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GRADE 12A: Physics 2 UNIT 12AP.2 15 hours The nature of matter

About this unit Previous learning Resources This unit is the second of seven units on physics To meet the expectations of this unit, students should already know that a The main resources needed for this unit are: for Grade 12 advanced. force can cause deformation, and know the relationship between force and a • blocks of upholstery foam The unit is designed to guide your planning and change of momentum. They should understand and use the term pressure. • samples of materials for tensile and shear testing They should be able to describe the kinetic particle model for solids, liquids teaching of physics lessons. It provides a link • large masses and gases, and define a mole of a substance in terms of the Avogadro between the standards for science and your • apparatus for determining Young’s modulus of a wire lesson plans constant. They should define temperature and explain how a temperature scale is constructed. They should be able to recall and use the formula for • air blower The teaching and learning activities should help kinetic energy. • apparatus to show the Bernoulli effect in flowing water you to plan the content and pace of lessons. • simple wind tunnel (or apparatus to construct one using a fan or air- Adapt the ideas to meet your students’ needs. blower) For consolidation activities, look at the scheme Expectations • apparatus to demonstrate Boyle’s law of work for Grade 11A. By the end of the unit, students classify solids according to stiffness, • apparatus to demonstrate Charles’s law You can also supplement the activities with tensile strength, compressive strength and shear strength, plot and interpret • constant volume gas thermometer appropriate tasks and exercises from your stress–strain graphs for different solids and define and use Young’s • Internet access school’s textbooks and other resources. modulus. They know how these properties are used by engineers and Introduce the unit to students by summarising understand the usefulness of composite materials. They explain surface what they will learn and how this builds on earlier tension. They solve problems related to ideal gas behaviour and show Key vocabulary and technical terms work. Review the unit at the end, drawing out the mathematically the relationship between temperature and the kinetic energy Students should understand, use and spell correctly: main learning points, links to other work and real of molecules. world applications. • terms relating to properties of solids: stiffness, stress, strain, strength, Students who progress further explain qualitatively how fluid flow past tensile, compressive, shear, Young’s modulus, composite material solid bodies can give rise to pressure. They explain how the behaviour of • terms relating to fluids: surface tension, adhesion, cohesion, Bernoulli real gases deviates from ideal behaviour at high pressures and low effect temperatures, and derive relationships between the molecular kinetic energy and the pressure, volume and temperature of an ideal gas. • terms relating to gases: ideal gas, Boyle’s law, Charles’s law, absolute temperature, absolute zero, universal gas constant, mean square speed, Boltzmann constant Standards for the unit Unit 12AP.2

SUPPORTING STANDARDS CORE STANDARDS EXTENSION STANDARDS 15 hours Grade 12 standards

6 hours 10A.26.3 Know that a force acting on an object 12A.26.1 Classify solids according to stiffness, tensile strength, compressive can cause deformation ... strength and shear strength. Plot and interpret stress–strain graphs for different solids. Define and use the concept of Young’s modulus.

3 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.2 | Physics 2 © Education Institute 2005 Properties of 12A.26.2 Relate the uses of materials to their characteristic behaviour under different solids types of stress and note the importance of composite materials, both natural and synthetic. 12A.26.3 Explain surface tension in terms of interparticle forces. 6 hours Ideal and real 10A.27.7 Understand and use the term 12A.26.4 Explain qualitatively how fluid flow past solid bodies can generate pressure gases pressure... changes in the fluid; give practical examples of this.

10A.27.1 Describe the kinetic particle model 12A.26.5 Apply the kinetic particle model to an ideal gas and explain, in terms of 3 hours for solids, liquids and gases, and molecular size and intermolecular forces, how the behaviour of real gases Fluids relate the difference in the structures deviates from the ideal model at high pressures and low temperatures. and densities of solids, liquids and gases to the spacing, ordering and motion of particles. 11A19.2 Define a mole of a substance in 12A.26.6 Derive, know and use the gas laws and the general gas equation terms of the Avogadro constant ... PV = nRT and show how the general gas equation leads to a concept of 11A.28.1 Define temperature and explain how absolute zero of temperature. a temperature scale is constructed ... 11A.26.2 Know that ... a momentum change 12A.26.7 Show that a theoretical treatment of molecular movement and gas on a body is equal to the force pV 1 mNc 2 pressure leads to the relationship  3 and hence, by combining causing it. with the gas equation, that the average kinetic energy of a particle is 11A.27.3 Recall, derive and apply the formulae proportional to its absolute temperature. 1 2 Ek  2 mv …

4 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.2 | Physics 2 © Education Institute 2005 Activities Unit 12AP.2

Objectives Possible teaching activities Notes School resources

6 hours Choosing materials Use this column to note your own school’s Properties of solids Set up a display of objects made from a wide variety of materials. Ask students to visit each Suitable objects include: cooking utensils, exhibit in turn and make brief notes in which they identify the types of material used (e.g. wood, clothing, footwear, bicycle, sports equipment, resources, e.g. Classify solids according to textbooks, worksheets. stiffness, tensile strength, metal, ceramic, polymer, textile) and suggest why each material was chosen for making that packaging. compressive strength and object. Use pictures if actual objects are unobtainable. shear strength. Plot and After students have explored the display, hold a brainstorming session in which they suggest interpret stress–strain graphs the types of question that a designer or engineer might consider when choosing a material for a for different solid. Define and particular purpose. Questions might include: use the concept of Young’s • Is it waterproof? modulus. • Does it bend easily? Relate the uses of materials • Does it stretch easily? to their characteristic • What does it look like? behaviour under different • How big a force can it withstand without breaking? types of stress and note the • Does its production harm the environment? importance of composite • How dense is it? materials, both natural and synthetic. • How much does it cost? Explain that in this part of the unit most of the attention will be on how materials respond to forces – though many of the other questions suggested are also relevant in practice to the choice of materials. By suitable questioning, find out how much students recall of work in earlier units in which they tested material samples, and remind them of Hooke’s law. Stress and strain Use blocks of upholstery foam to demonstrate how the dimensions of a sample affect the The foam blocks should all be made for the deformation produced by a force. same material (ideally all cut from a single larger First use two blocks of the same height but different cross-sectional area. Place a sheet of stiff block). card on top of each, and the same load on top of each card. Students should observe that the Suitable dimensions for the blocks are: narrower block experiences the greater deformation: if it has half the area of cross-section it • 10 cm × 10 cm × 10 cm; experiences twice the deformation. Increase the load on the wider block so as to produce the • 20 cm × 10 cm × 10 cm; same deformation of each block. Establish that if both blocks have the same load ÷ area, they • 10 cm × 10 cm × 5 cm. experience equal deformation. Arrange the blocks with their largest dimensions Introduce the term stress defined as force ÷ area. Discuss the SI units of stress and establish horizontal, otherwise they may buckle under a that (recalling work on pressure from earlier grades) they can be expressed as N m--2 or Pa. load. Next use two blocks of the same cross-sectional area but different height. As before, give each You will need to experiment beforehand to find the same load. The shorter block experiences a smaller deformation. Establish that suitable loads to produce noticeable deformation deformation ÷ original height is the same for each block. without flattening the blocks. Sets of 100 g Introduce the term strain defined as change in length ÷ original length. Discuss its units and hanger masses are a good starting point. point out that strain is length ÷ length so has no units. Establish that strain can be expressed as This activity also relates to Standard 10A.25.1. a ratio, a fraction, a decimal number or a percentage.

5 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.2 | Physics 2 © Education Institute 2005 Objectives Possible teaching activities Notes School resources Ask students what results they would expect if differently shaped samples of a given material were all subject to the same stress (they would each experience the same strain). Ask what they would expect if samples of a second material were also subject to the same stress (the resulting strain would probably differ from that found for the first material). Establish that measuring stress and strain enable the properties of different materials to be compared reliably, even though the samples might have different dimensions. Point out that these examples with the foam blocks involve compressive stress and strain. Provide students with some examples that allow them to practise calculations relating stress to force and area, and relating stress to deformation and original length.

Testing materials Ask students to work in pairs, each using a sample of a different material, to investigate how Suitable materials include: metal wires strain depends on the applied tensile stress. Provide basic apparatus then encourage students (e.g. copper, steel), nylon, polythene. to design and modify their experiments so as to ensure accuracy and precision and to obtain Safety: Goggles should be worn to protect results as efficiently as possible. against injury when samples fail under high Students should obtain and tabulate data for a range of applied loads. They should explore what tension. happens when a load is removed (does the sample return to its original length?) and should, Enquiry skills 12A.1.1, 12A.1.3–12A.1.5, where possible, increase the load until the sample breaks. They should plot a graph to show the 12A.3.1–12A.3.3, 12A.4.1, 12A.4.2 relationship between stress and strain. Photocopy the graphs and distribute to the whole class. This activity also relates to Standard 10A.25.2.

Young’s modulus and breaking stress Discuss the graphs obtained in the previous activity with the whole class and draw attention to This also relates to Standard 10A.25.1 key features. Close to the origin, most graphs will approximate to straight lines, and for some materials this behaviour continues until the sample nears breaking point. Establish that if stress is directly proportional to strain, the material obeys Hooke’s law, which students should recall as a direct proportion between force and extension. Introduce Young’s modulus E =  ⁄ , where  is stress and  is strain and establish that it is the gradient of the part of a stress–strain graph where Hooke’s law is obeyed. Discuss the SI units of Young’s modulus and establish that they are the same as the units of stress: N m–2 or Pa. Ask students how they would describe the difference between materials with a small and a large Young’s modulus. A material with large E requires a large stress to produce even a small strain; it is very stiff. The term stiffness is sometimes used loosely in place of Young’s modulus (though it can also be used to mean k in the expression F = kx). If available, show students apparatus specially made to measure Young’s modulus for a metal wire. Point out the features designed to increase accuracy and precision (e.g. Vernier scale). If time allows, let students use this apparatus themselves. Return to the discussion of the graphs. Point out that some samples were tested to destruction, and define the tensile strength or ultimate tensile stress as the maximum stress that a material can withstand before breaking. Provide plenty of algebraic and numerical examples that allow students to practise calculations involving stress, strain and Young’s modulus.

6 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.2 | Physics 2 © Education Institute 2005 Objectives Possible teaching activities Notes School resources

Shear Use foam blocks to demonstrate how a material can be sheared, and define shear stress and Mathematics: A knowledge of angles measured strain. Using a labelled diagram, show that deformation is measured at right-angles to the in radians is required. length of a sample and so (for small deformations) shear strain corresponds to an angle Enquiry skills 12A.1.1–12A.1.5, 12A.3.1– measured in radians. 12A.3.4, 12A.4.1. Ask students to work in pairs or small groups to design and carry out a test to see how a This activity also relates to Standard 10A.25.2. material behaves under shear stress. Tell them to produce a written report of their work explaining how they attempted to ensure accuracy and precision in their measurements. Composites Assign each student, or pair of students, a natural or synthetic composite material (e.g. wood, ICT opportunity: Use of the Internet. concrete, fibreglass resin). Tell them to use the Internet and library resources to research Enquiry skills 12A.1.8, 12A.3.4 information about the material, addressing such questions as: • What is its composition? • What does it look like on a small scale? • How do its properties differ from those of its individual components? • What is it used for? Ask students to produce an informative poster summarising their findings. Hold a conference-style poster session. Display the posters around the room and allow students time to visit one another’s posters and discuss their work.

3 hours Surface tension Fluids Set up a circus of activities illustrating the effects of surface tension. For each, provide brief Suitable examples include: instructions telling students what to do and what to look for. They should visit each in turn and Explain surface tension in • observe the meniscus on water and on mercury; make notes. terms of interparticle forces. • observe water rising up a capillary tube; Introduce and define the term surface tension. Ask students to suggest explanations for their Explain qualitatively how fluid • sprinkle fine power on the surface of water observations in terms of the kinetic particle model. Introduce the terms adhesion and cohesion flow past solid bodies can then add a drop of detergent; to describe the observations. generate pressure changes • blow bubbles using different soap and in the fluid; give practical detergent solutions. examples of this. Fluid flow Carry out a series of demonstrations to show that the flow of a fluid (liquid or gas) gives rise to the Bernoulli effect (i.e. there is a drop in pressure transverse to the flow). Suitable examples include the following. • Each student holds a sheet of A4 paper by one short edge so that it forms a curved surface, then blows gently over it. • Each student holds two sheets of A4 paper by their short edges so that they hang vertically a few centimetres apart, then blows gently between them. • Place a table-tennis ball in a fast-moving air stream from a blower. Tilt the blower and show that the ball remains supported even when the air-stream is almost horizontal.

7 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.2 | Physics 2 © Education Institute 2005 Objectives Possible teaching activities Notes School resources Use specially designed apparatus to demonstrate the Bernoulli effect. Water flows through a Note that the Bernoulli effect is not primarily horizontal tube with a narrow section. Vertical tubes indicate the transverse pressure, which is responsible for the lift of an aircraft wing. Rather, lowest where the water flows fastest. Relate the difference in pressure (and hence in force) to a downward deflection of air from the lower the change in the water’s velocity as it enters and leaves the narrow section. surface produces an upward force. Ask students to suggest other examples of the Bernoulli effect in operation. Explain how the shape of an aerofoil can help generate lift. If time and apparatus permit, ask students to work in teams to plan and carry out wind-tunnel Enquiry skills 12A.1.1–12A.1.5, 12A.3.1– tests of different aerofoil sections to investigate the lift produced. Ask them to try to predict and 12A.3.4, 12A.4.1, 12A.4.2 explain their results, and to produce a written report of the procedure adopted, apparatus used and results obtained.

6 hours Boyle’s law Ideal and real gases Using specially designed demonstration apparatus, obtain data to show how the volume, V, of a If there is enough apparatus, students should Derive, know and use the gas fixed mass of gas depends on its pressure, p. Ask students to plot graphs of p against V, and p work in pairs to obtain their own data.

laws and the general gas against 1 ⁄ V. Establish that, for a fixed mass of gas at constant temperature, pV is a constant equation PV = nRT and show (i.e. Boyle’s law is obeyed). how the general gas equation In practice, the data may deviate from Boyle’s law. Ask students to use the kinetic particle model leads to a concept of to suggest explanations. In order to increase the pressure, a force is applied to the gas (i.e. absolute zero of temperature. work is done) and energy is supplied, so the gas temperature rises and the gas tends to expand. If the gas is allowed to return to room temperature after each change in pressure, then Show that a theoretical deviations from Boyle’s law are reduced. treatment of molecular movement and gas pressure Provide students with some examples that allow them to practise using Boyle’s law in leads to the relationship calculations. pV 1 mNc 2  3 and hence, by Absolute temperature combining with the gas Set up and demonstrate apparatus to how the volume of a fixed mass of gas changes with If there is enough apparatus, students should equation, that the average temperature measured in °C. Similarly, use a constant volume gas thermometer to demonstrate work in pairs to obtain their own data. kinetic energy of a particle is how pressure depends on temperature. This activity also relates to Standard 10A.25.1. proportional to its absolute Ask students to plot graphs of volume against temperature, and pressure against temperature, temperature. and establish that the volume and pressure each vary linearly with temperature. Apply the kinetic particle Discuss and show how the graphs can be extrapolated to find the temperature at which p and model to an ideal gas and V become zero. Tell students that this temperature is called absolute zero and is found to be explain, in terms of molecular close to –273 °C. Point out that, in practice, the volume of a gas cannot become zero (its size and intermolecular molecules have finite size), and that real gases condense to liquids before reaching absolute forces, how the behaviour of zero, so the extrapolation strictly applies only ‘ideal’ gases. (However, absolute zero is still a real gases deviates from the meaningful concept and, as will be seen later in this unit, can be understood in terms of ideal model at high pressures molecular kinetic energy.) and low temperatures. Explain how the existence of absolute zero enables a scale of absolute temperature to be defined. Establish that the SI unit of absolute temperature, T, is the kelvin, K, and that a temperature change of 1 K is exactly equal to a change of 1 °C. Use several quick-fire oral questions to give students practice in converting between temperatures expressed in K and in °C.

Gas laws Refer to the previous activity and ask students to sketch graphs showing how pressure and This activity also relates to Standards 10A.25.1 volume of a fixed mass of gas depend on absolute temperature, T. and 10A.25.3. Introduce Charles’s law: V  T for a fixed mass of gas at constant pressure. Similarly, state the pressure law: p  T for a fixed mass of gas whose volume is constant. On the board or OHP, show how these two laws can be combined with Boyle’s law to produce pV  T. Discuss the point that pV must also be proportional to the amount of gas present: doubling the amount will double the volume at a given pressure. But ‘amount’ is a loose term, so explain that, more precisely, the relationship is expressed in terms of the number, n, of moles present. This leads to the ideal gas equation pV = nRT, which defines the value of the universal gas constant, R. Show students that the SI units of pV are 1 N m–2 × 1 m3 = 1 N m = 1 J. Ask students to deduce the SI units of R. Point out that the behaviour of real gases can deviate markedly from that described by the ideal gas equation, particularly when they are close to condensing, but that in solving problems it is often useful to assume ideal behaviour. Provide several examples of algebraic and numerical calculations that allow students to practise using the ideal gas equation. Molecular behaviour On the board or OHP, show students how the pressure of a gas can be related to the motion of 1 2 its molecules and hence derive the equation pV  3 mnc . To make this derivation more engaging and interactive, pause frequently and ask students questions to check that they have understood each step, and questions that anticipate the next step. Start by considering a single molecule mass m travelling at speed c parallel to one edge of a rectangular box of dimensions x × y × z = V and repeatedly making elastic collisions with one face. Derive expressions for the momentum change at each collision (2mc) and for the time interval between collisions (2x ⁄ c), and hence expressions for the force exerted on one face (mc2 ⁄ x) and for the pressure exerted on that face (mc2 ⁄ xyz = mc2 ⁄ V). Work through an argument to derive the pressure, p, exerted by N molecules, of which one- third will, on average, be travelling at speed c in each of three perpendicular directions (p = mc2 ⁄ 3V). Explain that, in practice, there will be a range of speeds, so we must use the average value of c2 (i.e. the ‘mean square speed’), represented as c 2 . Show how to combine the final expression with the ideal gas equation to get Nm c 2 ⁄ 3 = nRT.

Show that, as N ⁄ n is equal to the Avogadro number NA (the number of molecules per mole), we To avoid confusion between the number of 2 can write m c ⁄ 3 = RT ⁄ NA = kT, where k (= R ⁄ NA) is the Boltzmann constant. Hence show how moles (e.g. in the ideal gas equation) and the

to relate the average molecular kinetic energy Ek to absolute temperature: number of molecules, use N rather than n to 1 2 represent the number of molecules. Ek  2 mc  3kT 2 Establish that this expression allows another interpretation of absolute zero: it is the temperature at which molecular motion ceases. Ask students to derive the SI units of k (i.e. J K–1). Work through some examples of calculations relating molecular kinetic energy to temperature, pressure and density, and give students some numerical and algebraic examples that allow them to practise using the relationships. Real gases Point out to students that all the relationships listed above apply to ideal gases. Establish that in This activity relates to Standard 10A.25.3. such a gas the molecules: • make frequent elastic collisions with each other and the walls of their container; • exert no forces on one another except while in contact; • are in contact for a very short time compared with the time between collisions; • have a very small volume compared with the volume available for them to move in. Ask students, in small groups, to list differences between real and ideal gas molecules, and suggest how these might affect the equations describing their behaviour. Hold a reporting back session to collect ideas together. The main points are that molecules do exert long-range forces on one another (the van der Waals force) and they occupy a finite volume. These factors become particularly important when the pressure of a gas is high and/or the temperature is low (i.e. it is close to condensing). In practice, a real gas behaves most like an ideal gas when the pressure is low and the temperature high. Students should appreciate that, in solving problems, it is usually convenient to assume ideal gas behaviour. With more advanced students, it might be appropriate to introduce and discuss the van der Waals gas equation.

Understanding particles Ask students, in small groups, to use the Internet and library resources to research historical In addition to, or in place of, the examples developments of theories about particles. Allocate each group a different task and tell them to suggested here, include at least one example prepare a ten-minute PowerPoint presentation (including an aknowledgment of sources relating to Islamic science and scientists. consulted). Suitable tasks include the following. Enquiry skills 12A.1.6, 12A.1.8, 12A.2.1, • The idea that matter is made up of tiny indivisible particles originated with the ancient Greeks. 12A.2.2, 12A.2.4, 12A.2.5, 12A.2.6 Who were the main people famous for recording this idea? How did the ancient Greek ideas compare with our modern view of atoms? • Modern ideas about atoms can be traced back to the European scientist John Dalton. When did he live? What were his ideas about atoms? • Even as recently as 1900, many scientists did not believe atoms existed. Albert Einstein carried out some important work that convinced most people that atoms were real. What did he do? • Scientists today believe that all matter is made up of particles, and that some particles are ‘fundamental’ (cannot be divided further). Which particles are currently believed to be fundamental? When were they discovered? Hold a conference in which each group presents its work to the rest of the class. The presentations should be made in chronological order. Allow time for questions after each presentation. Bring out the point that our understanding of the nature of matter has developed unevenly through history, with the postulation of major theories being followed by long periods of slow development. Some theories are abandoned permanently, whereas others (such as Greek atomic ideas) are discarded then ‘reinvented’. As a follow-up to the conference, discuss with students the apparent contradiction between the random behaviour of the particles believed to make up the Universe, and the deterministic nature of major world religions. First establish some rules of behaviour: students should respect one another’s views, even though they may disagree strongly; in later conversations outside the classroom, views expressed during the discussion must not be attributed to individuals. Then encourage students to express their views and to ask questions of you and one another. Do not attempt to resolve the paradox at this stage; as students will learn in later units, random behaviour can still be described by definite laws.

Assessment Unit 12AP.2

Examples of assessment tasks and questions Notes School resources

11 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.2 | Physics 2 © Education Institute 2005 Assessment A student estimates that the total cross-sectional area of his leg bones is 20 cm2. His mass is

Set up activities that allow 70 kg. What is the stress in his leg bones when he stands on both feet? students to demonstrate what A metal wire of diameter 0.5 mm and length 4.0 m extends by 3.0 mm when the applied tension they have learned in this unit. is 75 N. What is the Young’s modulus of this metal? The activities can be provided informally or Using the terms adhesion and cohesion, and with the help of labelled diagrams, explain why formally during and at the water rises up a narrow tube whereas mercury does not. end of the unit, or for A bubble of gas, diameter 2 mm, is trapped in a container of liquid at normal atmospheric homework. They can be pressure (1 × 105 Pa) and a temperature of 25 °C. The container is opened on board an aircraft selected from the teaching where the temperature is 22 °C and the surrounding pressure is 0.9 × 105 Pa. What is the activities or can be new diameter of the bubble as it escapes from the liquid? experiences. Choose tasks and questions from the What is the average kinetic energy of molecules in the air at room temperature 25 °C? At this examples to incorporate in temperature, what is the average speed of an oxygen molecule? Use k = 1.38 × 10 J K–1. Mass –27 the activities. of oxygen molecule (O2) m = 32 × 1.67 × 10 kg.