Chapter 2: Kinetic Particle Model of Matter PDF

2.1 Kinetic particle model of matter 2.1.1 States of matter FOCUS POINTS ★ Know the properties of solids, liquids and gases. ★ Understand that changes in state can occur and know the terms to describe these changes. In this...

2.1 Kinetic particle model of matter 2.1.1 States of matter FOCUS POINTS ★ Know the properties of solids, liquids and gases. ★ Understand that changes in state can occur and know the terms to describe these changes. In this topic you will learn about the three states of matter: solids, liquids and gases. The particles in each are ordered differently and this leads to each state having different properties. You will find that solids have a high level of internal order, a liquid has less, and in a gas the particles have no order and move about randomly. The state of a material can be altered by heating or cooling. In a solid the bonds between particles break down on heating and it melts into a liquid; for example, ice melts into water. Boiling a liquid produces a gas with well separated particles; water turns into steam. The three states of matter can be represented in a particle diagram. Matter is made up of tiny particles (atoms, molecules, ions and electrons) which are too Properties of solids, liquids small for us to see directly. But they can be ‘seen’ and gases by scientific ‘eyes’. One of these is the electron Matter can exist in different states and each state microscope. Figure 2.1.1 is a photograph taken with has different characteristics. such an instrument, showing molecules of a protein. Solids Molecules consist of even smaller particles called atoms and these are in continuous motion. Solids have a definite shape and volume and are not easily compressed. The particles in a solid are close together and in fixed positions. When a force is applied to a solid the atoms move slightly further apart in the direction of the force and stretching occurs (see Topic 1.5.1). When a solid is heated (see Topic 2.2), the distance between atoms increases. If enough heat is supplied to the solid the atoms move even further apart and melting into a liquid occurs. Liquids Liquids have a definite volume but their shape depends on the container they are kept in. They are more easily compressed or stretched than solids and also expand more when heat is applied. The particles in a liquid are further apart than they are in a solid and have a less ordered structure. They are not fixed in position and can slide over each other when the liquid is poured. The liquid then takes on the shape of the new container. ▲ Figure 2.1.1 Protein molecules 86 9781398310544.indb 86 19/02/21 8:14 PM  2.1.2 Particle model When a liquid is cooled sufficiently, solidification are heated. When a gas is cooled sufficiently it will occurs and it returns to the solid state. The density of return to the liquid state in a process known as a material in its solid state is usually higher than it is condensation. in its liquid state. When a liquid is heated, particles Drops of water are formed when steam condenses can escape from its surface by a process called on a cold window pane, for example. evaporation. When sufficient heat is supplied to the liquid boiling occurs and the liquid turns into a gas. Test yourself Gases 1 Using what you know about the compressibility Gases have no definite shape or volume as these (squeezability) of the different states of matter, explain why depend on the dimensions of the container. The a air is used to inflate tyres particles in a gas are much further apart than they b steel is used to make railway lines. are in a liquid and the density of a gas is much lower 2 Name the processes in which than that of a liquid. The particles have no ordered a a solid turns into a liquid structure and are able to move about freely in a b a liquid turns into a gas random manner. Gases are more easily compressed c a liquid turns into a solid d a gas turns into a liquid. than solids or liquids and expand more when they 2.1.2 Particle model FOCUS POINTS ★ Describe the particle structures of solids, liquids and gases and represent these states using particle diagrams. ★ Understand how temperature affects the movement of particles. ★ Understand the factors that affect the properties of solids, liquids and gases. ★ Understand the relationship between the kinetic energy of particles and temperature, including the concept of absolute zero. ★ Know how a change in pressure in a gas affects the motion and number of collisions of its particles. ★ Describe how a change in pressure of a gas affects the forces exerted by particles colliding with surfaces (force per unit area). ★ Describe Brownian motion and know that it is evidence for the kinetic particle model of matter. ★ Distinguish atoms or molecules from microscopic particles, and understand how these microscopic particles may be moved by collisions with much lighter molecules. The properties of solids, liquids and gases can be related to the arrangement, separation and motion of the particles in each. In the previous section, you learnt about the properties of solids, liquids and gases. In this topic, you will learn that in a gas, the particles are well separated and in constant random motion, producing pressure on a container by their collisions with its surfaces. In a solid, the particles are closely arranged and firmly bound together, with a regular pattern in crystals. In a liquid the particles are further apart, with only local ordering between particles that have more freedom of movement than those in a solid. Although particles are too small to be seen with the unaided eye, their influence can be detected. When tiny particles in a fluid are observed under a microscope, they can be seen to move slightly in a random manner under the impact of collisions with many much lighter molecules. This effect is known as Brownian motion and provides evidence for the kinetic particle model of matter. 87 9781398310544.indb 87 19/02/21 8:14 PM  2.1 KINETIC PARTICLE MODEL OF MATTER Particle model of matter Liquids As well as being in continuous motion, particles Structure (atoms, molecules, ions and electrons) also exert In liquids the particles are slightly further apart than strong electric forces on one another when they are in solids but still close enough together to have a close together. The forces are both attractive and definite volume (Figure 2.1.2b). As well as vibrating, repulsive. The former hold particles together and they can at the same time move rapidly over short the latter cause matter to resist compression. distances, slipping past each other in all directions. The particle model can explain the existence of A model to represent the liquid state can be made the solid, liquid and gaseous states. by covering about a third of a tilted tray with marbles (‘particles’) (Figure 2.1.4). It is then shaken back and Solids forth and the motion of the marbles observed. The Structure marbles are able to move around but most stay in the In solids the particles are close together and the lower half of the tray, so the liquid has a fairly definite attractive and repulsive forces between neighbouring volume. A few energetic marbles escape from the molecules balance. Also, each particle vibrates about ‘liquid’ into the space above. They represent particles a fixed position. Particles in a solid can be arranged that have evaporated from the liquid surface and in a regular, repeating pattern like those formed by become gas or vapour particles. The thinning out of crystalline substances. Figure 2.1.2a represents the the marbles near the liquid surface can also be seen. arrangement of particles in a solid. a b c solid liquid gas ▲ Figure 2.1.2 Arrangements of particles in a solid, liquid tilted and gas tray Properties marbles We can imagine springs (Figure 2.1.3) representing ▲ Figure 2.1.4 A model of particle behaviour in a liquid the electric forces between particles that hold them together and determine the forces and distances between them. These forces enable the Properties solid to keep a definite shape and volume, while In a liquid the forces between particles are less still allowing the individual particles to vibrate than in a solid and so the distance between backwards and forwards. Owing to the strong particles is greater. Liquids have a definite intermolecular forces, solids resist compression volume but individual particles can slide over and expand very little when heated. each other and are never near another particle long enough to get trapped in a regular pattern. This allows liquids to flow and take on the shape of the vessel containing them. The forces between particles are strong enough that liquids are only slightly more easily compressed than solids. When heated, the particles move further apart, enabling liquids to expand more easily than solids. As the temperature increases some particles may have ▲ Figure 2.1.3 The electric forces between particles in a sufficient energy to escape from the surface of solid can be represented by springs. the liquid resulting in evaporation of the liquid. 88 9781398310544.indb 88 19/02/21 8:14 PM  2.1.2 Particle model Gases Temperature and kinetic energy Structure In a solid at room temperature, the particles vibrate The particles in gases are much further apart than in about fixed positions. When heat is supplied to the solids or liquids (about ten times; see Figure 2.1.2c) solid and its temperature increases, the particles and so gases are much less dense and can be vibrate more strongly and the average kinetic energy squeezed (compressed) into a smaller space. of the particles increases. When the temperature is The particles dash around at very high speed (about reduced, the average kinetic energy of the particles 500 m/s for air molecules at 0°C) in all the space reduces, and eventually a temperature is reached available. It is only during the brief spells when they where particle motion ceases and the kinetic energy collide with other particles or with the surfaces of of the particles is zero. We call this temperature the container that the particle forces act. absolute zero and it occurs at −273°C. A model of a gas is shown in Figure 2.1.5. The faster the vibrator works, the more often Pressure and kinetic energy the ball-bearings have collisions with the lid, the The particle model can explain the behaviour tube and with each other, representing a gas at a of gases. higher temperature. Adding more ball-bearings is like pumping more air into a tyre; it increases the Gas pressure pressure. If a polystyrene ball (1 cm diameter) is All the particles in a gas are in rapid random dropped into the tube, its irregular motion represents motion, with a wide range of speeds, and repeatedly Brownian motion. Brownian motion provides evidence hit and rebound from the surfaces of the container for the kinetic particle model of matter. in huge numbers per second. This causes a pressure on the surfaces of the container. When the temperature of the gas rises, lid so does the average speed and kinetic energy of the particles. Collisions with the surfaces of the container occur more frequently and so the pressure Perspex tube of the gas increases. Force and gas pressure ball-bearings At each collision of a gas particle with a surface of the container, it undergoes a change of momentum which produces a force on the surface rubber sheet (see Topic 1.6). At a constant temperature the average force and hence the pressure exerted on vibrator driven the surface is constant, since pressure is force by motor per unit area. When the temperature rises and the ▲ Figure 2.1.5 A model of particle behaviour in a gas rate at which collisions with the surfaces of the container increases, so does the average force and Properties hence the gas pressure. Owing to the high speed and the large distance between particles in a gas the interaction between them is small. Gases have no shape and their volume is determined by the volume of the container. They are easily compressed, and expand much more than solids or liquids when heated. 89 9781398310544.indb 89 19/02/21 8:14 PM  2.1 KINETIC PARTICLE MODEL OF MATTER Practical work Brownian motion The apparatus is shown in Figure 2.1.6a. For safe experiments/demonstrations related First fill the glass cell with smoke using a match to this topic, please refer to the Cambridge (Figure 2.1.6b). Replace the lid on the apparatus IGCSE Physics Practical Skills Workbook that and set it on the microscope platform. Connect is also part of this series. the lamp to a 12 V supply; the glass rod acts as a lens and focuses light on the smoke. a microscope window lid lamp b glass plate smoke c smoke burning match glass cell glass rod glass cell ▲ Figure 2.1.6 Carefully adjust the microscope until you see 1 What are the specks of light in the glass cell of bright specks dancing around haphazardly the Brownian motion experiment? (Figure 2.1.6c). The specks are smoke particles 2 In a glass cell set up to show Brownian motion, seen by reflected light; their random motion is describe how the specks of light move. called Brownian motion and is evidence for the kinetic particle model of matter. This motion 3 What do you think might cause microscopic is due to collisions between the microscopic particles to move in the way they do in a particles in a suspension and the particles of the Brownian motion experiment? gas or liquid. Explanation of Brownian motion Test yourself The random motion of the microscopic smoke 3 Explain the structure of particles in the cell in Figure 2.1.6 is due to a solids random molecular collisions of fast-moving air b liquids molecules in the cell. A smoke particle is massive c gases. in terms of the particle model. compared with an air molecule, but if there are 4 Explain what is meant by the term absolute zero. more high-speed molecules striking one side of it than the other at a given instant, the particle 5 Explain how smoke particles can be moved will move in the direction in which there is a net by air molecules in a Brownian motion force. The imbalance, and hence the direction experiment. of the net force, changes rapidly in a random manner. 90 9781398310544.indb 90 19/02/21 8:14 PM  2.1.3 Gases and the absolute scale of temperature 2.1.3 Gases and the absolute scale of temperature FOCUS POINTS ★ Describe, in terms of particles, the effect of change of temperature or volume on the pressure of a fixed mass of gas. ★ Use the correct equation to calculate pressure and volume of a fixed mass of gas, and be able to represent this relationship graphically. ★ Convert temperatures between the Celsius and Kelvin temperature scales using the correct equation. Gases show the simplest behaviour of the three states of matter and respond to changes of temperature or volume by a change of pressure. By keeping either volume or temperature constant in an experiment, their relationships with pressure can be determined and explained in terms of the kinetic particle model of matter. The properties of gases can be exploited for use in thermometers to measure temperature. You will be familiar with the Celsius scale of temperature for everyday measurements; the freezing temperature of water is set at 0°C and the boiling temperature of water at 100°C. In both the Kelvin and Celsius temperature scales, there are 100 degrees between the freezing temperature and boiling temperature of water, but the Kelvin scale starts from −273°C where the motion of particles ceases. Pressure of a gas to vacuum The air forming the Earth’s atmosphere stretches pump upwards a long way. Air has weight; the air in a normal room weighs about the same as you do, can about 500 N. Because of its weight the atmosphere exerts a large pressure at sea level, about 100 000 N/m2 = 105 Pa (or 100 kPa). This pressure acts equally in all directions. A gas in a container exerts a pressure on the surfaces of the container. If air is removed from a can by a vacuum pump (Figure 2.1.7), the can collapses because the air pressure outside is greater ▲ Figure 2.1.7 Atmospheric pressure collapses the than that inside. A space from which all the air evacuated can. has been removed is a vacuum. Alternatively, the pressure in a container can be increased, for When a gas is heated, as air is in a jet engine, its example by pumping more gas into the can; a pressure as well as its volume may change. To study Bourdon gauge (Topic 1.8) is used for measuring gas the effect of temperature on these two quantities pressures. we must keep one fixed while the other is changed. When investigating relationships between properties only one variable should be changed at a time. 91 9781398310544.indb 91 19/02/21 8:14 PM  2.1 KINETIC PARTICLE MODEL OF MATTER Effect on pressure of a change in temperature the number of particles per cm3 will be doubled. (constant volume) There will be twice as many collisions per second When a gas is heated and its temperature rises, the with the surfaces, i.e. the pressure is doubled. average speed of its particles increases. If the volume piston of a fixed mass of gas stays constant, its pressure increases because there are more frequent and more violent collisions of the particles with the surfaces. V Effect on pressure of a change in volume cylinder V (constant temperature) 2 If the volume of a fixed mass of gas is halved by halving the volume of the container (Figure 2.1.8), ▲ Figure 2.1.8 Halving the volume doubles the pressure. Practical work rubber tubing Bourdon Effect on pressure of temperature (volume pressure constant) gauge Safety l The Bourdon gauge should be firmly clamped to prevent toppling. l Eye protection must be worn. l Take care with hot apparatus. thermometer The apparatus is shown in Figure 2.1.9. The rubber tubing from the flask to the pressure gauge should be as short as possible. The flask must be in can water almost to the top of its neck and be securely clamped to keep it off the bottom of the can. Heat water can be supplied to the water by standing the can on a hot plate or on a tripod over a Bunsen burner. flask (250 cm3) Record the pressure over a wide range of temperatures, but before taking a reading from the thermometer, stop heating, stir and allow time for the gauge reading to become steady; the air in the flask will then be at the temperature of the water. heat Take about six readings and tabulate the results. ▲ Figure 2.1.9 Plot a graph of pressure on the y-axis and temperature on the x-axis. Effect on volume of pressure (temperature 4 a Name the independent variable in the constant) experiment. Changes in the volume of a gas due to pressure b Name the dependent variable. changes can be studied using the apparatus in 5 Why must the volume be kept constant in the Figure 2.1.10. The volume V of air trapped in the experiment? glass tube is read off on the scale behind. The 6 What precautions should you take to obtain pressure is altered by pumping air from a foot accurate results in the experiment? pump into the space above the oil reservoir. This forces more oil into the glass tube and increases the pressure p on the air in it; p is measured 92 9781398310544.indb 92 19/02/21 8:14 PM  2.1.3 Gases and the absolute scale of temperature by the Bourdon gauge. Take about six different 8 A graph of pressure against 1/volume for measurements. Plot a graph of pressure versus the results of the experiment is shown in volume as shown in Figure 2.1.11a. Figure 2.1.11b. Name the features of the graph which suggest that pressure is proportional to 0 0 glass tube 1/volume. 10 10 air a b 20 20 Bourdon gauge p p 30 30 40 40 p 50 50 to foot doubled oil pump V reservoir halved ▲ Figure 2.1.10 0 V 0 1 V 7 a Name the independent variable in the ▲ Figure 2.1.11 experiment. b Name the dependent variable. Variations in gas pressure Worked example with volume The variation of the pressure of a fixed mass of gas A certain quantity of gas has a volume of 40 cm3 at a pressure of 1 × 105 Pa. Find its volume when the pressure with changes in volume (at constant temperature) is 2 × 105 Pa. Assume the temperature remains constant. is shown in Figure 2.1.11a. Close examination of the curve shows that if p is doubled, V is halved. Using the equation pV = constant we have That is, p is inversely proportional to V. In symbols p1V1 = p2V2 p ∝ 1 or p = constant × 1 Rearranging the equation gives V V V2 = p1 × V1/p2 ∴ pV = constant = 1 × 105 Pa × 40 cm3/2 ×105 Pa If several pairs of readings, p1 and V1, p2 and = 20 cm3 V2, etc. are taken, then it can be confirmed that p1V1 = p2V2 = constant Now put this into practice 1 A fixed mass of gas has a volume of 9 cm3 at a pressure This is Boyle’s law, which is stated as follows: of 1 × 105 Pa. Find its volume when the pressure is The pressure of a fixed mass of gas is inversely 3 × 105 Pa. proportional to its volume if its temperature is kept 2 A certain quantity of gas has a volume of 40 cm3 at a pressure of 2 × 105 Pa. Find its pressure when the constant. volume is 20 cm3. Since p is inversely proportional to V, then p is directly proportional to 1/V. A graph of p against 1/V is therefore a straight line through the origin (Figure 2.1.11b). 93 9781398310544.indb 93 19/02/21 8:14 PM  2.1 KINETIC PARTICLE MODEL OF MATTER Celsius and Kelvin temperature vessel, over the edge and down the outside. Some metals and compounds become superconductors scales of electricity and a current, once started in them, The volume–temperature and pressure–temperature flows forever, without a battery. Figure 2.1.13 shows graphs for a gas are straight lines (Figure 2.1.12). research equipment that is being used to create They show that gases expand linearly with materials that are superconductors at very much temperature as measured on a mercury thermometer, higher temperatures, such as −23°C. i.e. equal temperature increases cause equal volume or pressure increases. volume or pressure !273°C 0°C temperature 0K 273 K ▲ Figure 2.1.12 The graphs do not pass through the Celsius temperature origin (0°C). If graph lines are extrapolated backwards, they cut the temperature axis at about −273°C. This temperature is called absolute zero because we believe it is the lowest temperature possible. It is the zero of the absolute or Kelvin scale of temperature. At absolute zero molecular motion ceases and a substance has no internal energy. ▲ Figure 2.1.13 This equipment is being used to make films Degrees on this scale are called kelvins and are of complex composite materials that are superconducting denoted by K. They are exactly the same size as at temperatures far above absolute zero. Celsius degrees. Since −273°C = 0 K, conversions from °C to K are made by adding 273. For example Worked example 0°C = 273 K a Convert 27°C to K. 15°C = 273 + 15 = 288 K Substitute in the equation T = 273 + θ to give 100°C = 273 + 100 = 373 K T = 273 + 27 = 300 K Kelvin or absolute temperatures are represented by b Convert 60 K to °C. the letter T, and if θ (Greek letter ‘theta’) stands for a Rearrange the equation T = 273 + θ to give degrees Celsius scale temperature then, in general, θ = T − 273 = 60 − 273 = −213°C T = 273 + θ Now put this into practice Near absolute zero strange things occur. Liquid 1 Convert 80°C to K. helium becomes a superfluid. It cannot be kept in 2 Convert 100 K to °C. an open vessel because it flows up the inside of the 94 9781398310544.indb 94 19/02/21 8:14 PM  2.1.3 Gases and the absolute scale of temperature Going further Practical work Effect on volume of temperature The pressure of (and on) the air column is (pressure constant): Charles’ law constant and equals atmospheric pressure plus the pressure of the acid index. Safety ruler l Eye protection must be worn. (30 cm) thermometer l Take care as concentrated sulfuric acid is highly corrosive. Do not touch it if any capillary can tube leaks out of the tube. concentrated Arrange the apparatus as in Figure 2.1.14. air sulfuric acid The index of concentrated sulfuric acid column index traps the air column to be investigated and rubber also dries it. Adjust the capillary tube so band water that the bottom of the air column is opposite a convenient mark on the ruler. heat Note the length of the air column (between the ▲ Figure 2.1.14 lower end of the index and the sealed end of the capillary tube) at different temperatures 9 a Name the independent variable in the but, before taking a reading, stop heating and experiment. stir well to make sure that the air has reached b Name the dependent variable. the temperature of the water. Put the results in 10 The results of the experiment are plotted a table. in a graph of volume versus temperature and appear similar to those shown in Plot a graph of volume (in cm, since the length Figure 2.1.12. What do the results indicate of the air column is a measure of it) on the about the relationship between volume and y-axis and temperature (in ºC) on the x-axis. temperature? The gas laws Charles’ law may be stated as follows: Using absolute temperatures, the gas laws can be The volume of a fixed mass of gas is directly stated in a convenient form for calculations. proportional to its absolute temperature if the pressure is kept constant. Charles’ law In Figure 2.1.12 the volume–temperature graph passes Pressure law through the origin if temperatures are measured on the From Figure 2.1.12 we can say similarly for the pressure Kelvin scale, that is, if we take 0 K as the origin. We can p that then say that the volume V is directly proportional to the absolute temperature T, i.e. doubling T doubles V, etc. p ∝ T or p = constant × T Therefore or V ∝ T or V = constant × T p = constant (2) or T V = constant (1) T 95 9781398310544.indb 95 19/02/21 8:14 PM  2.1 KINETIC PARTICLE MODEL OF MATTER The pressure law may be stated as follows: Combining the laws The pressure of a fixed mass of gas is directly The three equations can be combined, giving proportional to its absolute temperature if the volume pV is kept constant. = constant T Variations in gas pressure with volume For cases in which p, V and T all change from, say, p1, V1 For a fixed mass of gas at constant temperature and T1 to p2 , V2 and T2 , then pV = constant (3) p1V1 p2V2 = (4) T1 T2 Worked example A bicycle pump contains 50 cm3 of air at 17°C and at Note that: (i) all temperatures must be in K; (ii) any units 1.0 atmosphere pressure (atm). Find the pressure when can be used for p and V provided the same units are used the air is compressed to 10 cm3 and its temperature rises on both sides of the equation; (iii) in some calculations the to 27°C. volume of the gas has to be found at standard temperature and pressure, or ‘s.t.p.’. This is temperature 0°C and We have pressure 1 atmosphere (1 atm = 105 Pa). p1 = 1.0 atm p2 = ? Now put this into practice V1 = 50 cm3 V2 = 10 cm3 1 A fixed mass of gas has a volume of 9 cm3 at a pressure of 1 × 105 Pa at 27°C. Find its pressure when the T1 = 273 + 17 = 290 K T2 = 273 + 27 = 300 K volume is compressed to 5 cm3 and its temperature rises to 37°C. From equation (4) we get 2 A certain quantity of gas has a volume of 40 cm3 V T 50 300 at a pressure of 2.0 × 105 Pa at 27°C. Find its p2 = p1 × 1 × 2 = 1 × × = 5.2 atm V2 T1 10 290 temperature when the volume is 30 cm3 and the pressure is 3.2 × 105 Pa. 96 9781398310544.indb 96 19/02/21 8:14 PM  2.1.3 Gases and the absolute scale of temperature Test yourself 6 In terms of particle motion describe the effect 8 a Why is −273ºC chosen as the starting on the pressure of a fixed mass of gas when the temperature for the Kelvin scale of temperature? temperature rises but the volume is kept constant. b How do the size of units on the Celsius and Kelvin 7 Describe the effect on the pressure of a fixed mass scales of temperature compare? of gas if the volume is reduced but the temperature of the gas is kept constant. Revision checklist After studying Topic 2.1 you should know and After studying Topic 2.1 you should be able to: understand: ✔ recall the terms describing changes in state of ✔ the different physical properties of solids, liquids solids, liquids and gases and gases ✔ explain temperature, absolute zero and change in ✔ particle diagrams for the different states of matter pressure in terms of molecular motion ✔ the different particle structure of solids, liquids ✔ describe and explain an experiment to show and gases Brownian motion ✔ describe the effect on the pressure of a fixed ✔ how the particle model explains the physical mass of gas caused by a change in temperature properties of solids, liquids and gases. (at constant volume) and a change of volume (at constant temperature) ✔ convert temperatures between the Celsius and Kelvin scales of temperature ✔ recall and use the equation pV = constant (for a fixed mass of gas at constant temperature). 97 9781398310544.indb 97 19/02/21 8:14 PM  2.1 KINETIC PARTICLE MODEL OF MATTER Exam-style questions 1 Solids, liquids and gases are composed of iii The pressure increases if the volume particles. Which one of the following statements of the container increases at constant is not true? temperature. A The particles in a solid vibrate about a fixed b i Explain the significance of a position. temperature of −273°C in terms of B The particles in a liquid are arranged in a particle motion. regular pattern. ii State the value of a temperature of C The particles in a gas exert negligibly small −273°C on the Kelvin temperature forces on each other, except during collisions. scale. D The densities of most liquids are about iii Calculate the value of a temperature 1000 times greater than those of gases of −200°C on the Kelvin scale of because liquid particles are much closer temperature. together than gas particles. [Total: 7] [Total: 1] 2 Sketch particle diagrams for 6 The piston in Figure 2.1.15 is pulled out of the a a solid cylinder from position X to position Y, without b a liquid changing the temperature of the air enclosed. c a gas. If the original pressure in the cylinder was [Total: 6] 1.0 × 105 Pa, calculate 3 a Name the state of matter in which the a the air pressure when the piston is at particles are furthest apart. position Y b Use the particle model of matter to b the air pressure when the piston is moved explain how a gas exerts pressure on the a further 10 cm to the left of position Y. surfaces of its container. [Total: 6] c State and explain how the pressure changes when the temperature of the piston 30 cm 10 cm gas increases. [Total: 7] 4 Smoke particles and air exist in a sealed glass box. The box is illuminated, and the motion of the smoke particles is observed through a microscope. a Describe the motion of the smoke particles. Y X cylinder b Explain the reason the smoke particles ▲ Figure 2.1.15 move in this way. 7 A certain quantity of gas has a volume of 30 cm3 at a pressure of 1 × 105 Pa. [Total: 5] Assuming the temperature remains constant, 5 a The following statements refer to the pressure calculate the volume of the gas when the exerted by a gas in a container. pressure is Write down whether each statement is true a 2 × 105 Pa or false. b 5 × 10 Pa. 5 i Pressure is due to the particles of the [Total: 6] gas bombarding the surfaces of the container. ii The pressure decreases if the gas is cooled at constant volume. 98 9781398310544.indb 98 19/02/21 8:14 PM  Alternative to Practical Alternative to Practical 8 The variation in pressure of a fixed mass of gas is a Plot a graph of pressure against volume. measured for different volumes. b Work out values for 1/volume and enter The results obtained are listed in the following them into the table. table: c Plot a graph of pressure against 1/volume. d Are the results in agreement with the Pressure/105 Pa Volume/cm3 1/volume/cm3 equation pV = constant? 24 1.0 [Total: 9] 12 2.0 8 3.0 6 4.0 4 6.0 99 9781398310544.indb 99 19/02/21 8:14 PM  2.2 Thermal properties and temperature 2.2.1 Thermal expansion of solids, liquids and gases FOCUS POINTS ★ Describe thermal expansion in solids, liquids and gases and know some everyday applications of thermal expansion. ★ Use the motion and arrangement of particles in solids, liquids and gases to explain the relative order of magnitudes of their expansion as temperature increases. As thermal energy is transferred to a material, the particles tend to move further apart. As you saw in Topic 2.1, the effect on heating a gas is large because the particles are free to move and expansion can easily occur. Expansion is much smaller in solids but thermal effects in a solid can still be important in conditions where there are wide temperature variations. Special features to absorb expansion need to be included in railway tracks and engineered structures such as bridges so that they do not distort on very hot days. In this topic you will encounter some everyday applications and consequences of expansion in solids and liquids. When solids, liquids and gases are heated, the magnitude of the expansion for a given temperature rise is less for a liquid than a gas and even less for a solid where the particles are close together and the force of attraction between them is high. Thermal expansion Relative expansion of solids, According to the kinetic particle model (Topic 2.1.2) the particles of solids and liquids are in constant liquids and gases vibration. When heated they vibrate faster, so force The linear (length) expansion of solids is small each other a little further apart and expansion and for the effect to be noticed, the solid must results. be long and/or the temperature change must be The particles in a gas are free to move about large. For a 1 m length of steel it is 0.012 mm for rapidly and fill the entire volume of the container. a 1°C rise in temperature. When a gas is heated and its temperature rises, the The particles in a liquid are further apart, less average speed of its particles increases and there ordered and are more mobile than in a solid so are more frequent collisions with the surfaces of the the interaction between the particles is less and container. If the pressure of the gas is to remain expansion is easier for liquids than for solids. constant, the volume of the container must increase Liquids typically expand about five times more so that the frequency of collisions does not increase; than solids for a given temperature rise. In gases, that means expansion of the gas must occur. the interactions between particles are few because they are far apart and move about very quickly; this means they are able to expand much 100 9781398310544.indb 100 19/02/21 8:14 PM  2.2.1 Thermal expansion of solids, liquids and gases Bimetallic strips have many uses. more easily than liquids. Typically, gases expand a about 20 times more than liquids for a given copper temperature rise. These figures indicate that iron gases expand much more readily than liquids, and liquids expand more readily than solids. b copper Uses of expansion iron Axles and gear wheels are major components of ▲ Figure 2.2.2 A bimetallic strip: a before heating; clocks on the small scale and wheeled vehicles from b after heating cars to trains on the large scale. In Figure 2.2.1 the axles have been shrunk by Fire alarm cooling in liquid nitrogen at −196°C until the gear Heat from the fire makes the bimetallic strip bend wheels can be slipped on to them. On regaining normal and complete the electrical circuit, so ringing the temperature, the axles expand to give a very tight fit. alarm bell (Figure 2.2.3a). A bimetallic strip is also used in this way to work the flashing direction indicator lamps in a car, being warmed by an electric heating coil wound round it. a electric bell contact bimetallic strip heat ▲ Figure 2.2.1 ‘Shrink-fitting’ of axles into gear wheels b control knob In the kitchen, a tight metal lid can be removed from a glass jar by immersing the lid in hot water so that it expands and loosens. The expansion of insulator a liquid or a gas can be used in thermometers to measure temperature (see p. 103). An expanding gas to heater drives the pistons in the engine of a motor car. contacts circuit Bimetallic strip bimetallic strip If equal lengths of two different metals, such as copper and iron, are riveted together so that they ▲ Figure 2.2.3 Uses of a bimetallic strip: a fire alarm; cannot move separately, they form a bimetallic strip b a thermostat in an iron (Figure 2.2.2a). When heated, copper expands more than iron and to allow this the strip bends with copper Thermostat on the outside (Figure 2.2.2b). If they had expanded A thermostat keeps the temperature of a room or an equally, the strip would have stayed straight. appliance constant. The one in Figure 2.2.3b uses a bimetallic strip in the electrical heating circuit of, for example, an iron. When the iron reaches the required temperature the strip bends down, breaks the circuit at the 101 9781398310544.indb 101 19/02/21 8:14 PM  2.2 THERMAL PROPERTIES AND TEMPERATURE contacts and switches off the heater. After cooling a little, the strip remakes contact and turns the Test yourself heater on again. A near-steady temperature results. 1 Explain why If the control knob is screwed down, the strip has a the metal lid on a glass jam jar can be to bend more to break the heating circuit and this unscrewed easily if the jar is inverted for a few seconds with the lid in very hot water requires a higher temperature. b furniture may creak at night after a warm day c concrete roads are laid in sections with pitch Precautions against expansion (a compressible filling) between them. In general, when matter is heated it expands and 2 A bimetallic strip is made from aluminium and copper. When heated it bends in the direction when cooled it contracts. If the changes are resisted shown in Figure 2.2.5. large forces are created, which are sometimes useful a Which metal expands more for the same rise in but at other times are a nuisance. temperature, aluminium or copper? Gaps used to be left between lengths of railway b Draw a diagram to show how the bimetallic strip lines to allow for expansion in summer. They caused would appear if it were cooled to below room a familiar ‘clickety-click’ sound as the train passed temperature. over them. These days rails are welded into lengths aluminium of about 1 km and are held by concrete ‘sleepers’ that can withstand the large forces created without at room buckling. Also, at the joints the ends are tapered temperature and overlap (Figure 2.2.4a). This gives a smoother after journey and allows some expansion near the ends of heating copper each length of rail. For similar reasons slight gaps are left between lengths of aluminium guttering. In central heating pipes ‘expansion joints’ are used to join lengths of pipe (Figure 2.2.4b); these allow the copper pipes to expand ▲ Figure 2.2.5 in length inside the joints when carrying very hot water. Going further Linear expansivity An engineer has to allow for the linear expansion of a bridge when designing it. The expansion can be calculated if all the following are known: l the length of the bridge, l the range of temperature it will experience, and l the linear expansivity of the material to be used. The linear expansivity of a substance is the increase in length of 1 m for a 1°C rise in temperature. ▲ Figure 2.2.4a Tapered overlap of rails The linear expansivity of a material is found by experiment. For steel it is 0.000 012 per °C. This means nut nut that 1 m will become 1.000 012 m for a temperature rise of 1°C. A steel bridge 100 m long will expand by 0.000 012 × 100 m for each 1°C rise in temperature. rubber seal If the maximum temperature change expected is 60°C (e.g. from −15°C to +45°C), the expansion will be pipe pipe 0.000 012 per °C × 100 m × 60°C = 0.072 m, or 7.2 cm. In general, expansion = linear expansivity × original length × temperature rise ▲ Figure 2.2.4b Expansion joint 102 9781398310544.indb 102 19/02/21 8:14 PM  2.2.1 Thermal expansion of solids, liquids and gases Unusual expansion of water contracts and being denser sinks to the bottom. Warmer, less dense water rises to the surface to be As water is cooled to 4°C it contracts, as we would cooled. When all the water is at 4°C the circulation expect. However, between 4°C and 0°C it expands, stops. If the temperature of the surface water falls surprisingly. Water has a maximum density at 4°C below 4°C, it becomes less dense and remains at (Figure 2.2.6). the top, eventually forming a layer of ice at 0°C. volume Temperatures in the pond are then as in Figure 2.2.8. ice ice at 0°C ice and water water maximum density water at 0°C 1°C 2°C 3°C 4°C –4 0 4 8 12 16 temperature/°C ▲ Figure 2.2.6 Water expands on cooling below 4°C. At 0°C, when it freezes, a considerable volume expansion occurs and every 100 cm3 of water becomes 109 cm3 of ice. This accounts for the bursting of ▲ Figure 2.2.8 Fish can survive in a frozen pond. unlagged water pipes in very cold weather and for the fact that ice is less dense than cold water and so The volume expansion of water between 4°C and 0°C floats. Figure 2.2.7 shows a bottle of frozen milk, is due to the breaking up of the groups that water the main constituent of which is water. particles form above 4°C. The new arrangement requires a larger volume and more than cancels out the contraction due to the fall in temperature. Liquid-in-glass thermometer The temperature of a body tells us how hot the body is. It is measured using a thermometer usually in degrees Celsius (0°C). In the liquid-in-glass thermometer the liquid in a glass bulb expands up a capillary tube when the bulb is heated. The liquid must be easily seen and must expand (or contract) rapidly and by a large amount over a wide range of temperature. It must not stick to the inside of the tube or the reading will be too high when the temperature is falling. Mercury and coloured alcohol are commonly used liquids in this type of thermometer. Mercury freezes at −39°C and boils at 357°C but is a toxic material. ▲ Figure 2.2.7 Result of the expansion of water on freezing A non-toxic metal alloy substitute for mercury, such as Galinstan, is often used nowadays; it melts The unusual (anomalous) expansion of water between at −19°C and boils at 1300°C. Alcohol freezes at 4°C and 0°C explains why fish survive in a frozen −115°C and boils at 78°C and is therefore more pond. The water at the top of the pond cools first, suitable for low temperatures. 103 9781398310544.indb 103 19/02/21 8:14 PM  2.2 THERMAL PROPERTIES AND TEMPERATURE Going further Scale of temperature A scale and unit of temperature are obtained by choosing two temperatures, called the fixed points, and dividing the range between them into a number of equal 100°C steam point divisions or degrees. On the Celsius scale (named after the Swedish scientist Anders Celsius who suggested it), the lower fixed point is the temperature of pure melting ice and is taken as 0°C. The upper fixed point is the temperature of the steam above water boiling at normal atmospheric pressure, 105 Pa (or N/m2), and is taken as 100°C. 100 When the fixed points have been marked on the degrees thermometer, the distance between them is divided into 100 equal degrees (Figure 2.2.9). The thermometer now has a linear scale, in other words it has been calibrated or graduated. 0°C ice point ▲ Figure 2.2.9 A temperature scale in degrees Celsius Test yourself 4 a What is meant by the anomalous expansion of 3 Explain the relative order of magnitude of the water? expansion of solids, liquids and gases. b Name two consequences of the unusual expansion of water. 5 Discuss the action of a liquid-in-glass thermometer. 2.2.2 Specific heat capacity FOCUS POINTS ★ Know that an object’s internal energy is increased when its temperature rises. ★ Explain a change in an object’s temperature in terms of the change in kinetic energy of all its particles. ★ Define specific heat capacity, use the correct equation in calculations and describe experiments to measure it. 104 9781398310544.indb 104 19/02/21 8:14 PM  2.2.2 Specific heat capacity Some materials require more heat than others to raise their temperature. As discussed in the previous topic, when the temperature of an object rises, its particles move more rapidly. The increase in the kinetic energy associated with this motion raises the internal energy of the object. The extent of the increase in kinetic energy of the particles in a material when it is heated depends on the nature of the material and its state, and is measured in terms of specific heat capacity. The specific heat capacity of aluminium is higher than that of copper, so copper is a more energy efficient material to use for saucepans. In this topic you will find out how to measure and calculate the specific heat capacity of some solids and liquids. The internal energy of an object is the energy same temperature. For example, if the red-hot spark associated with the motion of its particles. landed in the boiling water, thermal energy would be When an object is heated and its temperature transferred from it to the water even though much rises, there is an increase in the internal energy more thermal energy could be obtained from the water. of the object. Specific heat capacity Internal energy If 1 kg of water and 1 kg of paraffin are heated in The kinetic particle theory (Topic 2.1.2) regards turn for the same time by the same heater, the temperature as a measure of the average temperature rise of the paraffin is about twice kinetic energy (Ek) of the particles of the body. that of the water. Since the heater gives equal The greater this is, the faster the particles move amounts of thermal energy to each liquid, it and the higher the temperature of the body. seems that different substances require different Increasing the temperature of an object increases amounts of energy to cause the same temperature its internal energy because the kinetic energy of rise in the same mass, say 1°C in 1 kg. all the particles increases. The amount of heat required to raise the temperature of a particular substance by one degree is measured by its specific heat capacity Thermal energy and temperature (symbol c). It is important not to confuse the temperature of a The specific heat capacity of a substance is body with the thermal energy that can be obtained defined as the energy required per unit mass per from it. For example, a red-hot spark from a fire is unit temperature increase. at a higher temperature than the boiling water in a In physics, the word ‘specific’ means that unit saucepan. In the boiling water the average kinetic mass is being considered. energy of the particles is lower than in the spark; but In general, for a mass m, receiving energy ΔE since there are many more water particles, their total which results in a temperature rise Δθ, this can energy is greater, and therefore more thermal energy be written in equation form as can be supplied by the water than by the spark. ∆E Thermal energy is transferred from a body at a c= m∆θ higher temperature to one at a lower temperature. where c is the specific heat capacity of a material This is because the average kinetic energy (and speed) of mass m whose temperature rises by Δθ when of the particles in the hot body falls as a result of its internal energy increases by ΔE. the collisions with particles of the cold body whose Internal energy is measured in joules (J) and average kinetic energy, and therefore temperature, the unit of specific heat capacity is the joule per increases. When the average kinetic energy of the kilogram per °C, i.e. J/(kg °C). particles is the same in both bodies, they are at the 105 9781398310544.indb 105 19/02/21 8:14 PM  2.2 THERMAL PROPERTIES AND TEMPERATURE The equation for specific heat can be rearranged A 40 W heater transfers 40 joules of energy to to give the equation: thermal energy per second. If the power is not ΔE = mcΔθ = mass × specific heat capacity × marked on the heater, ask about it. temperature rise Water Key definition Weigh out 1 kg of water into a container, such as an aluminium saucepan. Note the Specific heat capacity the energy required per unit mass per unit temperature increase temperature of the water, insert the heater (Figure 2.2.10), switch on the 12 V supply and start timing. Stir the water and after 5 minutes switch off but continue stirring and note the Worked example highest temperature reached. If 20 000 J is supplied to a mass of 5 kg and its temperature electric immersion rises from 15°C to 25°C, calculate the specific heat thermometer heater capacity of the mass. ∆E Using c = 12 V m∆θ supply 20000 J 20000 J c= = (5kg × (25 − 15) °C) 50 kg °C 400 J = kg °C water Now put this into practice aluminium 1 If 25 000 J of energy is supplied to a mass of 2 kg and pan its temperature rises from 10°C to 35°C, calculate the specific heat capacity of the mass. 2 How much energy must be supplied to a mass of 3 kg of material of specific heat capacity = 500 J/(kg °C) to ▲ Figure 2.2.10 raise its temperature by 10°C? Assuming that the energy supplied by the heater equals the heat received by the water, work out the specific heat capacity of water in Practical work J/(kg °C), as shown below: heat received by water (J) = power of heater (J/s) × Finding specific heat capacities time heater on (s) For safe experiments/demonstrations then the related to this topic, please refer to the Cambridge IGCSE Physics Practical Skills specific heat heat received by water (J) = Workbook that is also part of this series. capacity of water mass (kg) × temp.rise (°C) Safety 1 Suggest sources of error in the experiment described above to find the specific heat l Eye protection must be worn. capacity of water. l Take care as the pan and water and 2 In an experiment to determine the specific aluminium block may become hot. heat capacity of water, the temperature You need to know the power of the 12 V rise of 1 kg of water is found to be 2.5°C electric immersion heater to be used. when the water is heated by a 40 W heater Precaution: Do not use one with a for 5 minutes. Calculate the specific heat cracked seal. capacity of water. 106 9781398310544.indb 106 19/02/21 8:14 PM  2.2.2 Specific heat capacity soil for its temperature to rise by 1°C. Water also has Aluminium to give out more energy to fall 1°C. Since islands are An aluminium cylinder weighing 1 kg and surrounded by water, they experience much smaller having two holes drilled in it is used. Place the changes of temperature from summer to winter than immersion heater in the central hole and a large land masses such as Central Asia. thermometer in the other hole (Figure 2.2.11). The high specific heat capacity of water (as Note the temperature, connect the heater to well as its cheapness and availability) accounts for a 12 V supply and switch it on for 5 minutes. its use in cooling engines and in the radiators of When the temperature stops rising, record its central heating systems. highest value. Calculate the specific heat capacity as before. Worked example electric immersion a A tank holding 60 kg of water is heated by a 3 kW electric heater immersion heater. If the specific heat capacity of water thermometer is 4200 J/(kg °C), estimate the time for the temperature to rise from 10°C to 60°C. ∆E 12 V Rearranging c = gives ΔE = mcΔθ supply m∆θ Energy supplied to water = 3000 J/s × t, where t is the time of heating in seconds. Assuming energy supplied = energy received by water 3000 J/s × t = ΔE = mcΔθ (60 × 4200 × 50) J aluminium ∴t = = 4200 s (70 min) 3000 J/s block b A piece of aluminium of mass 0.5 kg is heated to 100°C and then placed in 0.4 kg of water at 10°C. If the resulting temperature of the mixture is 30°C, what is the specific heat capacity of aluminium if that of water is 4200 J/(kg °C)? When two substances at different temperatures ▲ Figure 2.2.11 are mixed, energy flows from the one at the higher 3 Suggest a source of error in the experiment temperature to the one at the lower temperature until both are at the same temperature – the temperature of to measure the specific heat capacity the mixture. If there is no loss of energy, then in this case: of aluminium and suggest how the energy given out by aluminium = energy taken in by water experiment could be improved. Using the heat equation ΔE = mcΔθ and letting c be the 4 In an experiment to determine the specific heat capacity of aluminium in J/(kg °C), we have specific heat capacity of aluminium, the energy given out = 0.5 kg × c × (100 − 30)°C temperature rise of an aluminium cylinder energy taken in = 0.4 kg × 4200 J/(kg °C) × (30 − 10)°C weighing 1 kg is found to be 12.5°C when the cylinder is heated by a 40 W heater ∴ 0.5 kg × c × 70°C = 0.4 kg × 4200 J/(kg °C) × 20°C for 5 minutes. Calculate the specific heat c= (4200 × 8) J = 960 J/ kg °C capacity of aluminium. 35 kg °C Now put this into practice Importance of the high specific 1 An electric kettle rated at 3 kW containing 1 kg of water is switched on. If the specific heat capacity of heat capacity of water water is 4200 J/(kg °C), estimate the time for the water The specific heat capacity of water is 4200 J/(kg °C) temperature to rise from 30°C to 100°C. 2 A metal sphere of mass 100 g is heated to 100°C and and that of soil is about 800 J/(kg °C). As a result, then placed in 200 g of water at 20°C. If the resulting the temperature of the sea rises and falls more temperature of the mixture is 25°C, what is the specific slowly than that of the land. A certain mass of water heat capacity of the metal if that of water is 4200 J/(kg °C)? needs five times more energy than the same mass of 107 9781398310544.indb 107 19/02/21 8:14 PM  2.2 THERMAL PROPERTIES AND TEMPERATURE Test yourself 6 Which one of the following statements is not true? 7 How much thermal energy is needed to raise the A Temperature tells us how hot an object is. temperature by 10°C of 5 kg of a substance of B When the temperature of an object rises so does specific heat capacity 300 J/(kg °C)? its internal energy. 8 How long will it take a 3 kW immersion heater to C Heat flows naturally from an object at a lower raise the temperature of 5 kg of water from 30°C temperature to one at a higher temperature. to 50°C? D The particles of an object move faster when its temperature rises. 2.2.3 Melting, boiling and evaporation FOCUS POINTS ★ Describe melting and boiling, including the temperatures for both for water. ★ Describe condensation, solidification and evaporation in terms of particles. ★ Understand the differences between boiling and evaporation. ★ Describe the factors that affect evaporation. To melt a bar of chocolate you will need to heat it. Melting and boiling require the input of energy to change the state of matter from solid to liquid or from liquid to gas. In the reverse changes, heat is released. During a change of state there is no change in temperature until the process is complete. The kinetic particle model can help us to understand the processes which occur during a change of state. In this section you will also learn how the model explains evaporation and cooling in terms of the escape of energetic particles from the surface of a liquid. You will learn the differences between the processes of evaporation and boiling and the factors which affect the rate of cooling of an object. When a solid is heated, it may melt and change A pure substance melts at a definite temperature, its state from solid to liquid. If ice is heated it called the