their momentum is not zero! You will know it in more detail in higher grades. For Academic year 2024 now, we will refer to momentum as the product of mass and velocity. Momentum is expressed by the English letter p. If mass and velocity are m and v respectively then p = mv and the unit of momentum is obtained by multiplying the unit of mass (kg) and unit of velocity (ms-1). That is, kg ms-1 is the unit of momentum. 6  Force, pressure and energy As velocity has direction, momentum also has direction; the direction of an object's velocity is its direction of momentum. Example: In the previous paragraph, values for the velocity of the bicycle, car, and stone were given, but not for the mass. If the mass of the bicycle is 75 kg, the mass of the car is 2000 kg and the mass of the stone is 5 g, what is the momentum in all four cases? Solution: The momentum of the bicycle is p1 = m1v1 = 75 x 1 = 75 kg ms-1 Momentum of car p2 = m2v2 = 2000 x 1 = 2000 kg ms-1 Momentum of stone thrown by hand is p3 = m3v3 = 0.005 x 1 = 0.005 kg ms-1 The momentum of the slingshot is p3 = m3v3 = 0.005 x 100 = 0.5 kg ms-1 1.2.2 Rate of Change In order to understand Newton's second law, we need to understand one more thing, that is the rate of change. We are all familiar with the term ‘change’, if the value of any quantity increases or decreases then we say that the quantity has changed. The amount that has increased or decreased is the amount of change. We use the term rate of change to describe how fast the change is occurring. Suppose you and your friend have gone out for a bicycle ride, both start from rest and reach a velocity of 10 ms-1, it takes you 2 seconds and your friend 2.5 seconds. We can tell without calculating that your rate of change of velocity is greater because you reached the same velocity in less time. If we calculate, then, Rate of change of your velocity = (10 ms-1 – 0)/2s = 5 ms-2 Rate of change of velocity of your friend = (10 ms-1 – 0)/2.5s = 4 ms-2 By calculating we get the same answer. Suppose again you and your friend have gone for a bicycle ride, this time both start from rest and cycle for 5s and find that your velocity is 20 ms-1 and your friend's velocity is 25 ms-1. This time also we can say Academic year 2024 without calculation that this time the rate of change of velocity of your friend is higher because the value of his velocity is higher by cycling for the same amount of time. If we calculate, 7  Science Rate of change of your velocity = (20 ms-1 – 0)/5s = 4 ms-2 Rate of change of velocity of your friend = (25 ms-1 – 0)/5s = 5 ms-2 This time too we got the same answer. So you must have understood that the rate of change of a quantity with time is called the rate of change. In the previous grade, we learned about velocity and acceleration. Now we can say, velocity was the rate of change of displacement with time, and acceleration was the rate of change of velocity with time. Example: If each object in the example from the previous paragraph is stopped for 1 minute, what is the rate of change in momentum in each case? Solution: Rate of change in momentum = (initial momentum – final momentum)/ elapsed time Here, the objects are coming to rest, i.e. the final velocity is zero, hence the final momentum is also zero Rate of change in momentum of bicycle = (75 - 0)/60 = 1.25 kg ms-2 Rate of change in momentum of car = (2000 - 0)/60 = 33.33 kg ms-2 Rate of change in momentum for stone thrown by hand = (0.005 - 0)/60 = 8.33 x 10-5 kg ms-2 Rate of change in momentum for a stone thrown in a sling = (0.5 - 0)/60 = 8.33 x 10-3 kg ms-2 1.2.3 Newton’s Second Law: Definition and Explanation Newton’s second law is one of the most important laws in Physics. With this simple formula, almost everything related to motion in our known world can be done. Everything from children's marble games to rockets into space can be explained with this formula. You already know how small the atom is, and you also know how fast the speed of light is; in these two cases - that is, in the case of very small lengths comparable to the size of atoms or very large speeds comparable to the speed of light, Academic year 2024 Newton's law does not apply. The first case requires quantum theory, and the second case requires relativity theory. You will learn about both in the next chapter. Since we do not even come close to it in our daily lives, we cannot feel their need separately. Newton's second law applies perfectly to almost everything in the visible world around 8  Force, pressure and energy us. Newton's second law is: » Newton’s Second Law: The rate of change in momentum of an object is proportional to the force applied to it, and the change in momentum also takes place in the direction the force applied. Newton's second law states the proportional relationship between force and rate of change in momentum. Consider an object of mass m moving with velocity u, when a force of magnitude F is applied to it from outside for time t, the velocity changes to v. That is, the momentum at the beginning of the application of the force is mu and the momentum at the end of the application of the force is mv, and the change in momentum will be their difference, That is, change in momentum = mv - mu Then, rate of change in momentum = (mv - mu)/t Since there is no change in mass, rate of change in momentum = m(v - u)/t But we know acceleration a = (v - u)/t So rate of change in momentum = ma According to Newton's law, the rate of change in momentum is proportional to the applied force, ie ma ∝ F or F ∝ ma If we want to write this as an equation rather than as a proportional relationship, then a constant of proportionality is needed. That is, we write like this, F = kma where k is the proportionality constant. Since Newton's second law does not say anything about the value of the constant of proportionality, it has to be determined by experiment. That is, by applying a certain amount of force (F) on an object of a certain mass (m), the acceleration (a) has to be seen, and then the value of the proportionality constant (k) will be found out. But here a very surprising thing happened. Nowhere Academic year 2024 does it say what is meant by a 'certain amount of force' because the method of measuring force had not been fixed until then! So scientists decided to use Newton's second law to measure force! That is, it was fixed that the amount of force which causes 1 unit of acceleration of 1 unit mass is 1 unit of force. That is, if m=1 and a=1 then F=1. Then 9  Science there is no need to find the value of k separately, because then the value of k becomes 1! Thus Newton's second law takes a very simple form: F = ma The unit of force is named Newton (abbreviated N) in honor of Newton's memory, i.e. the force required to move an object of mass 1 kg with an acceleration of 1 ms-2 is exactly 1 N. Since force is the rate of change in momentum, and since momentum has a definite direction, force has a definite direction. Example: What is the amount of the force exerted on each object in the example from the previous paragraph? Solution: Since, force = rate of change in momentum Force applied on the bicycle = 1.25 N Force applied on the car = 33.33 N Force applied on stone thrown by hand = 8.33 x 10-5 N Force applied on the stone thrown by sling = 8.33 x 10-3 N Example: A car of mass 750 kg moving at 50 ms-1 increases its velocity to 70 ms-1 in 10 s, what is the force applied by the engine of the car? Solution: Here, the acceleration of the car is a = (v - u)/t = (70 - 50)/2 = 10 ms-2 The mass of the car is m = 750 kg That is, the force applied by the engine is F = ma = 750 x 10 = 7500 N 1.3 Concept of Fundamental Force As you can imagine there are many types of force in the world! It is a force when a railway engine pulls a train carrying passengers, a force when houses are blown away Academic year 2024 in a storm, the attraction or repulsion of magnets is a force, a force when cricketers hit a six with the bat in cricket, when a crane does heavy Pulling is also a force —you can't actually count the number of forces! Although there are so many different types of forces around you, the amazing thing about science is that there are actually only four 10  Force, pressure and energy types of force in nature! They are: Gravitational Force, Electromagnetic Force, Weak Nuclear Force, and Strong Nuclear Force. If you analyze the surrounding forces, it will be seen that there are none beyond these four types! These are called fundamental forces. Among them, in our daily life, we only feel the force of gravity and the force of electromagnetism, the other two are in nature but not easily perceived. Four types of force Gravitational force is the force by which all objects in this universe attract each other due to their mass. Due to this gravitational force, the stars in the galaxy rotate or the earth rotates around the sun, and the moon rotates around the earth! When the earth's gravitational force acts on us, we call it gravity. Many of us have done it at one time or another, combing our hair and attracting a piece of paper with it, or using a magnet to attract and repel another magnet. Although electric and magnetic forces seem to be different forces, they are actually two same forces. Its name is electromagnetic force. The third fundamental force is called the weak nuclear force. The neutrons that accompany the protons in the nucleus of an atom are stable inside the nucleus, but when free, they split into protons, electrons, and neutrons within ten minutes. This process is known as beta (β) radiation and is caused by the weak nuclear force. The last fundamental force is called the strong nuclear force. The protons and neutrons in the center of the atom are held together by this very strong force. Due to this force, it is possible to generate electricity in nuclear power plants by releasing the huge energy stored inside the nucleus. Variation of Values in Basic Forces If we compare these four basic forces, it can be seen that their values vary greatly. For example, the first fundamental force of physics is the gravitational force, which we experience all the time in our daily lives. Any object that has mass attracts other objects with a gravitational force. It is very surprising that this ball is the weakest compared to the rest of the balls. Academic year 2024 Electromagnetic force can both attract and repel, while others can only attract and not repel. This force is 1036 times stronger than the force of gravity. It can be easily verified that the statement is true. A bit of paper can be easily pulled out by combing the hair 11  Science with a comb. Then the earth tries to pull that piece of paper with all its gravitational force, yet a little bit of electricity from the comb defeats the entire gravitational force of the huge earth. The weak nuclear force is called weak because it is about a hundred billion times (10-11) weaker than the electromagnetic force, yet much stronger than the gravitational force. The strongest force in the universe is the strong nuclear force, which is about a hundred times stronger than the electromagnetic force. It is because of this force that protons and neutrons can stay very close to the nucleus of an atom against the electromagnetic repulsion force. Variation of Range in Basic Forces After learning about the difference in value of the four fundamental forces in the previous paragraph, you must be wondering, since the strong nuclear force is so strong, how come the other weak forces are in effect? This question is very logical, but so far the proportion of the basic forces has been discussed, but not the distance at which the forces are effective. The extent to which a force can spread its influence is called the range of that force. Gravitational and electromagnetic forces can act at any distance, so their range is infinite. At great distances, the effect of these forces becomes very weak, but never zero. That is why, the galaxies from the solar system to the giants survive under the influence of the gravitational force despite it being very weak. On the other hand, nuclear forces act over very short distances. For example, the strong nuclear force acts at a distance of 10-15 m and the weak nuclear force acts at a thousand times less distance of 10-18 m. If the range of the nuclear force was greater than the force of attraction of gravity or the electromagnetic force, nothing from the galaxy to the atom could have been formed, which means that the universe would not have existed. ୗ Food for thought: » Gravity and electromagnetic forces can act at any distance, but why do we Academic year 2024 see the gravitational force being most effective at cosmic distances, even though the electromagnetic force is 1036 times stronger than the gravitational force? 12  Force, pressure and energy 1.4 Newton's Third Law From Newton's first law, we know what happens when no force is applied to an object. And we know what happens when force is applied to the object from Newton's second law. When one object exerts a force on another object, we will know the interaction between the two objects from Newton's third law. Newton's third law explains our walking or running. Newton's third law is also used in jet engines or rocket engines going to space (Figure 1.4). When discussing Newton's first and second laws, we talked about force, but not who or what is exerting the force. In real life, force is always exerted by some object on another object. Newton's third law tells us what reaction occurs between two objects when one exerts a force on Figure 1.4: Space Rocket another. Newton's third law is written in many ways but for ease of understanding, can be simply and clearly written as: » Newton's Third Law: When one object exerts a force on another object, that object also exerts an equal force on the first object in the opposite direction. The force applied is often called action and the force returned in the opposite direction is called reaction. You see, the force never stands alone, it always comes in pairs— meaning that if there is an action, there must be a reaction. It is never possible to get Academic year 2024 only action or only reaction separately. One thing that is often confused when learning Newton's third law is that if two forces are equal and opposite to each other, why doesn't one cancel the other? Therefore, 13  Science before learning the third law, it is very important to understand that if there are two separate objects A and B, and when A exerts a force on B, B exerts a force on A. That is, the two forces are equal and opposite but they act on two different objects, never on the same object. If the two forces were applied to the same object, they could only cancel each other out, but there is no Reaction Action chance of that here. One of the forces applied to Figure 1.5: Action and Reaction these two separate objects is action, the other is reaction (Figure 1.5). A few examples will make the matter more clear. If you push a heavy table, you will feel the table pushes you back (Figure 1.6). You can see there are two objects, one is yourself, and the other is the table. You exert a force (or action) on the table, so Figure 1.6: The table pushes back if the table exerts a force (or reaction) on you push it you. This is action and reaction. If you had to throw a punch in a vacuum, you probably wouldn't mind, because of how little or no force can be exerted on the air. But if you were asked to punch a hard concrete wall, you would probably not agree, because the concrete would cause you enough pain. The easiest way to understand Newton's third law is to understand how one walks. From a stationary position one can walk, which means there is an acceleration while walking, which means that force is applied to walk. But we all know that when someone walks, no one exerts a force on them, so where does the force come from? Without the concept of action and reaction, we could never explain walking. Because Academic year 2024 of this reaction, one can walk! That's why you can't walk in -F very slippery places. If the foot on the floor is not able to exert F a backward force on the slippery surface, the foot slips. As no Figure 1.7: Action and reaction force can be applied, there is no opposite force. are at work during walking 14  Force, pressure and energy The same thing happens in a jet engine of a plane or a rocket. The hot gas from the engine is ejected backward with great velocity, in response the plane or rocket moves forward. Example: A chair can exert a maximum reaction force of 525 N. If your mass is 50 Kg and your friend's mass is 55 Kg, can you stand up on this chair? Solution: Your weight = 50 x 9.8 = 490 N Weight of your friend = 55 x 9.8 = 539 N Here, the weight will act as the action of standing up on the chair. That is, the chair must also react with a force exactly equal to the weight. Now, 490 N < 525 N, means you can stand up on the chair. Again, 539 N > 525 N, means your friend will not be able to stand up on the chair, the chair will break. 1.5 Gravitational Force We have got an idea about force from Newton's laws of motion. We have discussed four types of fundamental forces but have not yet been introduced to any of them. Newton first mathematically introduced us to one of these four fundamental forces with his laws of gravitation. Now we can discuss the gravitational force as an example of a specific force. 1.5.1 From Information to Law Many inquisitive people on Earth have long looked at the sky night after night, trying to understand the movements of the planets and stars. Intelligent people have drawn parallels between the movements of the planets from these observations. Many have discovered the relationship of the positions of the planets with the possible timing of Academic year 2024 seasonal changes or various natural events. Gradually observation became an important part of science. However, it is not enough to observe in isolation; if you want to use it or find a mathematical formulation, you need well-organized complete information. Tycho Brahe was a Danish astronomer (Figure 1.8). He observed the sky night after 15  Science Nicolaus Copernicus Tycho Brahe Johannes Kepler 1473-1543 1546 - 1601 1571-1630 night for information and recorded the positions of the planets in a notebook at various times. By the time Nicolaus Copernicus spoke of a heliocentric solar system, Tycho Brahe accepted it as true for other planets but did not believe it applied to Earth! Tycho Brahe collected a large amount of correct data but did not have the opportunity to analyze it. After his death, the notebook passed to his associate astronomer Johannes Galileo Galilei Kepler. Kepler analyzed this vast amount of data and 1564-1642 derived three mathematical formulas for the motions of all the planets as heliocentric. In this way, through observation and mathematical formulas, people came to know the fact that the planets and stars in the sky are also subject to certain scientific rules. Isaac Newton Kepler's theory explains how the planets revolve around 1542-1727 the sun. Galileo, another contemporary scientist Galileo, Figure 1.8: Five important experimentally proved that all objects fall to the ground scientists of Astronomy 'simultaneously' due to the gravity of the earth, with Academic year 2024 the same rate of increase in velocity, that is, there must be a force behind it. These two apparently separate phenomena were united by the scientist Isaac Newton with the startling concept of the gravitational force 16  Force, pressure and energy (Figure 1.9). That force can explain everything from the apple falling from the tree to the rotation of the planets around the sun. Figure 1.9 It is said that Newton discovered the explanation of the force of gravity by watching an apple fall while sitting under an apple tree. 1.5.2 Newton’s Law of Gravitation: Definition and Explanation » Newton’s Law of Gravitation: Every particle attracts every other particle in the universe along the line intersecting both centres with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. That is, two objects of mass m1 and m2 are located at a distance R, if the force between them is F, then mathematically, Academic year 2024 R m1 m2 F=G R2 m 1 m 2 Figure 1.9: Gravitational Force between two masses 17  Science Here G is the gravitational constant, whose value is: 6.67 x 10-11 Nm²kg-2. Note that, here, the mass m1 attracts the mass m2 towards itself with F force and the mass m2 attracts m1 towards itself with the same (Fig. 1.9). Example: How much will an object of mass 1 kg placed on the earth's surface attract the earth? (Earth mass 6x1024 kg and radius 6.4x106 m) Solution: According to Newton's law of gravitation Mm 6.67 x 10-11 x 6 x 1024 x 1 F=G = = 9.8 N d2 6 2 (6.4 x 10 ) The earth will attract the object to itself with the same amount of force. 1.5.3 Concept of Weight If one of the two masses is the earth during the gravitational force and if we assume its mass M and another object of mass m is placed on top of the earth then the earth will attract the mass m towards its center with the force F. F= GMm/R2 Actually, this force is the weight of the object. Remember that weight is not mass, weight is force. Here R is not the distance from the Earth's surface, but the distance from the center of the Earth to the mass m. Since the Earth's radius is large (about 6000 km), there is no need to take small elevations on the Earth's surface as a factor for now. (The distance from the center of the earth is measured because every point on the earth attracts m mass to itself, and if all the attractions are added together, it can be shown mathematically that all the mass of the earth is concentrated at the center of the earth.) Note here that the gravitational force of the earth is called gravity. If an object of mass m is placed on the earth's surface, the gravitational force it will experience towards the center of the earth will cause an acceleration on the object according to Newton's second law. The acceleration due to gravity is written as g instead of a, so instead of F = ma we can write: Academic year 2024 F = mg Or, mg = GMm/R2 So, g = GM/R2 18  Force, pressure and energy If we use earth's mass as 6x1024 kg, radius as 6.4x106 m and value of G as 6.67 x 10-11 Nmkg-2, then, 6.67 × 10-11 × 6 × 1024 g= = 9.8 ms-2 6 2 (6.4 ×10 ) Earlier this value was used for the acceleration due to gravity, now you must understand how this value is arrived at. Example: You bought a 102 ml bottle of water from the store, what is the weight of the water? Solution: Since the density of water is 1gm/ml, 102 ml of water is actually 102 gm of water = 0.102 kg of water. So, weight of water = 0.102 x 9.8 = 1 N That is, 1 newton of force means the weight of about 102 gm or 0.102 kg of water! 1.6 Pressure A very important quantity/term related to force is pressure. This chapter has discussed various types of force, but has not specified exactly how the force should be applied. For example, you can push a stone with one hand, with both hands, or with your whole body (Figure 1.10). Even though you apply the same amount of force each time, the amount of pressure applied to the stone in these three cases will be different because the pressure is the force applied per unit area. That is, when force F is applied to a point of area A, the pressure P becomes F P = A Academic year 2024 Figure 1.10: Pressure depends on the area where the force is applied 19  Science N The unit of pressure is or Pa (Pascal). That is, 1 "Pa" (1 Pascal) of pressure is m2 applied when 1 "N" force is applied to 1 m2 area. Example: Suppose your mass is 50 kg, the area of one side of your body is 0.5 m2 and the area of the soles of both feet is 0.03 m2. How much pressure will you exert on the floor if you lie down and how much pressure will you exert on the floor if you are standing? Answer: Mass is 50 kg so weight is 50 ×9.8 N= 490 N When lying down the Pressure is 490N N P= = 980 0.5 m2 m2 When standing, the Pressure is 490N N P= = 16,333 0.3 m2 m2 In other words, when lying down, the force is spread over a larger area, so less pressure is applied. Just as applying force over a larger area produces less pressure, applying the same amount of force over a smaller area produces much greater pressure. The surface area of the sharp point of a nail is very small, so when it hits the wood or wall with force applied by hammering it, the nail head can easily drive into the wood or wall with a lot of pressure. You know the force has a definite direction, but the pressure has no direction. This is very important to know, because the concept of pressure is much more important in liquids or gases than in solids. When a liquid or gas exerts pressure, it does not actually depend on direction. 1.6.1 Pressure in Liquids Academic year 2024 All of you who have been in a pond, river or swimming pool have noticed that you can feel a kind of pressure when you go deeper into the water. It is very easy to find out exactly how much pressure can be felt when going deep into water or any other liquid. 20  Force, pressure and energy Suppose you want to determine the pressure at a depth h of the liquid. Imagine a surface of area A there (Fig. 1.11). The weight of the column of liquid above it will exert a force on this surface A. The volume of the liquid above the surface A is Ah. If the density of the liquid is ρ, then the mass of the liquid is m: m=Ahρ Hence the weight or applied force F = mg = (Ahρ)g So pressure: Figure 1.11: Pressure is created on the F Ahpg P = = = hpg bottom surface for the height of the A A liquid That is, pressure increases with the increase of depth in a liquid of a given density. In water, the pressure increases approximately every ten meters of depth, equal to the air pressure. Example: Kerosene (800 kg m-3 ), water (density 1000 kg m-3) and mercury (density 13,600 kg m-3). What is the pressure below 50 cm for these three liquids? Answer: Pressure P=hρg For Kerosene, P = 0.50 m × 800 kg m -3 × 9.8 N kg-1 = 3,920 N m-2 For Water, P = 0.50 m × 1000 kg m-3 × 9.8 N kg-1 = 4,900 N m-2 For Mercury, P = 0.50 m × 13,600 kg m-3 × 9.8 N kg-1 = 666,400 N m-2 1.6.2 Archimedes' Principle and Buoyancy You all must have heard of Archimedes’ formula and the story behind it. The formula Academic year 2024 is simple; when an object is immersed in a liquid, the amount of liquid it displaces equals the weight of the object. We will now derive this formula. Figure 1.12 shows a cylinder immersed in some liquid. (It could have been any other shape instead of cylinder, we have taken cylinder for ease of calculation.) 21  Science Say the height of the cylinder is h and the cross- sectional area of the top and bottom is A. We imagine the cylinder is immersed in the liquid such that its upper surface has a depth h1 and its lower surface has a depth h2. Pressure in liquids (or gases) does not act in any particular direction. It works equally in all directions. Hence the amount of pressure acting downwards on the upper surface of the cylinder is P1 = h1 ρg Figure 1.12: An object loses weight equal And the amount of pressure acting upwards on to the amount of liquid it displaces. the lower surface of the cylinder is P2 = h2 ρ Since, F1 P1= A Therefore, force applied downward on the upper surface is F1 = AP1 = Ah1ρ Similarly, F2 P 2= A Therefore, force applied upward on the lower surface is F2 = AP2 = Ah2ρ We don't need to worry about how much force is applied to the side surfaces of the cylinder, because the force that the cylinder feels on one side is exactly the opposite of the force on the other side, and they cancel each other out. Since the value of h2 is greater than h1 we can see that the value of F2 is greater than F1. So the total force will be upward and amount to: Academic year 2024 F = F2 -F1 = A(h2 - h1) ρ F = Ahρg 22  Force, pressure and energy Since Ah is the volume of the cylinder, ρ the density of the liquid and g the acceleration due to gravity, the upward force is equal to the weight of the liquid equal to the volume of the cylinder. It is exactly what is known as Archimedes' law. This upward force is called ‘Buoyancy’. 1.6.3 Floating or Sinking of Objects Now you must have understood why one object floats and another sinks. You know that when an object is immersed in water, due to buoyancy it experiences a force equal to the weight of the water displaced above it. If that force is greater than the weight of the object, the object will float. It will only sink that much the weight of which equals to the amount of displaced water, the rest will not sink in the water. If the weight of the object is greater than the weight of the water it displaces, it will sink. However, when submerged in water, its weight will seem less than its actual weight. If somehow the weight of the object can be made exactly equal to the weight of the displaced water, then the object will stay in the water wherever it is placed, neither floating nor sinking. Although not seen in everyday life, it is routinely done in submarines to navigate underwater. Example: If a piece of wood is floated in water, what percentage of it will be submerged? (Density of wood ρ = 0.5 × 103 kg/m3 Density of water ρW = 103 kg/m3 ) Answer: For the wood to float, the weight of the submerged part of the water must be equal to the weight of the wood. That is, if the volume of wood is V, its weight is Vρg, and if V1 part of the wood is submerged in water, then the weight of that amount of water is V1 ρW , so ρ = 1 or ρ= 1ρ 0.5× 103 kg/m3 Academic year 2024 1 = = × 100 = 50% ρ 103 kg/m3 23  Science 1.7 Energy In the previous grade, we have already known the examples of different forces. We also know that energy is the ability to do work. But here we do not mean the work that we do in our daily life, the word ‘work’ has a specific meaning in the language of science. Here we will discuss the relationship between energy and work. 1.7.1 Kinetic and potential energy Work is said to be done if an object can be moved a certain distance in the direction of the force by applying the force. If an object is moved s distance in the direction of the force by a force F, then the amount of work done is, W = Fs The unit of work is joule (J); 1 J of work is done when an object is moved 1 m by applying a force of 1 newton. From Newton's second law we know F = ma, so we can write, W = mas We know from the equation of motion, v2 = u2 + 2as If the object starts from rest then initial velocity u = 0, Then v2 = 2as 2 and as = v 2 So the amount of work will be, W = mas W = 12 mv2 Academic year 2024 which is actually the kinetic energy of an object. That is, when work is done on an 24  Force, pressure and energy object, that work is converted into kinetic energy. We don't always see that in real life. Because the frictional force acts in the opposite direction and sometimes converts the energy into heat, sound, etc. instead of converting into kinetic energy. Not only can kinetic energy be created by doing work, but that work can also be stored as potential energy. If you want to lift an object up, you must apply an upward force equal to the weight of the object. If an object of mass m is lifted to a height h by an upward force F = mg equal to the object's weight, the amount of work done will be: W = Fh Or W = mgh After the object is raised to a height h, since it remains at rest, there is no kinetic energy in it, it has not been converted into any other energy such as heat or sound due to friction, so this mgh amount of work energy must have actually been stored as potential energy. We can understand this when we see that when the object is released from a height h, it gains momentum as it falls downwards, and the stored potential energy is converted into kinetic energy. 1.7.2 Conservation of Mechanical Energy In the previous grade we learned about 'conservation of energy'. According to this principle, energy is neither created nor destroyed, only transformed from one form to another. Kinetic energy and potential energy together are called 'mechanical energy'. If the energy does not change in any way other than mechanical energy, the total amount of mechanical energy must remain the same. We can call this the 'conservation of mechanical energy'. If we lift an object some distance and drop it, it will continue to move. In the beginning the object has no motion, so it is all potential energy. A little later the potential energy will decrease when the altitude decreases, while the speed will increase so the kinetic energy will increase. In this way, when it comes down to the very bottom, it will be entirely kinetic energy. That is, as much potential energy is consumed, that much kinetic energy is gained. This is the conservation of mechanical Academic year 2024 energy! 25  Science Example: An object is dropped from point A in 5 kg the figure (Fig. 1.13). What is the total energy of the object at points A, B and C? A Solution: 2m At point A B Potential Energy mgh = 5 × 9.8 × 4 = 196 J 2m 1 1 Kinetic energy 2 mv2 = 2 × 5 × 02 = 0 J C 1 Total energy mgh + 2 mv2 = 196 + 0 = 196 J Figure 1.13: An object of 5kg mass At point B is dropped from a table of 4m height Potential Energy mgh = 5 × 9.8 × 2 = 98 J 1 2 2 Since the kinetic energy is 2 mv we need to find the value of v We can derive it from the formula v2 = u2 + 2as v2 = u2 + 2as or, v2 = 02 + 2 × 9.8 × 2 or, v2 = 39.2 ms-1 1 2 1 Kinetic energy 2 mv = 2 × 5 × 39.2 = 98 J 1 Total energy mgh + 2 mv2 = 98 + 98 = 196 J At point C mgh = 5 × 9.8 × 0 = 0 J Now v2 = u2 + 2as Academic year 2024 or, v2 = 02 + 2 × 9.8 × 4, or, v2 = 78.4 ms-1 1 2 1 Kinetic energy 2 mv = 2 × 5 × 78.4 = 196 J 26  Force, pressure and energy 1 Total energy mgh + 2 mv2 = 0 + 196 = 196 J That is, we have calculated in a specific example that the 200 conservation of mechanical Total Energy energy is indeed maintained. 150 When something is dropped Potential Kinetic from a height, how the Energy (Joule) Energy Energy potential energy and kinetic 100 energy change with height but the total energy does not 50 change is shown in the adjacent graph (Figure 1.14). 0 1 2 3 4 Height (m) Figure 1.14: As potential energy decreases, kinetic energy increases but total energy remains unchanged. ୗ Food for thought » What would this graph look like if it were drawn with time instead of height? Academic year 2024 27  Science Chapter 2 Temperature and Heat 28  Temperature and Heat Chapter 2 Temperature and Heat This chapter discusses the following topics: 5 Temperature and internal energy 5 Expansion of solids, liquids, and gases on application of heat 5 Change of state on application of heat 5 Calorimetry 5 Thermodynamics Heat Around us, we see various types of energy, which we use in our daily lives. Heat is one such energy. We are all familiar with this energy in our lives and have used it in various ways. We use heat to cook, heat water for tea or coffee, and dry clothes quickly by hanging them in the sun. Sometimes, we try to protect ourselves from excessive heat for personal comfort, sit in the shade to protect ourselves from the sun, and avoid wearing black clothes during hot weather. This list can be much longer. So, it is natural that we are all curious about how this heat energy came to be. Or, in other words, why is heat energy present in hot water but not in cold water? This is something we all need to know. At one time, scientists had many questions about this matter, but now we know that all Academic year 2024 substances are made up of atoms and molecules, and we see the motion or vibration of these atoms and molecules as heat energy. The more these atoms and molecules move, the hotter they will feel. The atoms of water inside a glass of cold water are not stationary, they are also moving. But when heat is applied, the atoms of that water 29  Science move much more. If more heat is applied, it is possible for the velocity of some water molecules to increase so much that they become free from the water. We call this process evaporation. Heat Transfer We need to transfer or conduct heat from one place to another for various purposes. Heat is transferred in three ways: conduction, convection, and radiation. Conduction Heat is conducted through the vibration of atoms of a solid substance. When one end of a solid substance is heated, the atoms at that end vibrate. If an atom vibrates, it starts to make the adjacent atoms vibrate too. That atom then vibrates its neighboring atoms. In this way, the vibration is transmitted from one end of the solid substance to the other. This process is called heat conduction. Convection When a fluid or gas is heated, it becomes less dense and rises because its molecules move faster and take up more space. If the same amount of fluid or gas is kept in a slightly larger space, its density decreases or it becomes lighter and rises. The cooler fluid or gas nearby then takes its place. This way, an internal circulation of fluid or gas starts, which mixes all the fluid or gas very well and heats it up. Radiation When we stand in the sun, the heat we feel is not transported to us by convection or conduction, but by radiation from the sun. Radiation does not require a medium, so even though the Sun and Earth remain in space, visible light and invisible infrared and ultraviolet rays can reach Earth through radiation. Specific Heat The amount of heat stored in an object depends on the object's temperature, its mass, Academic year 2024 and its specific heat. Since air has a very low density, it has a very low capacity to store heat. A substance with a low specific heat can be heated to a much higher temperature by giving off little heat. On the other hand, if a substance has a high specific heat, a lot of heat must be given off to bring it to the same temperature. 30  Temperature and Heat Heat Flow When two objects with different temperatures come into contact, heat flows from the object with a higher temperature to the object with a lower temperature. For that reason, temperature is often defined in terms of heat flow. Heat will continue to flow until the two temperatures reach the same point. If a needle is heated by fire, the amount of heat inside it will not be much. In comparison, a bucket full of water will contain much more heat. However, if the hot needle is dropped into water, even though the amount of heat in the ball is low, it will still transfer its heat to the water in the bucket. 2.1 Temperature and Internal Energy To know heat energy correctly we need to have a clear idea about temperature. Because the internal energy stored inside any object due to heat has a relationship with temperature. 2.1.1 Thermal energy Heat is one of our most familiar and necessary forms of energy. In our daily lives we regularly generate heat, use heat, and sometimes try to remove excess heat. The creation and control of heat has played a major role in the current civilization of the world. Heat is generated by the use of fuel in vehicles and the heat energy is converted into mechanical energy to drive the vehicles. In power plants most of the time, electricity is generated by turning generators using thermal energy. When using nuclear energy, it is available as thermal energy. Availability of the right thermal energy also played a major role in the development of life on Earth. Living organisms also consume food to survive and first convert it into heat energy. Unfortunately, humans misuse energy and create unnecessary heat in the world, changing the climate of the whole world and putting the people of the world at risk of danger. Since heat is energy, naturally the unit of heat like any other energy is joule (J). Another unit of heat is the calorie (cal). The amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius is known as calorie. 1 calorie contains 4.2 J of heat. Academic year 2024 31  Science 2.1.2 Motion of Molecules and Temperature Apparently, thermal energy seems to be a completely different type of energy from mechanical energy, but this energy comes from the combined kinetic energy or vibrational energy of the molecules of matter. In the case of solids, heat is the vibration of molecules. In the case of liquids, it means that the molecules move in contact with each other. In the case of gases, it is the free movement of molecules relative to one another. To understand heat energy we must first understand what temperature is. Heat is a quantity of energy and temperature is a measure of how hot or cold something is. Therefore, from a molecular point of view, temperature can be said to be a measure of the vibration or kinetic energy of the molecules of matter. The higher the speed or vibration of the molecules, the higher the temperature of the object. The international unit of temperature is Kelvin (K), but the unit we use most for temperature in our daily life is Celsius (°C). If you compare the Celsius and Kelvin scales, you will see that there is no difference in the Kelvin scale except for the addition of 273.15° to the Celsius scale temperature. The Kelvin scale is developed to take this absolute zero temperature as zero degrees. In Celsius scale, this temperature is -273.15° so adding 273.15 to Celsius scale gives Kelvin scale. In addition to the Celsius scale, another temperature scale called Fahrenheit is used in some countries and in thermometers to measure fever. On that scale the temperature of ice is 32°F and the temperature of boiling water is 212°F. Mathematically, the relationship between these three temperatures is: 2.1.3 Concept of Internal Energy Particles (atoms or molecules) in solids, liquids, and gases have kinetic energy because Academic year 2024 they are in motion. They also have potential energy because molecular bonds try to hold the particles together. Gas particles have the highest kinetic energy as they are almost free. The total kinetic energy and potential energy of all the particles of a substance is called its internal energy. The higher the temperature of an object, the more its particles 32  Temperature and Heat move, so the internal energy increases. In general, we may think of energy as flowing from higher energy to lower energy. But a bucket of water has much more heat energy than a hot needle. If we submerge the heated needle in water, a small amount of thermal energy from the needle will go into the bucket of water. That's because heat energy flow doesn't depend on heat energy, it depends on temperature difference. If a hot object comes in contact with a cold object, the hot object cools by losing internal energy, and, simultaneously, the cold object gains internal energy and becomes hot. Heat energy will continue to flow until the temperature of the two objects is equal. This transferable energy between objects due to temperature difference is known as heat or thermal energy. When a hot object is placed in contact with a cold object, the particles of that object lose kinetic energy as heat energy is transferred from the hot object to the cold object. Again, as the cooler object heats up its particles gain kinetic energy. When the two objects reach the same temperature, this transfer of energy stops as the average kinetic energy of each particle becomes equal. The higher the temperature, the higher the average kinetic energy of the particles. 2.2 Thermal Expansion of Matter If we take a closer look at the rail lines, we see that Figure: 2.1 (above) Gap between rail there is always a slight gap between them. This lines. (below) Crooked lines because is because heat causes expansion in the rail line, of hot weather causing the rail line to become crooked (Figure 2.1). In order to know exactly how much clearance in the rail lines will always be safe for trains, we need to understand the relationship between heat and expansion of matter. Academic year 2024 2.2.1 Expansion in Solids Figure 2.2: Spring model of You already know about the change in temperature of matter molecules of matter 33  Science and the vibration or speed increase and reduction of the molecules with the application of heat. In solids, molecules hold each other in fixed positions by molecular forces. We can compare this force with the spring shown in Figure 2.2. But this spring is a special kind of spring, one that stretches farther but contracts less—because one molecule doesn't let another molecule get too close. When heat is applied, the molecules vibrate more, they move a little farther during expansion but less distance during compression, so the vibrating molecules take up more space and the volume of the substance appears to have increased. When heat is applied, solids expand in all three directions: length, width, and height. Therefore, to measure expansion in solids, three quantities are used namely linear, area, and volume expansion coefficient. Because they are interrelated, by measuring any one we can get the other two. Linear expansion coefficients are used to measure the expansion of a material along its length only. It is expressed by the Greek letter α (pronounced alpha). That is, α is how much a substance increases in length for every degree of temperature increase. Suppose, the length of a solid at temperature T1 is L1 and on increasing the temperature to T2 the length of the object becomes L2. Then the total change in length is: L2 - L1 (L2 - L1) How much length has changed L1 (L2 - L1) Change in length per degree rise in temperature: L1 (T2 - T1) So, linear expansion coefficient α is, (L2 - L1) α= L1 (T2 - T1) That is, if we know the linear expansion coefficient α of a solid object, from this equation we can find out the length of an object if the temperature increases. If the length of a Academic year 2024 solid at temperature T1 is L1 then if its temperature is increased to T2 the length of the object will be L2 L2= L1 + α L1 (T2 - T1) 34  Temperature and Heat Example: A 10 m length of metal wire at a temperature of 290 K is exposed to the sun and its temperature rises to 325 K. Now what will be the length of the wire? (Linear Coefficient of wire material is 23 × 10-6 K-1) Solution: Expanded length L2 = L1 + α L1 (T2 - T1) = 10 + 23 × 10-6 × 10 × (325 - 290) = 10.008 m The area expansion coefficient is used to measure the expansion along the surface area of an object. It is expressed by the Greek letter β (pronounced beta). If an object of temperature T1 and area A1 changes into temperature T2 and area A2, then (A2 - A1) β= A1 (T2 - T1) Similarly, the volumetric (or cubical) thermal expansion coefficient is used to measure the volume expansion of a material. The volumetric expansion coefficient is expressed by the Greek letter γ (pronounced gamma). If the temperature of an object of temperature T1 and volume V1 changes to T2, then if the volume changes to V2 (V2 - V1) γ= V1 (T2 - T1) But interestingly, if the linear expansion coefficient α is known, there is no need to measure the area expansion coefficient β or the volumetric expansion coefficient γ separately, because: β = 2α γ = 3α ੌ Do it yourself: Academic year 2024 To find out the area expansion coefficient, assuming the area of the solid to be square, we can write for A1 and A2: A1 = L12 35  Science A2 = L22 = {L1 + α L1 (T2 - T1)}2 Since the value of linear expansion coefficient α is very small, the value of α2 is much smaller, so let α2 be zero and β = 2α। ੌ Do it yourself: Similarly, to find the volumetric coefficient of expansion, assuming a cube for the volume of solid, we can write for V1 and V2: V 1 = L 13 V2 = L23 = {L1 + αL1(T2 - T1)}3 Since the value of linear expansion coefficient α -is very small, the values of α2 and α3 -are much smaller, so let α2 and α3 be zero and show γ = 3α। Example: A square metal sheet of 5 cm length at 275 K is heated to 350 K. Now how much will the area of the sheet increase? (linear expansion coefficient of sheet material α = 22 × 10-6 K-1) Solution: Since the linear expansion coefficient α = 22 × 10-6 K-1 So area expansion coefficient β = 2α = 2 × 22 × 10-6 = 44 × 10-6 K-1 Here, the initial area is A1 = 5 × 5 = 25 cm2 Changed area A2 = A1 + βA1 (T2 - T1) That is, the change in area A2 - A1 = βA1 (T2 - T1) = 44 × 10-6 × 25 × (350 - 275) = 0.0033 cm2 Example: The density of gold is 19.30 gm/cc, iand ts linear expansion coefficient is 14×10-6 0C-1-What will be the density if the temperature is raised to 1000C? Answer: Density, ρ = m Academic year 2024 v where V is volume and m is mass. Increasing the temperature increases the volume even though the mass remains the same. So if the temperature is raised to 1000C its 36  Temperature and Heat volume V' will be: V' = V + γV(T2- T1 ) = V(1+3α × 100) α =14 × 10-6 0C-1 = (1+ 4.2× 10 3 ) ρ = = = ×0.9958 =0.9958ρ (1+ 4.2×1 0 3 ) ρ =0.9958× 19.30 gm/cc =19.22 gm/cc If the coefficient of expansion of a substance is known, the extent to which it will change with changing temperature can be calculated. Knowing the expansion coefficient C is very important in various practical applications. You A already know that since railway lines expand with heat, it is necessary to calculate in advance how much free space B is required for this. Otherwise, the railway line may bend and cause an accident. It is also necessary to know the coefficient of expansion while making engines or such machines, because these machines have a lot of temperature fluctuations. Again, rockets or artificial satellites heat up as they move at high speeds through the atmosphere. Here too the expansion coefficient needs to be known. The expansion Figure 2.3: Apparent and coefficient of the material that dentists use to repair tooth Real expansion of liquids decay must be exactly the same as the expansion coefficient of the tooth. Otherwise, it will be disjointed by being smaller when eating something cold, or expand more when eating something hot and put pressure on the tooth. 2.2.2 Expansion in Liquids Academic year 2024 Liquids have no length or area, only volume. So expansion of a liquid means the expansion of its volume. However, one has to be careful when measuring the expansion of a liquid because the liquid always needs to be kept in a container. So when the liquid is heated to measure expansion, the container also heats up and the container also 37  Science expands a bit. So the expansion seen in the liquid kept in the container is not the real expansion, it is the apparent expansion. If the expansion of the liquid is calculated taking into account the expansion of the container, it will be the real expansion or absolute expansion (Figure 2.3). If a glass container with a narrow tube is filled with liquid up to mark A and heated, we see that the height of the liquid first drops to B. This will happen because after heating, the temperature of the container will increase before the temperature of the liquid increases and it will expand, i.e. the volume of the container will increase slightly. If we continue to heat it, the height of the liquid will eventually rise. Since the expansion of the liquid is high, we will see the liquid pass A and finally reach height C. Thin curve By multiplying the cross-section of this part of the container by Mercury the height CB we get the actual expansion of the liquid. The simplest example of the expansion of a liquid is the Figure 2.4: Expansion of mercury or alcohol thermometer. There are different types ofmercury in thermometer thermometers, of which the fever thermometer is probably the most familiar to you. At the base of this thermometer is mercury in a glass tube. When heated, the mercury expands and rises in a very narrow tube (Figure 2.4). Temperature is measured by seeing how much mercury has risen in the marked thermometer. A very narrow bend is placed at the base of the narrow tube so that the mercury does not fall down after it is removed from the body. For this reason, once it expands and goes up, it cannot come down even after the temperature drops, it has to be shaken down. Example: 4 L of water at 280 K is heated to 360 Hot K. Now if the volume of Ice Water water is 4.0672 L, what is Academic year 2024 the coefficient of volume expansion of water? Figure 2.5: The air inside the balloon compresses when cooled and expands when heated. 38  Temperature and Heat Solution: Volumetric expansion coefficient γ = (V2 - V1)/{V1 (T2-T1)} = (4.0672 - 4)/{4 (360-280)} = 2.1 10-4 K-1 2.2.3 Diffusion of gaseous substances Since solid matter has both shape and volume, there is no problem understanding the expansion. Even though a liquid has no definite shape, it has volume, so we can see or measure its expansion. In the case of gas, the matter is slightly different because not only does it have no definite shape, but it also has no definite volume. A gas will immediately take up the volume of the container into which it is inserted. We do not see much of the expansion of solids and liquids in our daily life as it is quite low. Compared to that, the expansion of gas is much higher as we can see from simple experiment. If a balloon is inflated a little and placed in the mouth of a bottle and the bottle is immersed in ice water, the balloon will shrink, and if the bottle is immersed in hot water, the balloon will be inflated (Figure 2.5). In the case of solid or liquid we did not have to worry about the pressure applied to them, but in the case of gas the pressure is very important. Neither liquids nor solids can be greatly compressed by pressure. But gases can be compressed much more easily by pressing them. If the same amount of gas is placed in a container of different volume, its pressure also becomes different, that is, the expansion and contraction of the gas can be done by increasing or decreasing the pressure just like temperature. So if we want to measure how much the volume of a gas has increased with heat, we have to make sure that there is no change in its pressure (Figure 2.6). So first we need to know the relationship between Academic year 2024 pressure (P), volume (V) and temperature (T) of a given amount of gas. Remember, here T is Figure 2.6: Heat increases the pressure and volume of a gas temperature in Kelvin scale. This is called the 39  Science ideal gas law and mathematically the formula can be written as: PV = nRT Here R is the 'universal gas constant', its value is 8.314 JK-1mol-1 and n is the amount of gas per mole unit. The value of this constant is true for all gases. Example: If 128 g of oxygen gas is kept in a 100 ml container at a pressure of 108 Pa, what will be its temperature? Solution: Pressure P = 108 Pa, Volume V = 100 ml = 10-4 m3, Molecular mass of oxygen is 32 g, so 128 g oxygen means n = 128/32 = 4 moles of oxygen Since , PV = nRT So T= PV/nR = (108 x 10-4)/ (4 x 8.314) = 300K On the Celsius scale this temperature is 300 – 273 = 270C The result would have been the same for 4 moles of hyd