普通物理 General Physics 18 - First Law of Thermodynamics 郭艷光 Yen-Kuang Kuo 國立彰化師大物理系暨光電科技研究所 電子郵件：ykuo@cc.ncue.edu.tw 網頁：http://ykuo.ncue.edu.tw

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Outline 18-1 What Is Physics? 18-2 Temperature 18-3 The Zeroth Law of Thermodynamics 18-4 Measuring Temperature 18-5 The Celsius and Fahrenheit Scales 18-6 Thermal Expansion 18-7 Temperature and Heat 18-8 The Absorption of Heat by Solids and Liquids 18-9 A Closer Look at Heat and Work 18-10 The First Law of Thermodynamics 18-11 Some Special Cases of the First Law of Thermodynamics 18-12 Heat Transfer Mechanisms 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 18-1 What Is Physics? One of the principal branches of physics and engineering is thermodynamics, which is the study and application of the thermal energy (often called the internal energy) of systems. You also know how to control the temperature inside home and car, and how to protect yourself from wind chill and sunburn. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 18-2 Temperature Temperature is one of the seven SI base quantities. Physicists measure temperature on the Kelvin scale, which is marked in units called kelvins. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-3 The Zeroth Law of Thermodynamics The zeroth law of thermodynamics: If bodies A and B are each in thermal equilibrium with body T, then A and B are in thermal equilibrium with each other. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-4 Measuring Temperature 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-5 The Celsius and Fahrenheit Scales If Tc represents Celsius temperature and T is Kelvin temperature, then: TF is Fahrenheit temperature. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-1 Suppose you come across old scientific notes that describe a temperature scale called Z on which the boiling point of water is 65.0o Z and the freezing point is－14.0o Z. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 8

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-1 To what temperature on the Fahrenheit scale would a temperature of T =－98.0o Z correspond? Assume that the Z scale is linear; that is, the size of a Z degree is the same everywhere on the Z scale. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 9

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-1 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 10

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 18-6 Thermal Expansion Linear expansion: The metal rod of length L is increased by an amount ΔT. α is the coefficient of linear expansion. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 18-6 Thermal Expansion Depends on the material of the rod. The constant α does not change very much with temperature. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-2 On a hot day in Las Vegas, an oil trucker loaded 37000 L of diesel fuel. He encountered cold weather on the way to Payson, Utah, where the temperature was 23.0 K lower than in Las Vegas, and where he delivered his entire load. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 13

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-2 How many liters did he deliver? The coefficient of volume expansion for diesel fuel is 9.50×10－4/Co, and the coefficient of linear expansion for his steel truck tank is 11×10-6/Co. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 14

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-2 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 15

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 18-7 Temperature and Heat Heat is the energy transferred between a system. SI unit for Q: The Joule (J) Another non-SI unit : calorie (cal) Defined as : 1 cal = 4.1868 J 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-8 The Absorption of Heat by Solids and Liquids Heat Capacity: Q = CΔT = C (Tf－Ti) Specific Heat: Q = mc (Tf-Ti) Molar specific Heat The heat capacity that corresponds to one mole of a substance 1 mole = The same number 6×1023 of atoms and molecules 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-8 The Absorption of Heat by Solids and Liquids Heats of Transformation: = Lm The constant L is known as the heat of transformation For water at its normal boiling or condensation temperature: LV = 539cal/g = 40.7kJ/mol = 2256 kJ/kg For water at its normal freezing or melting temperature : LF= 79.5 cal/g = 6.01 kJ/mol = 333 kJ/kg 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-3 How much heat must be absorbed by ice of mass m = 720 g at －10oC to take it to liquid state at 15oC? 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 19

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-3 If we supply the ice with a total energy of only 210 kJ (as heat), what then are the final state and temperature of the water? 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 20

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-4 A copper slug whose mass mc is 75 g is heated in a laboratory oven to a temperature T of 312℃. The slug is then dropped into a glass beaker containing a mass mw = 220 g of water. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 21

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-4 The heat capacity Cb of the beaker is 45 cal/K. The initial temperature Ti of the water and the beaker is 12℃. Assuming that the slug, beaker, and water are an isolated system and the water does not vaporize, find the final temperature Tf of the system at thermal equilibrium. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 22

18-8 The Absorption of Heat by Solids and Liquids 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 23

18-8 The Absorption of Heat by Solids and Liquids 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 24

18-9 A Closer Look at Heat and Work 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 彰化師大教學卓越－普物教材－理學院長郭艷光主持

18-10 The First Law of Thermodynamics The quantity Q-W is the same for all processes. The first law of thermodynamics: ΔEint = Eint,f － Eint,i = Q－W In differential form: dEint = dQ – dW The internal energy Eint of a system tends to increase if energy is added as heat Q and tends to decrease if energy is lost as work W done by the system. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-11 Some Special Cases of the First Law of Thermodynamics Adiabatic process: No transfer of energy as heat occurs between the system. Putting Q = 0 in the first law of Thermodynamics, then: ΔEint = －W Constant volume process: Putting W = 0 in the first law : ΔEint = Q 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-11 Some Special Cases of the First Law of Thermodynamics Cyclical process: Putting ΔEint = 0 in the first law: Q = W The net work during a cyclical process is equal to the amount of heat transferred. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-11 Some Special Cases of the First Law of Thermodynamics Free expansion: Putting Q = W = 0 in the first law: ΔEint= 0 No work is done in the process. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 29

18-11 Some Special Cases of the First Law of Thermodynamics 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-5 Let 1.00 kg of liquid water at 100℃ be converted to steam at 100℃by boiling at standard atmospheric pressure (which is 1.00 atm or 1.01×105 Pa) in the arrangement of Figure. The volume of that water changes from aninitial value of 1.00×10－3 m3 as a liquid to 1.671 m3 as steam. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 31

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-5 How much work is done by the system during this process? How much energy is transferred as heat during the process? 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-5 What is the change in the system’s internal energy during the process? 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-12 Heat Transfer Mechanisms Conduction: The conduction rate Pcond (the amount of energy transferred per unit time) is: The constant k is known as “thermal conductivity”. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-12 Heat Transfer Mechanisms Convection and Radiation: σ (= 5.6703 × 10-8 W/m2 · K4) is the Stefan– Boltzmann constant. The rate Pabs at which an object absorbs energy via thermal radiation from its environment, which is at the uniform temperature Tenv : 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-6 Figure shows the cross section of a wall made of white pine of thickness La and brick of thickness Ld (= 2.0La), sandwiching two layers of unknown material with identical thicknesses and thermal conductivities. The thermal conductivity of the pine is ka and that of the brick is kd (= 5.0ka). 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 36

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-6 The face area A of the wall is unknown. Thermal conduction through the wall has reached the steady state; the only known interface temperatures are T1 = 25℃, T2 = 20℃, and T5 = －10℃. What is Interface temperature T4? 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

18-12 Heat Transfer Mechanisms 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 38

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-7 During an extended wilderness hike, you have a terrific craving for ice. Unfortunately, the air temperature drops to only 6.0℃ each night — too high to freeze water. However, because a clear, moonless night sky acts like a blackbody radiator at a temperature of Ts =－23℃, perhaps you can make ice by letting a shallow layer of water radiate energy to such a sky. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 39

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-7 To start, you thermally insulate a container from the ground by placing a poorly conducting layer of, say, foam rubber or straw beneath it. Then you pour water into the container, forming a thin, uniform layer with mass m = 4.5 g, top surface area A= 9.0 cm2, depth d = 5.0 mm, emissivity ε= 0.90, and initial temperature 6.0 ℃. Find the time required for the water to freeze via radiation. Can the freezing be accomplished during one night? 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-7 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 41

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-8 A tank of water has been outdoors in cold weather, and a slab of ice 5.0 cm thick has formed on its surface. The air above the ice is at －10°C. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-8 Calculate the rate of ice formation (in centimeters per hour) on the ice slab. Take the thermal conductivity of ice to be 0.0040 (cal/s · cm· C°) and its density to be 0.92 g/cm3. Assume no energy transfer through the tank walls or bottom. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-8 The rate of heat flow through the slab is Differentiate with respect to time and recognize that dQ/dt = P cond to obtain 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-8 dm/dt = rA(dh/dt) 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-9 Suppose 200 J of work is done on a system and 70.0 cal is extracted from the system as heat. In the sense of the first law of thermodynamics, what are the values (including algebraic signs) of (a) W (b) Q (c) DEint? 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 Example 18-9 (a) Since work is done on the system (perhaps to compress it) we write W = –200 J. (b) Since heat leaves the system, we have Q = –70.0 cal = –293 J. (c) The change in internal energy is DEint = Q – W = –293 J – (–200 J) = –93 J. 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授

普通物理教材-18，國立彰化師範大學物理系/郭艷光教授 End of chapter 18! 2018/12/5 普通物理教材-18，國立彰化師範大學物理系/郭艷光教授