3 THERMAL PHYSICS Introduction In this topic we look at at thermal processes We then go on to look at the effect of energy resulting in energy transfer between objects at changes in gases and use the kinetic theory to different temperatures. We consider how the explain macroscopic properties of gases in terms energy transfer brings about further temperature of the behaviour of gas molecules. changes and/or changes of state or phase. 3.1 Temperature and energy changes Understanding Applications and skills ➔ Temperature and absolute temperature ➔ The three states of matter are solid, liquid, ➔ Internal energy and gas ➔ Specifc heat capacity ➔ Solids have fxed shape and volume and ➔ Phase change comprise of particles that vibrate with respect ➔ Specifc latent heat to each other ➔ Liquids have no fxed shape but a fxed volume and comprise of particles that both vibrate Nature of science and move in straight lines before colliding with Evidence through experimentation other particles ➔ Gases (or vapours) have no fxed volume or Since early humans began to control the use shape and move in straight lines before colliding of fre, energy transfer because of temperature with other particles – this is an ideal gas diferences has had signifcant impact on society. ➔ Thermal energy is often misnamed “heat” By controlling the energy fow by using insulators or “heat energy” and is the energy that and conductors we stay warm or cool of, and we is transferred from an object at a higher prepare life-sustaining food to provide our energy temperature by conduction, convection, and needs (see fgure 2). Despite the importance of thermal radiation energy and temperature to our everyday lives, confusion regarding the diference between Equations “thermal energy” or “heat” and temperature is ➔ Conversion from Celsius to kelvin: commonplace. The word “heat” is used colloquially T(K) ( C) 273 to mean energy transferred because of a = θ ° + ➔ Specifc heat capacity relationship: Q mc T temperature diference, but this is a throwback to = : the days in which scientists thought that heat was ➔ Specifc latent heat relationship: Q = mL a substance and diferent from energy. Introduction From the 17th century until the end of the 19th century scientists believed that “heat” was a substance that fowed between hot and cold objects. This substance travelling between hot and cold objects was known as “phlogiston” or “caloric” and there were even advocates of a substance called “frigoric” that fowed from cold bodies to hot ones. In the 1840s James Joule showed that the temperature of a substance could be increased by doing work on that substance and that doing work was equivalent to heating. In his paddle wheel experiment (see fgure 1) he dropped masses attached to a mechanism connected to a paddle wheel; the wheel churned water in a container and the temperature of the water was found to increase. Although the caloric theory continued to have its supporters it was eventually universally abandoned. The unit “calorie” which is sometimes used relating to food energy is a residual of the caloric theory, as is the use of the word heat as a noun. 2 kg when masses fall they turn the 2 kg axle and cause the paddle wheels to churn up the water – this raises the water temperature thermometer paddles water Figure 1 Joule’s paddle wheel experiment. Temperature and energy transfer You may have come across temperature described as the “degree of hotness” of an object. This is a good starting point since it relates to our senses. A pot of boiling water feels very hot to the touch and we know instinctively that the water and the pot are at a higher temperature than the cold water taken from a refrigerator. The relative temperature of two objects determines the direction in which energy passes from one object to the other; energy will tend to pass from the hotter object to the colder object until they are both at the same temperature (or in thermal equilibrium). The energy fowing as a result of conduction, convection, and thermal radiation is what is often called “heat”. Temperature is a scalar quantity and is measured in units of degrees Figure 2 Dinner is served! Celsius (°C) or kelvin (K) using a thermometer. Nature of science Thermometers Most people are familiar with liquid-in-glass the thermometer slow to respond to rapid thermometers in which the movement of changes in temperature. a column of liquid along a scale is used to Liquid-in-glass thermometers are often calibrated measure temperature. Thermometers are in degrees Celsius, a scale based on the scale not just restricted to this liquid-in-glass type; reading at two fxed points, the ice point and the others use the expansion of a gas, the change steam point. These two temperatures are defned in electrical resistance of a metal wire, or to be 0 C and 100 C respectively (although the change in emf (electromotive force) at ° ° Celsius actually used the steam point for 0 and the junction of two metal wires of different ice point for 100). The manufacturer of the materials. A thermometer can be constructed thermometer assumes that the length of the liquid from any object that has a property that varies in the capillary changes linearly with temperature with temperature (a thermometric property). between these two points, even though it may not In the case of a liquid-in-glass thermometer actually do so. This is a fundamental assumption the thermometric property is the expansion made for all thermometers, so that thermometers of the liquid along a glass capillary tube. The only agree with each other at the fxed points – liquid is contained in the bulb which is a between these points they could well give reservoir; when the bulb is heated the liquid different values for the same actual temperature. expands, travelling along the capillary. Since the bore of the capillary is assumed to be Digital thermometers or temperature sensors constant, as the volume of the liquid increases have signifcant advantages over liquid-in-glass with temperature so does the length of the thermometers and have largely taken over from liquid. Such thermometers are simple but not liquid-in-glass thermometers in many walks particularly accurate. Reasons for the inaccuracy of life. The heart of such devices is usually a could be that the capillary may not be uniform, thermistor. The resistance of most thermistors or its cross-sectional area may vary with falls with temperature (they are known as “ntc” temperature, or it is diffcult to make sure that or “negative temperature coeffcient of resistance” all the liquid is at the temperature of the object thermistors). Since the thermistor is usually quite being investigated. Glass is also a relatively good small, it responds very quickly to temperature insulator and it takes time for thermal energy to changes. Thermistor thermometers are usually far conduct through the glass to the liquid, making more robust than liquid-in-glass ones. steam point fask ice point steam boiling water melting ice funnel beaker fnding the ice point fnding the steam point Figure 3 Calibration of a liquid-in glass thermometer at the ice point and steam point. Investigate! Calibrating a thermistor against an alcohol-in-glass thermometer This investigation can be performed by taking ● Plot a graph of resistance/E against readings manually or by using a data logger. Here temperature/°C (since this is a calibration we describe the manual way of performing the curve there can be no systematic uncertainties experiment. The temperature can be adjusted either and any uncertainties will be random – being using a heating coil or adding water at different suffciently small to be ignored in the context temperatures (including some iced water, perhaps). of this investigation). ● A multimeter set to “ohms” or an ohm-meter is ● The graph shown is typical for a “ntc” connected across the thermistor (an ammeter/ thermistor. voltmeter method would be a suitable alternative ● Suggest why, on a calibration curve, but resistance would need to be calculated). systematic uncertainties are not appropriate. ● The thermistor is clamped so that it lies below ● Would the designers of a digital thermometer the water surface in a Styrofoam (expanded assume a linear relationship between polystyrene) container next to an alcohol-in- resistance and temperature? glass thermometer. ● Would you expect the reading on a digital ● Obtain pairs of values of readings on the thermometer to correspond to that on a multimeter and the thermometer and record liquid-in-glass thermometer? these in a table. calibration of thermistor thermistor Ω thermometer 2.0×104 rubber seals 4 cardboard 1.5×10 square 4 Styrofoam cups 1.0×10 0.5×104 resistance of themistor/ of resistance 0 water 0 50 100 multimeter temperature/°C Absolute temperature The Celsius temperature scale is based on the ice point and steam point of water; by defnition all thermometers using the Celsius scale agree at these two temperatures. Between these fxed points, thermometers with different thermometric properties do not all agree, although differences may be small. The absolute temperature scale is the standard SI temperature scale with its unit the kelvin (K) being one of the seven SI base units. Absolute temperature is defned to be zero kelvin at absolute zero (the temperature at which all matter has minimum kinetic energy) and 273.16 K at the triple point of water (the unique temperature and pressure at which water can exist as liquid water, ice, and water vapour). Differences in absolute temperatures exactly correspond to those in Celsius temperatures (with a temperature difference of 1 °C being identical to 1 K). For this reason it is usual to write the units of temperature difference as K but not °C (although you are unlikely to lose marks in an examination for making Worked example this slip).