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Part Three: Thermodynamics

Part Three: Thermodynamics. Steam turbine converts the energy of high-pressure steam to mechanical energy and then electricity. World energy consumption (2008): ~ 15  10 12 (15 trillion / tera) watts., mostly from fossil fuels. Applications of the laws of thermodynamics:

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Part Three: Thermodynamics

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  1. Part Three: Thermodynamics Steam turbine converts the energy of high-pressure steam to mechanical energy and then electricity.

  2. World energy consumption (2008): ~ 151012 (15 trillion / tera) watts., mostly from fossil fuels • Applications of the laws of thermodynamics: • Combustion engines. • Sun  Heat flows on Earth  Climate. • Global warming. • Big bang: Heat flow in the universe.

  3. List of countries by electricity consumption

  4. Part Three: Thermodynamics • Temperature and Heat • The Thermal Behavior of Matter • Heat, Work, and the First Law of Thermodynamics • The Second Law of Thermodynamics

  5. 16. Temperature & Heat Heat , Temperature & Thermodynamic Equilibrium Heat Capacity & Specific Heat Heat Transfer Thermal Energy Balance

  6. How does this photo reveal heat loss from the house? And how can you tell that the car was recently driven? IR photo: engine & brakes hot • Studies of thermal properties: • Thermodynamics: Relations between macroscopic properties. • Statistical mechanics: Atomic description.

  7. 16.1. Heat , Temperature & Thermodynamic Equilibrium Thermodynamic equilibrium: State at which macroscopic properties of system remains unchanged over time. Examples of macroscopic properties: L, V, P, , , … 2 systems are in thermal contact if heating one of them changes the other. Otherwise, they are thermally insulated. Two systems have the same temperature they are in thermodynamic equilibrium A,B in eqm B,C in eqm A,C in eqm  0th law of thermodynamics: 2 systems in thermodynamic equilibrium with a 3rd system are themselves in equilibrium.

  8. Gas Thermometers & the Kelvin Scale Constant volume gas thermometer T P Kelvin scale: P = 0  0 K = absolute zero Triple point of water  273.16 K Triple point: T at which solid, liquid & gas phases co-exist in equilibrium Mercury fixed at this level by adjusting h P  T. All gases behave similarly as P 0.

  9. Temperature Scales Celsius scale ( C ) : Melting point of ice at P = 1 atm  TC= 0 C. Boiling point of water at P = 1 atm  TC= 100 C.  Triple point of water = 0.01C Fahrenheit scale ( F ) : Melting point of ice at P = 1 atm  TF= 32 F. Boiling point of water at P = 1 atm  TF= 212 F. Rankine scale ( R ) :

  10. Supplement Conditions for thermodynamic equilibrium Isolated ideal gas P, V, n, T P V = n R T P j V j = n j R T j j = 1, 2 Fixed, thermally conducting partition P1 , V1 , n1 , T1 P2 , V2 , n2 , T2 (Local eqm.) T 1 = T 2 P j V j = n j R T j j = 1, 2 Movable, thermally conducting partition P1 , V1 , n1 , T1 P2 , V2 , n2 , T2 T 1 = T 2 & P 1 = P 2 P j V j = n j R T j j = 1, 2 Porous, movable, thermally conducting partition P1 , V1 , n1 , T1 P2 , V2 , n2 , T2 T 1 = T 2 , P 1 = P 2 &  1 =  2 Same as no partition  = n / V

  11. Heat & Temperature A match will burn your finger, but doesn’t provide much heat.  Heat ~ amount Temperature ~ intensity • Brief history of the theory of heat: • Heat is a fluid (caloric theory: 1770s) that flows from hot to cold bodies. • B.Thompson, or Count Rumford, (late 1790s): unlimited amount of heat can be produced in the boring of canon  heat is not conserved. • J.Joule (1840s): Heat is a form of energy. Heat is energy transferred from high to low temperature regions.

  12. 16.2. Heat Capacity & Specific Heat Heat capacity C of a body: Q = heat transferred to body. Specific heat c = heat capacity per unit mass 1 calorie (cal) = heat needed to raise 1 g of water from 14.5C to 15.5C. 1 BTU = heat needed to raise 1 lb of water from 63F to 64F.

  13. c = c(P,V) for gases  cP , cV.

  14. Example 16.1. Waiting to Shower The temperature in the water heater has dropped to 18C. If the heater holds 150 kg of water, how much energy will it take to bring it up to 50C? If the energy is supplied by a 5.0 kW electric heating element, how long will that take?

  15. The Equilibrium Temperature Heat flows from hot to cold objects until a common equilibrium temperature is reached. For 2 objects insulated from their surroundings: When the equilibrium temperature T is reached: 

  16. GOT IT? 16.1. A hot rock with mass 250 g is dropped into an equal mass of pool water. Which temperature changes more? Explain. crock = 0.20 cal / g C cwater = 1.0 cal / g C  Trockchanges more

  17. Example 16.2. Cooling Down An aluminum frying pan of mass 1.5 kg is at 180C, when it was plunged into a sink containing 8.0 kg of water at 20C. Assuming none of the water boils & no heat is lost to the environment, find the equilibrium temperature of the water & pan.

  18. 16.3. Heat Transfer • Common heat-transfer mechanisms: • Conduction • Convection • Radiation

  19. Conduction Conduction: heat transfer through direct physical contact. Mechanism: molecular collision. Heat flow H , [ H ] = watt : Thermal conductivity k , [ k ] = W / mK

  20. conductor insulator

  21. Example 16.3. Warming a Lake A lake with flat bottom & steep sides has surface area 1.5 km2 & is 8.0 m deep. The surface water is at 30C; the bottom, 4.0C. What is the rate of heat conduction through the lake? Assume T decreases uniformly from surface to bottom. Power of sunlight is ~ 1 kW / m2 .

  22. applies only when T = const over each (planar) surface For complicated surface, use Prob. 72 & 78. Composite slab: H must be the same in both slabs to prevent accumulated heat at interface Thermal resistance : [ R ] = K / W   Resistance in series

  23. GOT IT? 16.2. Rank order the 3 temperature differences. H, A, x same for all three  k T = const

  24. Insulating properties of building materials are described by the R-factor ( R-value ) . = thermal resistance of a slab of unit area U.S.

  25. Example 16.4. Cost of Oil The walls of a house consist of plaster ( R = 0.17 ), R-11 fiberglass insulation, plywood (R = 0.65 ), and cedar shingles (R = 0.55 ). The roof is the same except it uses R-30 fiberglass insulation. In winter, average T outdoor is 20 F, while the house is at 70 F. The house’s furnace produces 100,000 BTU for every gallon of oil, which costs $2.20 per gallon. How much is the monthly cost?

  26. Convection Convection = heat transfer by fluid motion T      rises Convection cells in liquid film between glass plates (Rayleigh-Bénard convection, Benard cells)

  27. Examples: • Boiling water. • Heating a house. • Sun heating earth  Climate, storms. • Earth mantle  continental drift • Generation of B in stars & planets.

  28. Radiation Glow of a stove burner  it loses energy by radiation Stefan-Boltzmann law for radiated power:  = Stefan-Boltzmann constant = 5.67108 W / m2 K4. A = area of emitting surface. 0 < e < 1 is the emissivity ( effectiveness in emitting radiation ). e = 1  perfect emitter & absorber ( black body ). Black objects are good emitters & absorbers. Shiny objects are poor emitters & absorbers.

  29. Stefan-Boltzmann law : Wien‘s displacement law : max = b / T  P T4 Radiation dominates at high T. Wavelength of peak radiation becomes shorter as T increases. Sun ~ visible light. Near room T ~ infrared.

  30. GOT IT? 16.3. • Name the dominant form of heat transfer from • a red-hot stove burner with nothing on it. • a burner in direct contact with a pan of water. • the bottom to the top of the water in the pan once it boils. Radiation conduction convection

  31. Example 16.5. Sun’s Temperature The sun radiates energy at the rate P = 3.91026 W, & its radius is 7.0 108 m. Treating it as a blackbody ( e = 1 ), find its surface temperature.  = 5.67108 W / m2 K4

  32. 16.4. Thermal Energy Balance A house in thermal-energy balance. System with fixed rate of energy input tends toward an energy- balanced state due to negative feedback. Heat from furnace balances losses thru roofs & walls

  33. Example 16.6. Hot Water A poorly insulated electric water heater loses heat by conduction at the rate of 120 W for each C difference between the water & its surrounding. It’s heated by a 2.5 kW heating element & is located in a basement kept at 15 C. What’s the water temperature if the heating element operates continuously. Conductive heat loss T = ? Electrical energy in Heating element

  34. Example 16.7. Solar Greenhouse A solar greenhouse has 300 ft2 of opaque R-30 walls, & 250 ft2 of R-1.8 double-pane glass that admits solar energy at the rate of 40 BTU / h / ft2. Find the greenhouse temperature on a day when outdoor temperature is 15 F.

  35. Application: Greenhouse Effect & Global Warming Average power from sun : Total power from sun : Power radiated (peak at IR) from Earth :  C.f.  T   15 C natural greenhouse effect Mars: none Venus: huge Greenhouse gases: H2O, CO2 , CH4 , … passes incoming sunlight, absorbs outgoing IR.

  36. CO2 increased by 36% 0.6 C increase during 20th century. 1.5 C – 6 C increase by 2100.

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