B.1 Thermal Energy Transfers PDF

B.1 Thermal energy transfers Guiding questions How do m...

B.1 Thermal energy transfers Guiding questions How do macroscopic observations provide a model of the microscopic properties of a substance? How is energy transferred within and between systems? How can observations of one physical quantity be used to determine the other properties of a system? Thermal energy, internal energy and heat These three terms are often used interchangeably, which can be confusing! Unfortunately, different teachers and different books have varying interpretations, so it is important to clarify, from the beginning of this topic, exactly how these terms will be used in this course. All substances contain particles / molecules which can have individual kinetic energies and potential energies. There are more details about this later in this topic. We will describe the total of all these particle energies as the internal energy of a substance. We will not describe the energy inside substances as thermal energy, or heat. Energy is always transferred from hotter objects to cooler objects. We will describe this transfer as thermal energy, although the word ‘heat’ is also widely used to describe this type of energy transfer. TOK I B L E AR N HE The natural sciences ER T PROFILE l Does the precision of the language used in the natural sciences successfully eliminate all ambiguity? Ambiguities ◆ Ambiguity Open to There is, perhaps, nowhere else in the study of physics where such important terms have such ambiguous different interpretations. uses. It is interesting to consider how this has arisen, why it is not corrected, and whether it is truly important. If you understand the theory of particle energies inside matter, does it really matter if your teacher calls it ‘internal energy’, while a book refers to is as ‘thermal energy’ and your friend calls it ‘heat’? To what extent is precise language important to our understanding of underlying physics? Kinetic theory of matter SYLLABUS CONTENT  Molecular theory in solids, liquids and gases. m  Density, ρ, is given by: ρ = V. 176 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 176 04/01/2023 20:44  ◆ Kinetic theory of The essential idea that all matter contains countless billions of particles constantly moving matter All matter is (in various ways), with forces between them when they get close enough, is possibly the most composed of a very large important theory in the whole of science. The microscopic kinetic theory of matter is the starting number of small particles that are in constant motion. point that can be used to help explain so much of what we observe in our macroscopic everyday ◆ Ions An atom or life. To begin with, it can explain the different properties of solids, liquids and gases. molecule that has gained or Solids, liquids and gases lost one or more electrons. ◆ Atoms The The ‘particles’ we are referring to in the kinetic theory are usually molecules, but they could particles from which also be ions, or atoms. Figure B1.1 shows a simplified visual model of particle arrangements. chemical elements are Table B1.1 offers generalized comments on the major differences. composed. They contain subatomic particles. gas liquid solid Figure B1.1 Particle arrangements Table B1.1 Differences between particles in solids, liquids and gases Solid Liquid Gas Arrangement regular patterns no pattern no pattern of particles Forces attractive and large enough some particles have enough negligible (except in collisions) between to keep particles in their energy to overcome attractive under most conditions particles positions forces Separation of close together still close together much further apart particles Motion of vibrate in fixed positions some limited random movement all move in random directions particles is possible and usually with high speeds Density Clearly, the more massive the individual particles are, and/or the closer they are together, the greater will be the total mass of a given volume of a substance. mass m DB density = ρ= SI unit: kg m−3 volume V ◆ Expand Increasing in When solids and liquids are heated to a higher temperature, they will usually expand slightly in size. An expansion of a gas size because there will be a very small increase in the separation of particles. This means that is an increase in volume. there will be a small decrease in their densities. When gases are heated, they will only expand if they are in a container that will allow that to happen. B.1 Thermal energy transfers 177 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 177 04/01/2023 20:44  Table B1.2 Typical values for densities (gases at 0 °C and normal atmospheric pressure) Substance Density / kg m−3 helium 0.18 air 1.23 carbon dioxide 1.98 wood (pine, approx.) 500 ethanol 810 ice 910 water (at 20 °C) 998 water (at 4 °C) 1000 sea water (approx.) 1030 aluminium 2710 average density of Earth 5520 iron 7870 gold 19 300 black hole 1 × 1015 The particles in solids and liquids can be considered to be as close together as possible, that is, they are effectively ‘touching’ each other. Since gases are about 1000 × less dense than solids and liquids, their molecules are typically 10 molecular diameters apart from each other. 1 Calculate the density of olive oil in SI units, if a mass of 125 g has a volume of 137 cm3. 2 An iron bar has the dimensions 5.0 × 5.0 × 25.0 cm. What is its mass? 3 Explain how we can conclude from Table B1.2 that the molecules in air are approximately 10 times further apart than the molecules in water. 4 Outline why ice floats on water. (Refer to buoyancy forces from Topic A.2.) 5 Water has its maximum density at 4 °C. How does this affect the formation of ice on, for example, a lake in very cold weather? 6 In everyday life the volume of liquids is more often measured in litres, l, (and cl and ml) rather than in m3 or Figure B1.2 Placing gold foil on a statue of Buddha cm3. 1 litre is a volume of 1000 cm3. Determine the volume, in litres, of some ethanol which Gold is extremely malleable – meaning that it can has a mass of 1.0 kg. be hammered relatively easily into different shapes, including very thin foil (approximately 2 × 10–7 m). 7 It is common practice in many Asian countries to see people making merit by placing gold leaf on Buddhist Predict what area of gold foil of thickness 1.80 × 10−5 cm images, as shown in Figure B1.2. can be made from each 1.0 g of gold. 178 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 178 04/01/2023 20:44  Temperature SYLLABUS CONTENT  Temperature difference determines the direction of the resultant thermal energy transfer between bodies.  Kelvin and Celsius scales are used to express temperature.  A change in temperature of a system is the same when expressed with the Kelvin or Celsius scales. 3  Kelvin temperature is a measure of the average kinetic energy of particles: Ek = 2kBT. Macroscopic understanding of temperature ◆ Thermal equilibrium All temperatures within a In everyday life, temperature is a number obtained from a thermometer, which informs us how system are constant. hot, or cold, something is. But this is a long way from an acceptable scientific definition. Thinking ◆ Thermal contact a little more deeply, we realize that temperature values tell us something about energy transfer: Objects can be considered Energy always flows spontaneously from a hotter place to a colder place. As we have already to be in thermal contact if thermal energy (of any noted, we will call this a flow of thermal energy. kind) can be transferred between them. The resultant flow of thermal energy is always from higher temperature to lower temperature. Consider an isolated system such as shown in Figure B1.3. If there is no net transfer of thermal energy between A and B, then they must be at the same temperature, and we describe them as being in thermal equilibrium. Similarly for B and C. If B is in thermal equilibrium with A and C, then A and C are also in thermal equilibrium with each other, and at the same temperature. Consider the simple example of a system of two objects (or substances) at different A 20 ºC temperatures able to transfer thermal energy between themselves, but isolated from everything around them (their surroundings). The hotter object will transfer energy to the 20 ºC B colder object and cool down, while at the same time the colder object warms up. As the temperature difference between the two objects gets smaller, so too does the rate of thermal energy transfer (as represented by the gradients of the graphs). This is represented in C 20 ºC Figure B1.5, which shows how the temperature of two objects (A and B) might change when they are placed in good thermal contact with each other. Being in ‘thermal contact’ means Figure B1.3 Thermal equilibrium: same temperature, that thermal energy can be transferred between them, by any means. But the phrase is most no flow of thermal energy often used when referring to significant physical contact. Temperature Figure B1.4 This thermogram, taken using infrared radiation, uses colour to show A different temperatures in Figure B1.5 Two objects a saucepan on a cooker. (A and B) at different The scale runs from B temperatures, insulated white (hottest) through from their surroundings but red, yellow, green and not from each other, will blue to pink (coldest) Time reach thermal equilibrium Eventually A and B will reach the same temperature. If the temperatures have stopped changing and both objects are at the same temperature, the objects are in thermal equilibrium and there will be no net flow of thermal energy between them. In any realistic situation, it is not possible to completely isolate / insulate two objects from their surroundings, so the concept of thermal equilibrium may seem to be idealized. B.1 Thermal energy transfers 179 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 179 04/01/2023 20:44  The concept of hotter objects always getting colder, and colder objects always getting hotter, Common suggests an important concept: eventually everything will end up at the same temperature. mistake Temperature scales 0 °C is simply the freezing point of pure Celsius scale of temperature water. It has no other A temperature scale needs two fixed points. For the Celsius scale, these are the freezing point meaning. It is not a ‘true’ and the boiling point of pure water (under specified conditions). An instrument for measuring zero. For example, it temperature, a thermometer, can then calibrated by marking these two points as 0 °C and 100 °C, would be wrong to think that 20 °C was double the and then dividing the interval between them into one hundred equal divisions. Higher and lower temperature of 10 °C. temperatures can then be determined by extrapolation. Kelvin scale of temperature ◆ Celsius (scale of temperature) Temperature The choice of the two fixed points on the Celsius scale is arbitrary and mainly for convenience. scale based on the melting However, there is a more logical scale – the Kelvin scale – that is widely used in science, point (0 °C) and boiling but in everyday life, people around the world have become used to the Celsius scale (and point (100 °C) of pure water. Fahrenheit scale). ◆ Thermometer An instrument for measuring There is a temperature at which the kinetic energy of all particles reduces to (almost) zero. This temperature. is known as absolute zero and it is discussed in more detail in Topic B.3. On the Celsius scale ◆ Kelvin scale of absolute zero has the value of –273.15 °C. This temperature is the lower fixed point, zero, of the temperature Also known as the absolute Kelvin temperature scale, which is sometimes described as the absolute temperature scale. temperature scale. Temperature scale based Zero kelvin (0 K) is the lowest possible temperature (= –273.15 °C) on absolute zero (0 K) and the melting point of The upper fixed point of the Kelvin scale also effectively uses the melting point of pure water water (273 K). The kelvin, K, is the fundamental which, for convenience, is given the value of +273.15 K. This scale defines the SI unit of SI unit of temperature. temperature, the kelvin, K. Defining the Kelvin temperature scale in this way means that a change T (in K) = 0 °C + 273. of temperature has the same numerical value in both the Celsius and the Kelvin scales. Table B1.3 ◆ Absolute zero compares some Celsius and kelvin temperatures (to the nearest whole number). Temperature at which (almost) all molecular The symbol T is used for temperature in kelvin. Θ is often used for a temperature in motion has stopped (0 K or degrees Celsius. −273 °C). Table B1.3 A comparison of temperatures in degrees Celsius and Kelvin Temperature °C K absolute zero −273 0 melting point of water 0 273 body temperature 37 310 boiling point of water 100 373 DB Temperature in kelvin, T/K = temperature in Celsius, Θ/°C + 273 180 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 180 04/01/2023 20:44  WORKED EXAMPLE B1.1 a The freezing point of ethanol is –114 °C. Convert this temperature into kelvin. b The melting point of aluminium is 933 K. Convert this temperature to degrees Celsius. c On a cold night the temperature dropped from +10 °C to −10 °C. Calculate this change of temperature in kelvin. Answer a T = −114 + 273 = 159 K b Θ = 933 − 273 = 660 °C c (–10) – (+10) = −20 K Tool 2: Technology Use sensors The advantage of using sensors in this way are obvious: Electronic sensors respond to a particular physical l Data can be collected over very short times (less quantity by producing a corresponding voltage. That than a second), or times which are otherwise voltage must then be converted to digital form before inconveniently long. it can be understood, processed and displayed by l A large amount of data can be gathered. appropriate software. There are several possibilities, l The data can be stored. including where a separate data logger/interface, l The data can be very quickly processed and is connected between the sensor and a computer. graphs drawn. See Figure B1.6. The sensors which are in common use in physics Alternatively and more conveniently, the sensor may experiments at this level include: be connected to a corresponding all-in-one unit which l position and motion processes and displays results. In some cases, a mobile phone app can be used. Bluetooth connections are l pressure also available. l temperature l sound level l light level l current and voltage l magnetic field. www.africanews.com boiling water interface box computer Figure B1.6 Separate sensor, interface and computer B.1 Thermal energy transfers 181 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 181 04/01/2023 20:44  Measuring temperature, using sensors The part of the thermometer which is used to measure the temperature is placed in good thermal contact with In principle, any physical quantity which varies with the material whose temperature is to be measured (except temperature could be used to construct a thermometer. for infrared thermometers). After sufficient time for However, it is better to use a physical quantity that varies the thermometer to reach thermal equilibrium with the significantly and regularly over a wide range of temperatures. material, a reading can be taken. Other sources of thermal The most common types of thermometer involve: energy should be avoided. For example, when measuring l variation in length of a liquid along a thin (capillary) tube air temperature, the thermometer should not be receiving l variation in pressure of a fixed volume of gas thermal energy directly from the Sun. l variation of electrical resistance Electronic resistance thermometers (sensors) have an l variation in the voltage generated by wires of different obvious advantage in that they can provide immediate metals joined together digital data when they are connected to a computer l variation in infrared radiation from a surface. through an interface. 8 Convert the following kelvin temperatures into 10 The volume of a gas was 67 cm3 when the temperature degrees Celsius: a 175 b 275 c 10 000. was 22 °C. a If the volume is proportional to the absolute 9 The world’s highest and lowest recorded weather temperature, calculate the volume if the temperature temperatures are reported to be 56.7 °C (California – see increases to 92 °C. Figure B1.7) and −89.2 °C (Antarctica). b Predict the volume if the gas temperature could be a State values for these temperatures in kelvin. reduced to 0 K. b Some hot water at 68 °C cools down to 22 °C. What is this change of temperature in kelvin? 11 A student calibrated an unmarked liquid-in-glass thermometer. The liquid expands up a thin capillary tube as it gets hotter. She has correctly marked the upper and lower fixed points as 0 °C and 100 °C. The two marks were 10.7 cm apart. a She then wanted to use her thermometer to measure room temperature and she left it in the laboratory for 10 minutes. The level of the liquid was then 2.6 cm above the lower fixed point. Explain why the thermometer was left undisturbed for 10 minutes. b Calculate a value for room temperature. Figure B1.7 The world’s highest temperature c State an assumption that you have to make to answer to date was recorded in California, USA. part b. Higher temperature Lower temperature Microscopic understanding of temperature A true understanding of temperature is to be found in the kinetic theory of matter. Consider the example of two samples of the same gas, as shown in Figure B1.8. Suppose that the molecules on the right have a lower average kinetic energy (and speed) than the molecules on the left. After they have collisions, the faster moving molecules will slow down and the slower molecules will speed up (conservation of momentum in elastic collisions). In this way energy is transferred from the left to the right. This is equivalent to a transfer of thermal energy, so we must conclude that the thermal energy transfer left-hand side of the figure represents a higher temperature. Eventually, the average Figure B1.8 Energy transfers energies and speeds on both sides will become equal and a macroscopic interpretation between molecules would be that they were in thermal equilibrium at the same temperature. 182 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 182 04/01/2023 20:44  Average particle speed indicates different temperatures when we compare samples of the same gas. Increasing temperature corresponds to greater average speed. More generally, when we compare different gases, we need to consider the average kinetic energy of the particles, rather than their speeds. Temperature (K) is proportional to the average random translational kinetic energy,Ek, of particles in a gas. ◆ Vibrational kinetic All gases, at the same temperature, contain particles with the same average translational energy Kinetic energy due kinetic energy. to vibration/oscillation. The particles in most gases are molecules, which means that they also have other forms of ◆ Boltzmann constant, kB Important constant that kinetic energy (not just translational), for example, rotational kinetic energy and vibrational links microscopic particle kinetic energy. energies to macroscopic The all-important mathematical connection between macroscopic measurements of kelvin temperature measurements. temperature, T, and the microscopic concept of individual molecular kinetic energies is provided by the Boltzmann constant in the following equation: DB 3 Average random translational kinetic energy of a gas particle:E = kBT 2 DB kB is known as the Boltzmann constant. It has the value 1.38 × 10 −23 J K−1 LINKING QUESTION Top tip! l How is the In Topics A.2 and A.3 we discussed collisions between macroscopic objects, describing the collisions understanding of as either elastic (total kinetic energy of the objects is conserved) or inelastic. During inelastic collisions, systems applied energy is transferred to the surroundings, dissipated, mostly in the form of internal energy and thermal to other areas energy. That is, energy is transferred from the ordered kinetic energy of countless billions of particles of physics? moving together in the same direction in the objects as a whole, to the disordered random kinetic energies of individual particles. Energy dissipation is a macroscopic concept and cannot be applied to microscopic particle collisions. Total kinetic energy can only decrease in a collision between two particles if it is used to cause ionization (see Topic B.5). WORKED EXAMPLE B1.2 Calculate the average kinetic energy of translation of gas molecules at room temperature. Answer Using 20 °C (293 K) as room temperature, 3 Ek = kBT = 1.5 × (1.38 × 10 –23) × 293 = 6.1 × 10 –21 J 2 The energy of particles in liquids and solids is more complicated because of the significant forces between the particles. In general, however, the following is always true: A temperature rise is equivalent to the particles gaining kinetic energy. B.1 Thermal energy transfers 183 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 183 04/01/2023 20:44  12 Consider the gas in the previous worked example. If the particles have a mass of 5.3 × 10−26 kg, use the equation for linear kinetic energy to estimate their average speed. 13 The surface temperature of the Sun is 5800 K. Calculate the average kinetic energy of the particles it contains, assuming that the equation in Worked example B1.2 can be applied. 14 A cylinder of gas contains gas molecules moving with an average speed of 400 m s−1, which is characteristic of their temperature of 20 °C. If the cylinder is then put on an aircraft which is moving at 200 m s−1, discuss what will happen to the average speed of the gas molecules and the temperature of the gas. ◆ Sense perception 15 Nitrogen and oxygen are the two principal gases in air. Oxygen molecules are slightly more How we receive massive than nitrogen molecules. Explain how the average speeds of the molecules will information, using the five human senses. compare in the air you are breathing. TOK Knowledge and the knower consult an instrument capable of measuring the temperature (a l How do we acquire knowledge? thermometer) has obvious advantages, in everyday life as well as l To what extent are technologies merely extensions to the in scientific experiments. However, such reliable measurements human senses, or do they introduce radically new ways of were not possible until about 300 years ago. seeing the world? Sense perception (of temperature) ‘Information’ received directly by receptors in the human body and then processed by our brains, is described as sense perception. It is often said that we have five senses (hearing, sight, smell, touch and taste), but we also have a limited ability to detect changes in temperature and the flow of thermal energy into, or out of, our bodies. Most people are able to estimate the approximate temperature of the air around them. Figure B1.9 Fahrenheit with his thermometer However, this ‘way of knowing’ using sense perception can be unreliable. Whether we are hot or cold is a very common topic of A German physicist, Daniel Fahrenheit (Figure B1.9) invented conversation, but people in the same environment can sometimes the first accurate thermometer in 1709. He used the expansion of disagree about the temperature that they sense. Being able to mercury along a thin tube. Internal energy All substances contain moving particles. Moving particles have kinetic energy. The particles might be moving in different ways, which gives rise to three different forms of kinetic energy: l Particles might be vibrating about fixed positions (as in a solid) − this gives the particles vibrational kinetic energy. l Particles might be moving from place to place (translational motion) − this gives the particles translational kinetic energy in liquids and gases. l Molecules might also be rotating − this gives the molecules rotational kinetic energy. Particles can have potential energy as well as kinetic energy. In solids and liquids, it is the electrical forces (between charged particles) that keep particles from moving apart or moving closer together. Wherever there are electrical forces there will be electrical potential energy in a system, in much the same way as gravitational potential energy is associated with gravitational force. 184 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 184 04/01/2023 20:44  If the average separation of the particles in a solid or liquid increases, so too does their potential energy (and the total internal energy of the substance.) In gases, however, the forces between molecules (or atoms) are usually negligible because of the larger separation between molecules. This is why gas molecules can move freely and randomly. The molecules in a gas, therefore, usually have negligible electrical potential energy – all the energy is in the form of kinetic energy. So, to describe the total energy of the particles in a substance, we need to take account of both the kinetic energies and the potential energies. This is called the internal energy of the substance and is defined as follows: The internal energy of a substance is the sum of the total random kinetic energies and total potential energies of all the particles inside it. In the definition of internal energy given above, the word ‘random’ means that the particle movements are disordered and unpredictable. That is, they are not linked in any way to each other, or ordered – as their motions would be if they were all moving together, such as the particles in a macroscopic motion of a moving object. The particles in a moving object have both the ordered kinetic energy of macroscopic movement together and the random kinetic energy of internal energy. Nature of science: Theories Caloric fluid An understanding of thermal energy and internal energy depends on the kinetic theory of matter, but that theory is less than 200 years old. Before that, ‘heat’ was often explained in terms of a vague invisible ‘caloric fluid’ that flowed out of a hot object, where it was concentrated, to a colder place where it was less concentrated. This is an example of one of many serious scientific theories that were developed to explain observed phenomena, but which were never totally satisfactory because they could not explain all observations. The earlier ‘phlogiston’ theory of combustion is another such theory related to heat and combustion. Looking back from the twenty-first century, these theories may seem unsophisticated and inaccurate (but imaginative!). However, they should be judged in the context of their times, and at the time of these theories (seventeenth and eighteenth centuries) the kinetic theory of matter had not been developed, so the current understanding of the flow of thermal energy was not possible. Thermal energy SYLLABUS CONTENT  Conduction, convection and thermal radiation are the primary mechanisms for thermal energy transfer. Thermal energy is the name we give to the transfer of energy because of a temperature difference: a net flow from hotter to colder. There are three principal ways in which thermal energy can be transferred: l Thermal conduction. In which kinetic energy is transferred between particles. l Convection. In which differences in the densities of liquids and gases result in their movement. l Thermal radiation. In which electromagnetic radiation is emitted by surfaces. We will discuss each of these in detail in the next three sections. B.1 Thermal energy transfers 185 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 185 04/01/2023 20:44  Thermal conduction SYLLABUS CONTENT  Conduction in terms of the difference in kinetic energy of particles.  Quantitative analysis of rate of thermal energy transferred by conduction in terms of the type of material and cross-sectional area of the material and the temperature gradient as given by: ΔQ ΔT = –kA Δt Δx As mentioned earlier in this topic, when gas particles (usually molecules) have elastic collisions, the slower moving particles gain kinetic energy and the faster moving particles lose kinetic energy. In this way, over time, there will be a net transfer of energy from a place where particles, on average, are moving faster to a place where they are moving slower on average. That is, from hotter to colder. Such a transfer will continue until the whole of the gas has particles with the same average kinetic energy, when thermal equilibrium has been reached and a constant temperature reached. ◆ Conduction (thermal) Similar ideas can be applied to the transfer of energy between particles in liquids and solids. Passage of thermal energy This type of thermal energy transfer, from particle to particle, is called thermal conduction. through a substance as Figure B1.10 gives an impression of thermal conduction through a solid, although vibrations and energy is transferred from particle to particle. increasing kinetic energy are not easily represented in a single picture! Thermal conduction occurs because of the transfer of kinetic energy between particles. Common mistake Many students think that Figure B1.10 Thermal conduction through a solid thermal conduction only occurs in solids. This is In solids, the particles vibrate in fixed positions, with forces between them. In Figure B1.10, the not true, although some particles on the left-hand side are vibrating faster and have greater vibrational kinetic energy (on solids, especially metals, average) because the solid is at a higher temperature. Energy is transferred through the solid, to are by far the best the right, because of the forces / interactions between particles. thermal conductors. See Table B1.4. Solids are generally better thermal conductors than liquids, and liquids conduct better than gases. This can be explained by considering the closeness of particles and the strength of forces Consider again Figure between them. B1.10. The solid bar has gained its thermal Table B1.4 lists various substances and their thermal conductivities, which are explained later in energy by conduction this topic. A larger number means that the substance is better at conducting thermal energy: more from the hot gas in energy is transferred under similar conditions. (Metals are good conductors because they contain the flame. many free / delocalized electrons.) 186 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 186 04/01/2023 20:44  Table B1.4 Typical thermal conductivities at room temperature (some approximate) Thermal conductivity Substance / W m−1 K−1 vacuum 0.00 carbon dioxide 0.15 air 0.025 polyurethane foam 0.03 paper 0.05 rubber 0.13 wood 0.15 common plastics 0.2 water 0.59 concrete and brick 0.72 glass 0.86 carbon 1.7 ice 2.1 iron 84 aluminium 237 copper 385 ◆ Insulator (thermal) A We often describe a substance as being either a good thermal conductor or a good thermal material that significantly insulator (poor conductor). However, these are not precisely defined terms, although it should be reduces the flow of thermal clear from looking at Table B1.4 that the last three are much better at conducting thermal energy energy. than any of the rest. These three would be described as good thermal conductors; the rest are usually described as insulators. 16 How can you explain that a vacuum has a thermal conductivity of zero? 17 The last three substances in Table B1.4 are all good conductors of thermal energy. State what they have in common. 18 Compare the ability of air, water, glass and copper to conduct thermal energy. (Determine ratios.) 19 Explain why a metal door handle will often feel cooler Figure B1.11 Frying pan than a plastic handle at the same temperature. 22 Outline the transfers of thermal energy represented in 20 Discuss whether you would describe carbon as a Figure B1.12. conductor, or an insulator. 21 Explain the choice of materials in the manufacture of the frying pan shown in Figure B1.11. cup of coffee Figure B1.12 Transfer of thermal energy B.1 Thermal energy transfers 187 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 187 04/01/2023 20:44  23 Wetsuits are made from neoprene foam rubber (see Figure B1.13). Suggest how this can keep the surfer from getting too cold. Figure B1.13 Surfer wearing a wetsuit Quantitative treatment of thermal conductivity Consider Figure B1.14, which represents the flow of thermal energy by conduction through an isolated system of a specimen of a single substance, which has an area A, and a thickness Δx. TH TC The symbol Q will be used for thermal energy. A flow of thermal energy occurs because the left-hand side is at a higher temperature than the right-hand side: TH > TC. thermal energy, Q The rate of thermal energy flow, ΔQ / Δt, will be proportional to the temperature difference, ΔT, and the area, A, but inversely proportional to the thickness, Δx. It also obviously depends on the thermal properties of the substance involved. In summary: area A Rate of transfer of thermal energy by conduction: ΔQ ΔT ∆x DB = kA Δt Δx Figure B1.14 Thermal energy flowing through a block ◆ Thermal conductivity, k k is a constant, different for each substance. It is called the thermal conductivity of the substance Constant that represents (as shown in Table B1.4). Unit: W m−1 K−1. the ability of a substance to ΔQ conduct thermal energy. is a flow of energy per second (a power) so it is measured in watts. Δt 188 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 188 04/01/2023 20:44  WORKED EXAMPLE B1.3 The outside brick wall (single layer) of a house is 4.85 m × 2.88 m. It contains a closed glass window of dimensions 1.67 m × 1.23 m. On a hot afternoon the outside air temperature is 34.0 °C, while it is 27.0 °C inside the room. Use the equation above to calculate the flow of thermal energy through: a the wall of thickness 25 cm b the window of thickness 4.5 mm. Use data from Table B1.4. Answer ΔQ ΔT a = kA Δt Δx 7.0 = 0.72 × ((4.85 × 2.88) – (1.67 × 1.23)) × 0.25 = 2.4 × 102 W into the room. ΔQ ΔT b = kA Δt Δx 7.0 = 0.86 × (1.67 × 1.23) × 0.0045 = 2.7 × 103 W into the room. The thermal conductivities of brick and glass are similar. Much more thermal energy flows through each cm2 of the glass because it is significantly thinner. It should be noted that these calculations considerably overestimate the magnitude of thermal energy flows. This is because the surface temperatures of the glass and brick cannot be assumed to be the same as the surrounding air temperatures (as was done in answering the question). The best insulator for limiting thermal energy flowing out of, or into, homes is air. See Table B1.4. However, if the air can move, thermal energy can also be transferred by convection currents (see next section). Various kinds of foam consist mainly of air, but the foam limits the movement of that air. Figure B1.15 shows polyurethane foam between the outer and inner walls of the outside of a house. Similar insulation can be used under the roof and below the ground floor. Parallel sheets of glass (known as double glazing), as seen in Figure B1.16, can be used to trap air and limit thermal energy flow through a window. Obviously, no foam can be put between the sheets of glass, but convection is limited by keeping the separation small. Double glazing has the added benefit of reducing the transfer of sound. Figure B1.15 Foam insulation Figure B1.16 in a ‘cavity wall’. Double glazing B.1 Thermal energy transfers 189 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 189 04/01/2023 20:44  24 In an experiment to measure the thermal conductivity of a disc of wood, a sample of area 65 cm2 was used, with a thickness of 5.2 mm. When the surfaces of the wooden disc were kept at 0 °C and 100 °C, the flow of thermal energy through the wood was determined to be 16 W. Use this data to calculate a value for the thermal conductivity of the wood. 25 In 10 minutes, a total of 275 J of thermal energy was conducted through a block of material of area 12.5 cm2 when it had a temperature gradient of 4.2 °C cm−1 across it. a Determine a value for the thermal conductivity of the material. b Would you describe this material as a conductor or an insulator? c Suggest a material it might have been. 26 a If 5.6 W of thermal energy was flowing through each square metre of the insulating polyurethane foam seen in Figure B1.15, calculate the temperature difference between its surfaces if the foam had a thickness of 7.8 cm. b Determine a value for the outside temperature if the thickness of the brick walls was 10.9 cm and the inside temperature of the outer brick wall was 5.4 °C. c Determine the inside temperature of the interior wall. d Sketch the arrangement and annotate your drawing with all the known data. Thermal convection SYLLABUS CONTENT  Qualitative description of thermal energy transferred by convection due to a fluid density difference. ◆ Convection Passage of When part of a fluid (gas or liquid) is heated, there will be a localized decrease in density. thermal energy through Because of increased buoyancy (see Topic A.2), the warmer part of the fluid will then rise and liquids and gases due to the flow above the cooler part of the fluid, which has a slightly greater density. This movement of movement of the substance because of differences thermal energy in a fluid is called thermal convection. It is common for convection to produce in density. currents and a circulation of a gas or liquid. Figures B1.17 and B1.18 show two common laboratory demonstrations of convection. Thermal convection is the transfer of thermal energy because of the movement of a fluid due to changes in density. coloured dye movement movement of hotter of cooler water water Figure B1.17 Demonstrating convection in water Figure B1.18 Demonstrating convection in air 190 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 190 04/01/2023 20:44  There are large number of examples of convection currents, including: l The water in heaters, saucepans, kettles, and so on, is supplied with energy (by thermal conduction) near the bottom of the container. The heated water rises, to be replaced by cooler water, which in turn will be heated. Convection currents ensure that the thermal energy spreads evenly throughout the water. See Figure B1.19. Figure B1.19 Convection l Room heaters are placed near to the floor, but air-conditioners are near the ceiling. of water in a saucepan l The coolest part of a refrigerator is near the bottom. l Water is mixed in the oceans and lakes by convection currents. l Molten material in the Earth’s core circulates because of convection. l Convection currents occur in the very hot cores of stars, including the Sun. l Formation and movement of clouds and storms depend on convection. l The Earth’s climate and weather patterns are controlled by convection. l The direction of winds near coasts depends on convection. l Smoke usually rises because of convection, but a lack of convection can make air pollution problems worse. 27 Outline how the experiment shown in Figure B1.18 is demonstrating convection in air. 28 Figure B1.20 shows a tube of water being heated near to the water surface. A metal gauze is keeping some ice at the bottom of the tube. steam boiling water water ice Figure B1.21 Antarctic explorer metal gauze Bunsen 31 Outline the cooking process (in terms of thermal energy burner Figure B1.20 Tube of ice being heated transfers) for the pizza seen in Figure B1.22. a Explain what this demonstration shows us about the transfer of thermal energy in water. b Predict and explain how the observations will change if the gauze is removed, allowing the ice to rise, and the water is heated at the bottom of the tube. 29 Convection currents in the air often flow from the sea towards the land. This is because, in the daytime, the land changes temperature quicker, and gets warmer, than the sea. Sketch an annotated diagram to help to explain this phenomenon. 30 Discuss what features of the clothing of the Antarctic explorer seen in Figure B1.21 keep the explorer warm. Figure B1.22 Pizza oven B.1 Thermal energy transfers 191 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 191 04/01/2023 20:44  ATL B1A: Thinking skills Being curious about the natural world Under certain weather conditions, the normal convection currents which rise from the Earth’s Top tip! surface can be greatly reduced. This can result in trapping air pollutants that would usually This section on thermal disperse. Use the search term ‘temperature radiation requires some inversion’ to research into this phenomenon and understanding of waves, write a 200–300 word summary. Figure B1.23 The polluting effects of a radiation and spectra, temperature inversion over Almaty in Kazakhstan all of which are covered in Theme C. If you have not been introduced to Thermal radiation these topics before, it may be better to delay SYLLABUS CONTENT the study of this section  Quantitative description of energy transferred by radiation as a result of the emission of (thermal radiation) until electromagnetic waves from the surface of a body, which in the case of a black body can be modelled after Topics C.2 and C.3 by the Stefan–Boltzmann law as given by: L = σAT 4, where L is the luminosity, A is the surface area have been studied. and T is the absolute temperature of the body.  The emission spectrum of a black body and the determination of the temperature of the body using ◆ Emit To send out from Wien’s law: λmaxT = 2.9 × 10 –3 mK, where λmax is the peak wavelength. a source. ◆ Thermal radiation Electromagnetic radiation All matter / objects emit electromagnetic waves because of the movement of charged particles emitted because of the within their atoms. (There is no need to understand this process.) This is called thermal movement of charged radiation. Electromagnetic waves are explained in Topic C.2. Most commonly this radiation is particles in the atoms of all called infrared, but if the temperature is hot enough, visible light is also emitted. matter at all temperatures. Most commonly, infrared. A flame (Figure B1.24) is an obvious example, producing significant amounts of electromagnetic ◆ Infrared radiation: we can detect the infrared by holding a hand near the flame, and detect the light with Electromagnetic radiation our eyes. Figure B1.4 showed the infrared emitted by a saucepan. emitted by all objects (depending on temperature) Although it is true to say that thermal radiation is emitted continuously by all matter at all with wavelengths longer temperatures, we tend to only notice it coming from hot objects. The power of the emitted than visible light. radiation from any surface depends on: 1 Surface temperature The radiated power is proportional to the fourth power of the surface temperature (in kelvin), T 4. This means, for example, a metal bar at 600 K (323 °C) will emit 24 = 16 times as much radiation as the same bar at 300 K (23 °C). 2 Surface area The radiated power is proportional to the area, A. 3 Nature of the surface See next section. Note that the emitted power is not dependent on the chemical nature of the material. Figure B1.24 Thermal radiation from a flame 192 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 192 04/01/2023 20:44  Good absorbers and good emitters of thermal radiation Dark surfaces, especially black, are the best absorbers of thermal radiation. White and shiny surfaces reflect and scatter radiation well, so that they are poor absorbers. (Scattering is explained later in this topic.) The Sydney Opera House (Figure B1.25) is a poor absorber of thermal radiation. (The word absorption describes something taking in something else, a sponge absorbing water, for example.) Any surface which is a good absorber of radiation will also be a good emitter. Black surfaces emit and absorb radiation well; white surfaces are poor at absorbing and emitting. Figure B1.25 Sydney Opera House. ◆ Absorption When the Black bodies energy of incident particles or radiation is transferred A perfect black body is the term we use to describe an object which has a surface which to other forms within absorbs all of the infrared and light (and other electromagnetic radiation) that falls on it. a material. ◆ Black body An idealized No light is reflected, so we are unable to see a black body, except in outline (unless it is also object that absorbs all the electromagnetic hot enough to emit visible radiation: light). This is easily defined and understood; however, a radiation that falls upon perfect black body is also a perfect emitter of thermal radiation, but what exactly does that mean? it. A perfect black body Obviously, it cannot mean that all of the energy in the surface is emitted instantaneously! also emits the maximum possible radiation. All surfaces emit a range of different wavelengths with different powers, and this varies with ◆ Black-body radiation temperature. A perfect black body emits the maximum possible thermal radiation, and this is best (spectrum) Radiation described graphically by a black-body emission spectrum, as shown in Figure B1.26, for three emitted from a ‘perfect’ different high temperatures. A curve for 300 K (27 °C) would be too small to show on the scale emitter. The characteristic ranges of different of this graph and it would have its maximum value at a wavelength of about 10 × 10−6 m, which is radiations emitted at well off the horizontal scale to the right. different temperatures We can see from the graph that, as temperatures increase, more power is emitted and the are commonly shown in graphs of intensity against wavelength at which the maximum power is emitted, λmax, becomes smaller. wavelength. At 3000 K, only a small proportion of the emitted radiation is visible light. This proportion increases with temperature and, if the surface it hot enough, some ultraviolet radiation will also be emitted. If an object is heated (without chemical reactions occurring), a metal bar for example, it will begin to emit visible light (the red end of the spectrum) at about 850 K. If the temperature rises, other colours will be emitted, combining to give the overall effects seen in Figure B1.27. Note that ‘perfect’ emitters are called black bodies, but that does not mean that they will always appear black. The Sun has a surface temperature of about 5800 K and it is a good example of a black body, so we may assume that it absorbs all the radiation falling on it; however, it is so hot that it emits enormous quantities of visible light. We are familiar with the visible spectrum, but its full black-body spectrum extends into the infrared and ultraviolet. B.1 Thermal energy transfers 193 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 193 04/01/2023 20:44  per wavelength interval UV Visible Infrared 14 5000 K 12 –2 Relative power/mW 10 8 6 4000 K 4 2 3000 K 0 0 0.5 1 1.5 2 2.5 3 –6 m Wavelength/10 Figure B1.26 Black-body emission spectra at three different temperatures 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 Temperature/K Figure B1.27 Colours of hot surfaces ◆ Stefan–Boltzmann law Since everything emits thermal radiation, all bodies are continuously emitting and receiving An equation that can be radiation. In practice, we may assume that one of these is insignificant compared to the other. used to calculate the total For example, the radiation absorbed by the Sun is insignificant compared to the energy it emits. power radiated from the surface of a black body, However, this is not true when we consider the Earth. See next Topic B.2: Greenhouse effect. P = σAT 4. σ is known as The total power, P, emitted (across all wavelengths) from a perfect black body of surface area A the Stefan–Boltzmann can be calculated from the Stefan–Boltzmann law: constant. power emitted from a black body, P = σAT 4 D B σ is known as the Stefan–Boltzmann constant. It has the value of 5.67 × 10−8 W m−2 K−4 194 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 194 04/01/2023 20:44  ◆ Celestial objects Any When referring to celestial objects (stars, for example), the emitted power is usually called naturally occurring objects luminosity, as discussed below. that can be observed in space. WORKED EXAMPLE B1.4 A metal wire is heated (by an electric current) to a uniform 632 °C. If its length, l, is 80 cm and its radius, r, is 1.6 mm, calculate the total power it radiates into its surroundings. Assume that it acts as a perfect black body (which is almost true). Answer DB Surface area, A = 2πrl = 2π × 0.0016 × 0.80 = 8.04 × 10−3 m2 P = AσT 4 = (8.04 × 10−3) × (5.67 × 10−8) × (632 + 273)4 = 3.1 × 102 W Top tip! We can also use the same equation for the energy absorbed by an object from its surroundings: P = σT 4 A If the surrounding temperature is Ts, then the overall (net) radiant energy flow per second from, or to, a black body of area A is: P = σAT 4 – σATs4. For example, using this equation, we can calculate that a black-body surface at 100 °C radiates thermal energy at a rate of 1.1 kW m−2. At the same time, if the surrounding temperature is 20 °C, it will be receiving energy at a rate of 0.42 kW m−2. Tool 2: Technology Use sensors Infrared scanners and hand-held thermometers (Figure B1.28) have become commonplace in recent times. They detect the thermal radiation emitted by our skins and other surfaces. Their advantages are obvious: they are quick and easy to use, and they do not involve any physical contact. But they have their limitations. Infrared scanners assume that all skin behaves as a perfect black body. That is, the results from skins of different colours or textures are approximately the same. The radiation coming from the skin is focused onto a detector which effectively determines the power and calculates the corresponding temperature of the emitting surface. If the distance between the skin and the detector increases, the detector may receive less radiation from each square millimetre but may receive from a greater overall area: it depends on the geometry of the situation. Figure B1.28 Infrared thermometer B.1 Thermal energy transfers 195 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 195 04/01/2023 20:44  Wien’s displacement law There is a straightforward inverse relationship between surface temperature, T, and the wavelength at which the maximum power is received, λmax. 1 T∝ λmax This is known as Wien’s displacement law: DB λmaxT = 2.9 × 10 –3 mK ◆ Wien’s displacement law Relationship between WORKED EXAMPLE B1.5 absolute temperature and Determine the temperature corresponding to a surface which emits its maximum power the wavelength emitted with maximum power with a wavelength of 5.8 × 10−7 m. by a black body at that temperature. Answer λmaxT = 2.9 × 10−3 5.8 × 10−7 × T = 2.9 × 10−3 T = 5.0 × 103 K This is consistent with Figure B1.26. Although a ‘perfect’ black body is an idealized concept, the following may approximate to the ideal: l very hot objects l dark and dull surfaces l water l human skin l ice l soil l vegetation In Topic B.2, we will introduce the numerical concept of emissivity: the ratio of the power radiated per unit area by Figure B1.29 The Great Lakes in North America a surface compared to that of an ideal black surface at the appearing dark / black from Space same temperature. 32 Give an everyday example of: 34 An object’s surface is at 25 °C. Determine the a a dark surface being good at absorbing temperature (°C) to which it would have to be heated in thermal energy order to double the thermal radiation that it radiates. b a dark surface being good at emitting thermal energy 35 A water storage tank is in sunlight most of the day and c a white or shiny surface being good at reflecting its surface reaches a constant temperature of 36 °C. At thermal energy night the surroundings cool to 23 °C. Estimate the net d a white or shiny surface being poor at emitting flow of radiant thermal energy from each square metre of thermal energy. the tank’s surface assuming that the surface temperature 33 a Calculate the maximum thermal power radiated away remains constant. from each square centimetre of a coffee cup which has a surface temperature of 40 °C. b Explain why your answer will be an overestimate of the actual power emitted. 196 Theme B: The particulate nature of matter 369917_06_IB_Physics 3rd_Edn_SEC_B_1.indd 196