Thermal Physics - Engineering Physics PDF

Thermal Physics – Engineering physics Table of Contents 2. THERMAL PHYSICS 2 2.1 HEAT & TEMPERATURE 2 2.2 TEMPERATURE AND TEMPERATURE SCALES 2 2.3 THERMAL EX...

Thermal Physics – Engineering physics Table of Contents 2. THERMAL PHYSICS 2 2.1 HEAT & TEMPERATURE 2 2.2 TEMPERATURE AND TEMPERATURE SCALES 2 2.3 THERMAL EXPANSION 3 2.4 THERMAL EQUILIBRIUM (the 0th and the 2nd laws of thermodynamics) 4 st 2.5 HEAT TRANSFER (the 1 law) 5 2.6 THERMAL CONDUCTION 5 2.7 THERMAL INSULATION 6 2.8 CONVECTION 7 2.9 HEAT CAPACITY 8 2.10 LATENT HEAT 8 2.11 HEATING CURVE FOR WATER 9 2.12 RADIATION 12 2.14. EMISSIVITY 13 2.15. STEFAN’S LAW 13 A1 APPENDIX – WAVES - CHARACTERISATION 15 A2 APPENDIX – TYPES OF WAVES 16 A3 APPENDIX - ELECTROMAGNETIC WAVES 17 THERMAL PHYSICS SAMPLE PROBLEM SHEET 19 1  2. THERMAL PHYSICS 2.1 HEAT & TEMPERATURE Heat is a form of energy. Heat relates to the internal energy [total kinetic energy of all the molecules and the potential energy of their interaction] of the body. Often, symbol U denotes internal energy. The unit is Joules [J]. When heat is supplied to a material: The temperature of the material may increase. Its internal energy increases. Its volume usually expands [its density decreases]. The state [or phase] of the material may change. It may change from a solid to a liquid, or from a liquid to a gas. 2.2 TEMPERATURE AND TEMPERATURE SCALES Temperature The temperature of a material is related to the average kinetic energy of all the molecules. Commonly, T is used. Temperature is a macroscopic parameter (it characterises the body as a whole) and the average kinetic energy is a microscopic parameter (it characterises small particles that composes the body). Any body consists of a huge amount of particles, their energies have certain distribution and we cannot measure the kinetic energy of each particle, but we can measure the temperature of a body which relates to the average kinetic energy of the particles. Temperature is a measure of the ‘hotness’ of a material represented as a number on a chosen temperature scale (Celsius, Kelvin etc). When a body is heated its temperature will rise, other than at its melting and boiling points, where the heat is used to break chemical bonds. Thermometer Thermometers are devices for measuring temperature by indicating changes in the thermometric properties of substances in the sensing element of the thermometer. A thermometric property is a physical property of a thermometer, which changes continuously with changing temperature; should not be affected by other parameters; should change, ideally, linearly (but sometimes not linearly). Thermometer Thermometric Property Clinical thermometer Liquid expansion (glass thermometer) Resistance thermometer Resistance change Thermocouple Generation of a voltage Colour thermometer Colour change Temperature scales In order to establish a temperature scale on a thermometer it is necessary to have: 1. A thermometric property (in the sensing element) 2. A number of fixed points – reference or calibration points such as freezing/melting/triple points of pure substances. 3. A defined scale eg 0 to 100. Celsius scale Unit: Celsius; Symbol: oC. This has two fixed points: Lower fixed point: The freezing point of water. The temperature of pure melting ice at a pressure of 1 standard atmospheric pressure of 760 mm Hg. This point is zero on the scale (0 oC). Upper fixed point: The boiling point of water. The temperature of steam from water boiling at 1 Standard atmospheric pressure of 760 mm Hg. This point is 100 on the scale. 2 Between the lower and upper fixed points are 100 equal degrees. Temperatures below 0 oC have negative values. Kelvin scale (aka Absolute scale) Unit: Kelvin; Symbol K. Lower fixed point: 0K – ’Absolute Zero’. Absolute Zero – 0 Kelvin - is the temperature at which the pressure of a fixed mass of an ideal gas is zero. On this scale, this is the lowest possible temperature. There are NO negative temperatures. Upper fixed point: For 1954-2019, the Triple Point of Water was used as an upper fixed point of the absolute scale. A triple point of water is when pure distilled water, ice and water vapour at a pressure of 610 Pa are in equilibrium. This is defined as 273.16 K. A temperature of 1 Kelvin was defined as 1 K = 1/273.16 of the temperature of the triple point of water. Since May, 2019, the degrees of the Kelvin scale have been redefined through particle kinetic theory and statistical mechanics. In SI, the magnitude of the Kelvin is defined through various empirical measurements of the average kinetic energies of microscopic particles. 1 Kelvin is now evaluated in terms of the Boltzmann constant, which allows to link the temperature value in kelvin with the kinetic energy of the particles. Conversions (approx). between the Celcius and Kelvin scales Kelvin (K) Celcius (OC) 0 -273 273 0 (water mp/fp) 373 100 (water bp) Many formulas are written for temperature values in Kelvin. You should always check, if in doubt. If you need the temperature in K but you know the temperature in C, first convert C to K and then use the value in the formula. Ex.2.2 Prove: the change of temperature in K is equivalent to the change in temperature in C : ∆𝑇[𝐾] = ∆𝑇[𝐶]. Fundamental interval of a thermometer This is the change in value of the thermometric property between lower and upper fixed point temperatures. International temperature scale 1990 (ITS-90) This scale is used in Instrumentation and Control. The ITS- 90 not only defines a temperature scale, but also fixed points and reference thermometers to define the scale. 1. Uses the Kelvin as the unit of temperature measurement. 2. A number of primary and secondary fixed points are used to define the scale. These are equilibrium states (freezing points and triple points) of pure substances – see table. 3. Standard instruments are used to define the scale (reference thermometers to calibrate other thermometers): a. Platinum resistance thermometers (13.8 K to 1064OC) b. Radiation Methods (Pyrometers) – temperatures above 1064 OC. 2.3 THERMAL EXPANSION When materials are heated, they expand. Example: This physical phenomena has a practical application. The expansion of mercury is used as a thermometric property in a mercury thermometer: the length of the mercury column in a clinical thermometer increases as the measured temperature increases. The volume of mercury in the thermometer also increases. Different materials will expand by different amounts for the same temperature change. The property of a material which represents the expansion for a change in length is called the Coefficient of Linear Expansion (. This is the fractional change in length per unit temperature (i.e. per oC or K !). Units: oC-1 or K-1 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑙𝑒𝑛𝑔𝑡ℎ 𝛼= 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 3 Let’s consider a material that has an original length L0 and a new length L when the temperature changes from T 0 to T Original Temperature Higher Temperature L T0 T L0 L0 L L = L - L0 - is the change in length (expansion or contraction: for expansion ∆𝐿 > 0, for contraction ∆𝐿 < 0 ) ∆𝐿 – is the fractional change in length; 𝐿0 T = T - T0 - is the change in temperature Hence, the equation for the coefficient of linear expansion 𝛼 can be written as ∆𝐿 𝛼= 𝐿0 ∆𝑇 This equation tells how to define 𝛼 (in other words, its physical meaning) and gives that the change in length L is: ∆𝐿 = 𝛼𝐿0 ∆𝑇 Linear Thermal Expansion Equation Ex.2.3. How much will a steel bridge of length 200m expand if the temperature changes from 20C to 40C. For steel α=1.2x10-5 C-1. Answer: Known Solution  = 1.2 x 10-5 oC-1 for steel Expansion = L =  L0 T T0 = 20oC T = 40 oC T = T - To = 40 -20 = 20oC L0 = 200 m L = 12 x 10-6 x 200 x 20 Required L = 4.8 x 10-2 m [4.8 cm] L (change in length) - ? 2.4 THERMAL EQUILIBRIUM (the 0th and the 2nd laws of thermodynamics) The temperature changes when the heat is supplied to the body (temperature increases) or when the heat is lost (temperature decreases). When a material is at a constant temperature, it is said to be in thermal equilibrium with its surroundings: the material gains heat and loses heat at the same rate,s i.e. there is no NET change in its internal energy. Bodies in contact: When two bodies are in contact and there is no net transfer of heat between them, then they are in thermal equilibrium – they are at the same temperature. Zeroth Law: When two bodies A and B are in thermal equilibrium with a third body C, then they are also in thermal equilibrium with each other. Therefore, all the three bodies A, B and C have the same temperature. HEAT 20oC 20oC 50oC 0oC NO HEAT TRANSFER HEAT TRANSFERRED FROM HOT BODYTO COLD BODY 4 Heat will only flow between two bodies if there is a temperature difference between them. The second law: Heat always flows from the body with the higher temperature to the body with the lower temperature. Heat will flow until the two bodies will reach thermal equilibrium, meaning they will have the same temperature. Hotter body will cool down and the colder body will heat up until both of them will reach the same final temperature – the temperature of thermal equilibrium. The hotter body which cools down loses its internal energy, meaning the final value of internal energy 𝑈𝑓𝑖𝑛𝑎𝑙 is smaller than the initial value of the internal energy 𝑈𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑈𝑓𝑖𝑛𝑎𝑙 < 𝑈𝑖𝑛𝑖𝑡𝑖𝑎𝑙 Therefore, its change of energy is negative: ∆𝑈ℎ𝑜𝑡𝑡𝑒𝑟 = 𝑈𝑓𝑖𝑛𝑎𝑙 − 𝑈𝑖𝑛𝑖𝑡𝑖𝑎𝑙 < 0 The colder body that will heat up will have its internal energy increased, therefore the final value of internal energy 𝑈𝑓𝑖𝑛𝑎𝑙 is higher than the initial value of the internal energy 𝑈𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑈𝑓𝑖𝑛𝑎𝑙 > 𝑈𝑖𝑛𝑖𝑡𝑖𝑎𝑙 Then, the change of energy is positive: ∆𝑈𝑐𝑜𝑙𝑑𝑒𝑟 = 𝑈𝑓𝑖𝑛𝑎𝑙 − 𝑈𝑖𝑛𝑖𝑡𝑖𝑎𝑙 > 0. 2.5 HEAT TRANSFER (the 1st law) In order to raise the temperature of a body we must transfer the energy to raise its internal energy (ΔU > 0). This can be done in two ways: via supplying heat (Q) or doing the work (W): ∆𝑈 = 𝑄 + 𝑊 -this is the 1st law of thermodynamics. Sigh conversion: if the heat is added to the system, it is positive (Q > 0) (and it increases the internal energy), but if the energy is lost by the system, it is negative (Q < 0) (and the internal energy reduces). Similarly, if the work is done ON the system, it increases its internal energy and is positive (W > 0), if the system is doing the work, its internal energy reduces and W 10-4 < 1013 The values listed in the tables are approximate. The higher the frequency of the radiation, the higher the energy. 17 A5 APPENDIX - THERMAL PHYSICS EQUATIONS 𝑸 Power (heat rate) 𝑷= 𝒕 Thermal Expansion: L =  L0 T k A [T1 - T2 ] Thermal Conductivity Equation: P = L 𝑷 U-value 𝑼= 𝑨𝚫𝑻 Wien’s Law: max T = Constant = 2.9 x 10-3 m K (T in Kelvin) Stephan-Boltzmann Equation: P = σ A ε T4 (Negligible radiation absorbed from surroundings) P' = σ A ε (T4 - T04 ) (T in Kelvin) Heat Capacity Equation: Q = m C T Latent Heat Equations: Q = m Lf; (Latent Heat of Fusion) Q = m Lv (Latent Heat of Vaporisation) 18 THERMAL PHYSICS SAMPLE PROBLEM SHEET 1. The tungsten filament of a lamp has a length of 0.5 m and a diameter of 60 m. The power rating of the lamp is 60 W. Assuming the radiation from the filament is equivalent to 80% of that of a perfect black body radiator at the same temperature, estimate the steady state temperature of the filament. The absorption of radiation from the surroundings is negligible. 2. In a sterilising procedure, 0.50 kg of hot water at 95 oC is poured into a 0.35 kg aluminium container. If the container is at an initial temperature of 10 oC calculate the final temperature of the system. [Assume that the system comes to thermal equilibrium quickly and ignore heat losses to the surroundings]. [Cwater = 4200 J kg-1K-1; CAl = 900 J kg-1 K-1]. 3. Calculate the amount of heat required to melt 200g of ice at 0 oC. How much heat is given out by the same mass of steam when it condenses into water at 100 oC. (Lf = 330 kJ kg-1; Lv = 2.3 M J kg-1) 4. A camper has left his kettle boiling on a gas cooker. The cooker supplies 690 kJ of heat to boil 300 g of water in 4 minutes 35 seconds. What is the value of the Specific Latent Heat of Vaporisation of water? What is the power rating of the kettle? 5. The concrete block wall of a house has dimensions of 8.0 m length by 3.0 m height by 120 mm thickness. The thermal conductivity of concrete (kc) is 1.3 W K-1m-1]. The inside temperature is 18oC and the outside temperature is 10oC. Determine the: (a) Rate of loss of heat through the wall, (b) Total heat loss in 1 hour. 6. A cast iron fire grate has a width of 35 cm at 20 oC. How much will it expand when the fire reaches a temperature of 820 oC. (The coefficient of linear expansion of iron =  = 1.2 x 10-5 oC-1). 7. A round window of a room has a diameter of 2.50 m and a thickness of 4.0 mm. The internal temperature of the room is 20.0oC and the external temperature is -4.0oC. The thermal conductivity of the glass = kg = 0.60 Wm-1K-1. Determine the: (a) Rate of heat loss [P] through the window; (b) Total heat loss [Q] in 20 minutes. 19