PHYSICS 220. Lecture 25. Textbook Sections Lecture 25 Purdue University, Physics 220 1

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1 PHYSICS 220 Lecture 25 Heat Transfer Textbook Sections Lecture 25 Purdue University, Physics 220 1

2 Overview Last Lecture Heat is FLOW of energy Flow of energy may increase temperature Specific Heat ΔT = Q / (c m) Monatomic IDEAL Gas C V = 3/2 R Diatomic IDEAL Gas C V = 5/2 R Latent Heat Heat associated with change in phase Today Thermal Conduction Thermal Convection Thermal Radiation Lecture 25 Purdue University, Physics 220 2

3 Quiz 1 On a cool night you make your bed with a thin cotton sheet covered by a thick wool blanket. As you lay there all covered up, heat is leaving your body, flowing though the sheet and the blanket and into the air of the room. Compare the amount of heat that flows though the sheet to the amount of heat that flows through the blanket. A)More heat flows through sheet than through the blanket. B)More heat flows through blanket than through the sheet. C) The same amount of heat flows through sheet as the blanket. Lecture 25 Purdue University, Physics 220 3

4 Latent heat is always Quiz 2 A) part of the specific heat B) related to the specific heat C) the same as the mechanical equivalent of heat D) involved in a phase change Lecture 25 Purdue University, Physics 220 4

5 Heat Transfer Heat is the energy that flows between systems at different temperatures This transfer can take place in three ways Conduction Convection Radiation Lecture 25 Purdue University, Physics 220 5

6 Heat Conduction The bar is placed between two separate systems at different temperatures The bar conducts heat The bar s temperature varies smoothly from T 1 to T 2 Lecture 25 Purdue University, Physics 220 6

7 Heat Transfer: Conduction Hot molecules have more KE than cold molecules High-speed molecules on left collide with lowspeed molecules on right energy transferred to lower-speed molecules heat transfers from hot to cold I = rate of heat transfer = Q/t [J/s] I = κ A (T H -T C )/d Q/t = κ A ΔT/Δx κ = thermal conductivity Units: J/s-m-C good thermal conductors high κ good thermal insulators low κ R=d/(Aκ) = thermal resistance T H Hot Area A d = Δx T C Cold Lecture 25 Purdue University, Physics 220 7

8 Heat Conduction The amount of energy that flows depends on The area of the bar, A The length of the bar, L The temperature difference between the two ends A property of the bar called thermal conductivity, κ The rate of heat flow is given by Q t = κ A ΔT L Lecture 25 Purdue University, Physics 220 8

9 Conduction Which of the following is an example of conductive heat transfer? A) You stir some hot soup with a silver spoon and notice that the spoon warms up. B) You stand watching a bonfire, but can t get too close because of the heat. C) Its hard for central air-conditioning in an old house to cool the attic. Lecture 25 Purdue University, Physics 220 9

10 Conduction with 2 Layers Find I=Q/t in J/s Key Point: Continuity (just like fluid flow) I 1 = I 2 κ 1 A(T 0 -T C )/Δx 1 = κ 2 A(T H -T 0 )/Δx 2 solve for T 0 = temp. at junction then solve for I 1 or I 2 answers: T 0 =2.27 C I=318 Watts T H-T 0 = I R 1 and T 0-T C = I R 2 I 1 I 2 ΔT = (T H -T 0 ) + (T 0 -T C ) = I (R 1 + R 2 ) Outside: T C = 0C Inside: T H = 25C Δx = = m A 1 35 m k 1 = J/s-m-C Δx 2 = m A 2 = 35 m 2 k 2 = J/s-m-C T 0 Lecture 25 Purdue University, Physics

11 ILQ Touch the metal base of a chair and the top of a wooden desk in an air-conditioned room, which feels colder? A) Base B) Same C) Desk Both must be the same temperature (room temperature), t but metal feels colder because it conducts heat better/faster. Lecture 25 Purdue University, Physics

12 Metals Feel Cold If a metal and another material (such as Styrofoam) are at the same temperature, they generally do not feel the same The metal feels colder The thermal conductivity of metal is much higher than that of Styrofoam The rate of heat flow from your fingers to the metal is much higher than to the Styrofoam Therefore, e e, the metal causes your skin to have a lower temperature and it feels colder Lecture 25 Purdue University, Physics

13 Convection Convection is based on thermal expansion The warmer material on the bottom (nearer the heat source) becomes less dense The warm, low-density material moves upward due to the buoyant force associated with Archimedes principle Lecture 25 Purdue University, Physics

14 Convection As the warmer material moves upward, it cools through conduction to heat the cooler parts of the container and the air above A circular pattern is developed Convection plays a role in heating and transporting energy in A house Oceans Atmosphere Lecture 25 Purdue University, Physics

15 Heat Transfer: Convection Air heats at bottom Thermal expansion density gets smaller Lower density air rises Archimedes: low density floats on high density Cooler air pushed down Cycle continues with net result of circulation of air I = Q/t = h A ΔT h = coefficient of convection Practical aspects heater ducts on floor A/C ducts on ceiling stove heats water from bottom riding the thermals Lecture 25 Purdue University, Physics

16 Convection Lecture 25 Purdue University, Physics

17 Convection Which of the following is an example of convective heat transfer? A) You stir some hot soup with a silver spoon and notice that the spoon warms up. B) You stand watching a bonfire, but can t get too close because of the heat. C) Its hard for central air-conditioning in an old house to cool the attic. Lecture 25 Purdue University, Physics

18 Convection Lecture 25 Purdue University, Physics

19 Radiation Radiative heat flow involves energy carried by electromagnetic (em) radiation Electromagnetic radiation is a type of wave and can be characterized by frequency, wavelength and speed The waves carry energy Lecture 25 Purdue University, Physics

20 Radiation Electromagnetic radiation is generated any time an electric charge vibrates or undergoes an acceleration The vibrations of the atoms generate em radiation that carries energy away The vibration amplitude of the atoms depends on the temperature, so the radiated energy depends on temperature The energy is absorbed by another object when the radiation produces a force on the electric charges in that object Lecture 25 Purdue University, Physics

21 Electromagnetic Rainbow Lecture 25 Purdue University, Physics

22 Heat Transfer: Radiation All things radiate electromagnetic energy I emit = Q/t = eaσt 4 Stefan-Boltzmann Law e = emissivity (between 0 and 1) perfect black body has e=1 T is the temperature of the object (in Kelvin) σ = Stefan-Boltzmann constant = 5.67 x 10-8 J/s-m 2 -K 4 No medium required All things absorb energy from surroundings I absorb = eaσt 0 4 good emitters (e close to 1) are also good absorbers Lecture 25 Purdue University, Physics

23 Heat Transfer: Radiation All things radiate and absorb electromagnetic energy I =eaσt Surroundings at T 0 emit 4 I absorb = eaσt 4 T 0 I net = I emit -I absorb = eaσ(t 4 -T 04 ) if T > T 0, object cools down if T < T 0, object heats up g 0 Hot stove Lecture 25 Purdue University, Physics

24 Question One day during the winter, the sun has been shining all day. Toward sunset a light snow begins to fall. It collects without melting on a cement playground, but it melts immediately upon contact on a black asphalt road adjacent to the playground. How do you explain this. The black asphalt absorbs more heat from the sun. The black asphalt has an emissivity of 1 and absorbs energy from the surrounding (from the sun) compared to a smaller number for the cement. As a result, it is at a higher temperature than the cement and melts the snow. Lecture 25 Purdue University, Physics

25 Exercise The Earth has a surface temperature around 270 K and an emissivity of 0.8, while space has a temperature of around 2 K. What is the net power radiated by the earth into free space? (Radii of the Earth and the Sun are R E = m, R S = m) m.) I net = I emit -I absorb = eaσ(t 4 -T 04 ) ( )( 4π R 2 )( 0.8)( ) earth = = Watts Lecture 25 Purdue University, Physics

26 Radiation Which of the following is an example of radiative heat transfer? A) You stir some hot soup with a silver spoon and notice that the spoon warms up. B) You stand watching a bonfire, but cant get too close because of the heat. C) Its hard for central air-conditioning in an old house to cool the attic. Lecture 25 Purdue University, Physics

27 Blackbody When em radiation bombards an object, some of the radiation may be absorbed and some reflected A blackbody is an object that absorbs all em radiation at all frequencies A perfect blackbody does not exist, but the concept is very useful Radiation can be described by two laws Stefan-Boltzmann Wien s Lecture 25 Purdue University, Physics

28 Radiation Spectrum Infrared: 100 μm μm Visible Light: 0.7 μm μm Ultraviolet: < 0.4 μm Wien s Law: λ max T = mk max Lecture 25 Purdue University, Physics

29 Stefan-Boltzmann Law The amount of energy radiated by an object depends on its temperature If an object has a temperature T and a surface area A, the rate of energy radiated is given by the Stefan-Boltzmann Law = σεat σ = 5.67 x 10-8 W/m 2 is Stefan s constant Q t ε is the emissivity of the object It measures how efficiently it radiates energy ε = 1 for a blackbody 4 Lecture 25 Purdue University, Physics

30 Wien s Law The energy radiated is distributed as a function of wavelength The power is largest at λmax where λ max = x 10 T 3 m K Lecture 25 Purdue University, Physics

31 Stefan-Boltzmann and Heat Flow The total power varies as the fourth power of the temperature Radiated power increases rapidly as T is increased The power is proportional to the emissivity ε = 1 only for a blackbody It is smaller than 1 for any real object Its value depends on the properties of the material and will be a function of frequency Many objects are close to being blackbodies and so the Stefan-Boltzmann Law provides an approximate description of most radiating objects Lecture 25 Purdue University, Physics

32 Stefan-Boltzmann and Heat Flow The Stefan-Boltzmann Law applies to all objects at all temperatures Two objects will both radiate energy, but the net transfer will be from the hotter to the cooler The Stefan-Boltzmann Law also describes how heat is absorbed b by an object Q 4 = σ ε AT t absorbed In thermal equilibrium, (Q/t) absorbed = (Q/t) emitted Lecture 25 Purdue University, Physics

33 Sun and Earth s Temperature The Sun has a surface temperature of approximately 6000 K From the Stefan- Boltzmann Law, Q/t = 4.6 x W This is the rate at which the energy leaves the Sun This produces an Earth temperature of ~290 K Lecture 25 Purdue University, Physics

34 Temperature of the Sun The Sun appear yellowish, i.e., λ = μm. m What is the temperature at the surface of the Sun? λ m T = x 10-3 m K T = x 10-3 / 0.5 x 10-6 = 6000 K Lecture 25 Purdue University, Physics

35 Greenhouse Effect The atmosphere allows most of the Sun s visible radiation to reach the surface It absorbs much of the infrared radiation The Earth radiates in infrared This energy is absorbed by the atmosphere and not released to space The trapped infrared radiation makes the Earth s surface warmer than it would be without the atmosphere Lecture 25 Purdue University, Physics

36 Summary of Concepts Conduction - contact I = Q/t = κ A ΔT/d Convection - fluid motion I = Q/t = h A ΔT Radiation - electromagnetic radiation I emit = Q/t = eaσt 4 I absorb = Q/t = eaσt 4 0 Wien s Law: λ max T = mk Lecture 25 Purdue University, Physics