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Thermometry Mike Follows ... a hot topic Temperature and how we measure it is one of the most important and interesting areas of physics. This is reflected in the huge number and variety of thermometers that have been developed. In this article, Mike Follows describes the surprising range of thermometers available to scientists today. M any physical properties of materials depend on temperature. Our biochemical reactions work best at 37°C and we are in serious danger if our body temperature strays more than a couple of degrees either way. Being able to record the global mean surface temperature of the Earth is important in order to establish the magnitude of global warming. We have even found ways of working out how the temperature of the Earth has changed over the last half a million years as well as the temperature of distant stars and of Outer Space itself. Thermometer history The thermometer has been more of a development than a single invention. Philo of Byzantium (280 220 BC) was aware that air expands and contracts with changes in temperature and described a demonstration that was developed by Galileo to become his air thermometer or thermoscope in around 1600. This consisted of a glass bulb containing air with a long tube extending downward into a container of wine or other coloured liquid (see figure 2). Engraving a scale on the tube converted the thermoscope into the first thermometer. Key words temperature thermometer Kelvin scale ideal gas Air Some definitions The temperature of a substance is a measure of the average kinetic energy of the constituent molecules – the faster the molecules are moving or vibrating, the hotter the body will feel. Temperature also tells you the direction that heat or thermal energy will flow; it flows down a thermal gradient from a hotter body to a colder body. In the process, the hot body will lose thermal energy to the cold body. What is a thermometer? The word thermometer comes from the Greek thermos (meaning ‘hot’) and metron (‘measure’). Figure 1 shows a mercury-in-glass thermometer. As with most thermometers, it comprises a thermometric substance that changes in response to temperature (mercury expands on being heated) as well as a means of converting this physical change into a numerical value (the visible scale marked on the glass). Wine Figure 2 A thermoscope – as the air is heated, it expands and pushes the liquid down the tube. On cooling, the air contracts and atmospheric pressure pushes the liquid back up the tube. Figure 1 A mercury-in-glass thermometer The Galilean thermometer (Figure 3) was developed after Galileo’s death, based on principles that he developed. Each glass bulb is partially filled with a coloured liquid and has a metal disc, engraved with the temperature, suspended from it. The bulbs are adjusted by varying the mass of each metal disc so that they all have slightly different densities. When they are immersed in the column of liquid paraffin, they will float if they are less dense than the paraffin, and sink if they are more dense. – as the mercury gets warmer, it expands Figure 3 A Galilean thermometer shows and rises up the tube. the temperature of its surroundings. Catalyst February 2013 13 If the temperature rises, the paraffin expands and becomes less dense. One or more bulbs will now be too dense to float, and will sink. (The density of each bulb is fixed because neither its mass nor volume changes with temperature.) The temperature is then shown by the metal disc on a bulb which is free-floating in the gap. Galileo’s thermometer has the advantage that it is not affected by changes in air pressure in the way that his thermoscope was. The Galilean thermometer uses paraffin because the density of water changes very little in response to changes in temperature. temperature range from about minus 260 °C to 1000 °C. Driven by the voltage between the ends of the metallic resistor, the free electrons drift along. However, increasing the temperature of the resistor increases the vibration of the metal atoms. In turn, this increases the number of collisions between the atoms and the electrons, slowing them down. This reduces the current – the resistance has increased. Though the platinum resistance thermometer is fairly reproducible, it is regarded as a secondary thermometer as it needs to be calibrated against a primary thermometer. Ideal gases Glowing Many different thermometers followed but, in 1780, Jacques Charles returned to the gas thermometer. He showed that, for the same increase in temperature, all gases exhibit the same increase in volume. In a similar way, the pressure of a gas increases as it is heated if its volume is fixed – see figure 4. Hot objects glow – they radiate light. We can use this to find out the temperatures of hot objects, even distant stars and deepest space. When heated, the colour of metals pass through red, orange and yellow. Eventually, they become white hot when all the colours of the visible spectrum are emitted. They also glow more brightly because they are hotter and more thermal energy is emitted. Figure 5 shows how the spectrum of a hot object changes as it is heated. In this graph: • the x-axis shows the wavelength of the light • the y-axis shows the intensity of the light. You can see that, as the temperature increases, the peak in the graph gets higher – more energy is being radiated. At the same time, the peak moves to the left, to lower wavelengths which are more energetic. Figure 4 Measurements of the pressure of a gas show that pressure increases linearly with temperature. Notice that the graph in figure 4 can be extrapolated to zero pressure. The graph intersects the horizontal temperature axis close to minus 273.15 °C. This is absolute zero and so the absolute temperature scale was created. Sometimes called the Kelvin scale, it is regarded as the fundamental measure of temperature. The Celsius and Kelvin scales are related by the equation: K = °C + 273.15 Because the temperature can be calculated without any unknown quantities, thermometers based on an ideal gas are known as primary thermometers. Going electrical Gas thermometers are not very convenient or easy to use so, in 1871, Sir William Siemens introduced the Platinum Resistance Thermometer. This is now widely used as a thermometer and covers the 14 Catalyst February 2013 Figure 5 The spectrum of light radiated by a hot object depends on its temperature. The peak wavelength λmax (in m) is related to temperature T (in K) by the equation λmax × T = 0.0029. We can use this to find the temperature of a distant object such as a star. A telescope can be linked to a spectroscope that measures radiation intensity across the electromagnetic spectrum. The star’s temperature can be deduced from the peak wavelength. In 1964, Arno Penzias and Robert Wilson, two radio astronomers, accidentally discovered the cosmic background radiation, the afterglow of the Big Bang. From its spectrum, we now know its temperature to be 2.73 K – see figure 6. The cricket as a thermometer To many, the sound of chirping crickets is synonymous with summer. Only the males stridulate, which is the scientific term for chirping, and they do this to attract a female. Amos Dolbear noticed that the frequency of chirping of the narrow-winged tree cricket Oecanthus niveus depended on the prevailing air temperature and, in 1897, he published his law relating the temperature T to the number of chirps per minute N: T = 10 + (N - 40)/7 Figure 6 The spectrum of cosmic background radiation, as measured by the COBE satellite. The line shows that it corresponds to a temperature of 2.728 K. © Nick Strobel www.astronomynotes.com This is the equation of a straight-line graph. Why does the chirping frequency increase with temperature? Well, crickets are cold-blooded. As the temperature rises, it becomes easier to reach the activation energy required for the chemical reactions that drive the muscle contractions used to produce chirping, so they happen more often. Proxies We can work out the Earth’s past temperature and climate using proxy thermometers. Dendrochronology is probably the best known technique and uses the width of tree rings to infer past climate. Wide tree rings correspond to conditions that favour growth. We can go back almost half a million years using the ice cores that are being drilled out of the Antarctic ice at Lake Vostok. Apart from the measuring the concentration of greenhouse gases like methane, isotopes of oxygen can also be analysed. There are two important isotopes of oxygen, 16O and the heavier 18O. Water molecules with 16O atoms are lighter and evaporate more easily. Water with 18O atoms is heavier and is rained out more easily when the water vapour condenses. In a colder world, more of the heavier water is rained out before it reaches the poles so that polar ice has a smaller fraction of the 18O isotope. This can be used to infer past temperature – see figure 7. This graph shows that the rate of chirping of the snowy tree cricket Oecanthus fultoni shows the same pattern as Dolbear’s crickets as the temperature increases. Published by Thomas J. Walker in the Annals of the Entomological Society TJ Walker of America in 1962. Figure 7 Past temperature variations deduced from oxygen-isotope measurements of an Antarctic ice core. Ice formed 450 000 years ago was found at a depth of over 3 km. A male snowy tree cricket Mike Follows teaches Physics Catalyst February 2013 15