Thermal Physics A lecture notes

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6A: Thermal Physics (I) 6A-1 H2 Topic 6A Thermal Physics (I)

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6A: Thermal Physics (I) 6A-2 Content  Temperature scales  Specific heat capacity  Specific latent heat Learning Outcomes Candidates should be able to (a) show an understanding that regions of equal temperature are in thermal equilibrium. (b) show an understanding that there is an absolute scale of temperature which does not depend on the property of any particular substance, i.e. the thermodynamic scale. (c) apply the concept that, on the thermodynamic (Kelvin) scale, absolute zero is the temperature at which all substances have a minimum internal energy. (d) convert temperatures measured in Kelvin to degrees Celsius: T / K = T / °C + 273.15. (e) define and use the concept of specific heat capacity, and identify the main principles of its determination by electrical methods. (f) define and use the concept of specific latent heat, and identify the main principles of its determination by electrical methods.

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6A: Thermal Physics (I) 6A-3 6.0 Introduction In case you have not already realised, the concept of energy is central to the study of physics. As you have just learnt in the topic of Work, Energy & Power, energy can manifest in many different forms. The topic of The rmal Physics deals with several of these manifestations, which we term “heat”, “thermal energy” or, as you will learn later, “internal energy of a substance” . This study is important because energy in these forms is respo nsible for a host of phenomena which include how “hot ” an object is, s tate changes in substances, and chemical reactions. This topic is split into two different parts. This first set of notes deals with how we perceive heat at a macroscopic level. This involves temperature and a study of the thermal properties of matter. 6.1.1 Temperature & Thermometric Properties In general, w e measure the “hotness” of an object using a concept called “temperature”. In order to construct a suitable temperature “ruler” or scale, we may rely on the thermometric properties of substances. Intuitively, a thermometric property of a substance is a physical property that varies with hotness/temperature. Examples include:  Length (of a strip of metal)  Area (of a sheet of metal)  Volume (of a column of mercury)  Pressure (exerted by a gas on the surface of a container)

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6A: Thermal Physics (I) 6A-4 A good thermometric property to set up a temperature scale would exhibit the following traits:  Measurable  Substance remains in the same state over the range of temperatures to be measured  Property varies linearly over the range of temperatures to be measured For the temperature scale that we are about to construct, we will use a column of mercury with a fixed cross sectional area. If the surroundings of the bulb get warmer, the volume of the mercury will expand , causing the height of the liquid column to rise. Conversely, if the surroundings of the bulb get colder, the volume of the mercury will contract, causing the height of the liquid column to fall.

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6A: Thermal Physics (I) 6A-5 6.1.2 The Centigrade Scale & Thermometer Calibration In order to set up any scale, we need to define a lower and a higher reference (fixed) point. As we are going to chop up the difference between these two levels of hotness into 100 parts (degrees), we shall call this particular temperature scale the “centigrade” scale As water is so commonplace in both scientific study and everyday life, it makes sense that in the temperature scale that we are about to construct, water should be involved. The lower fixed point is the melting point of water . We designa te this as 0 degrees on the centigrade scale (0∘C). The upper fixed point is the boiling point of water . We designate this as 100 degrees on the centigrade scale (100∘C) With th ese two reference points and the column of mercury mentioned above , we are now ready to properly set up the temperature scale.

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6A: Thermal Physics (I) 6A-6 The following steps describe this process: Liquid-in-glass Thermometer Calibration 1. Place the bulb of the mercury column in crushed, melting, pure ice. Measure the height of the mercury column, 𝑥0  Ice must be crushed to ensure that maximum coverage of the bulb.  Ice must be melting to ensure that the temperature is at 0 degrees. 2. Immerse the bulb of the mercury column in steam. Measure the height of the mercury column 𝑥100.  Water must be boiling to ensure that the height represents 100 degrees. Thus, the height for each degree of temperature is given by Δx ΔT = x100 − x0 100 For an unknown temperature which causes the mercury column to have a height of 𝑥?, we may thus determine the temperature by taking T = x? − x0 x100 − x0 × 100 𝑥0 𝑥100

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6A: Thermal Physics (I) 6A-7 Example 1: At ice-point, the mercury column of an unmarked thermometer has a height of 2.0 cm. At boiling point, the mercury column has a height of 24.0 cm. What is the temperature when the mercury column reads 18.0 cm? T= x?-x0 x100-x0 ×100 T= 18.0-2.0 24.0-2.0 ×100=72.7∘C In practice, we may calibrate using different thermometers and thermometric properties, and may even set the upper and lower fixed p oints at different temperatures. In which case, the formula given above may be generalised to give T = x? − xlower xupper − xlower × (Tupper − Tlower) + Tlower Example 2: A resistance thermometer gives a resistance of 20 Ω when the temperature is known to be -10 ˚C. When the temperature is 110 ˚C, the resistance thermometer has a resistance of 500 Ω. What is the temperature when the resistance is 360 Ω. T = x? − xlower xupper − xlower × (Tupper − Tlower) + Tlower T = 360 − 20 500 − 20 × [110 − (-10)] + (-10) = 75 ∘C 6.1.3 Constant Volume Gas Thermometer

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6A: Thermal Physics (I) 6A-8 Learning outcomes (c) apply the concept that, on the thermodynamic (Kelvin) scale, absolute zero is the temperature at which all substances have a minimum internal energy. The constant volume gas thermometer makes use of the pressure of the gas contained as its thermometric property. Image from http://wikipremed.com/image_science_archive_68/010301_68/125150_24801_68.jpg At the lower fixed point, the mercury level on the left limb of the manometer is recorded. The gas pressure may be determined by P lower = ρHgghlower + Patmosphere At the upper fixed point, the higher temperature causes the gas pressure to increase and force the mercury up the tube. The flexible tube is adjusted until the me rcury in the left limb is the same level as before. The new pressure is thus calculated, P upper = ρHgghupper + Patmosphere

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6A: Thermal Physics (I) 6A-9 If ice and steam points are chosen for the lower and upper fixed points, for pressures recorded at unknown temperatures, the temperature may be determined using the calibration equation in the previous section, T = P?-P0 P100-P0 × 100 When we try to plot a graph of pressure against temperature, a linear graph is formed. If the gas pressure is suitably low and the temperature much h igher than the boiling point of the substance used