Presentation on theme: "Category: Thermodynamics"— Presentation transcript:
1 Category: Thermodynamics 1Category: ThermodynamicsII. Heat and Phase changesUpdated:2014March13
2 Outline Heat Capacity (Storage of Heat) Heat Flow Phases of Matter 2OutlineHeat Capacity (Storage of Heat)Heat FlowPhases of MatterReferences
3 A. Heat Capacity Heat is Energy Storage of Energy: Heat Capacity 3Heat is EnergyStorage of Energy: Heat CapacityAtomic Theory of Specific Heats
4 1. Heat is Energy Caloric Theory Friction creates heat 4Caloric TheoryFriction creates heatEquivalence of heat and energy
5 Antoine Lavoisier 1743-1794 (beheaded-French Revolution) 1a. Caloric Theory (1783)5“Caloric”: the substance of heatIt flows like a fluid from hot to cold objects until “level” (same temperature)It is conserved (heat cannot be created, only moved around)1 calorie raises 1 gm of water by 1C (Nicolas Clement 1824)Antoine Lavoisier (beheaded-French Revolution)
6 1b. Mechanical Equivalence of Heat 6Count Rumford: Inventor of the “drip” coffee pot1798 shows that heat is NOT conserved (boring a cannon creates enough heat via friction to boil water)Sir Benjamin Thompson Count Rumford
7 1c. Heat is Energy (Joule experiment) 7experiment, dropping weight drives paddlewheel that heats fluid.1 calorie of heat is equivalent to Joules of work1847 Helmholtz states principle of conservation of total energyJames Prescott Joule
8 2. Storage of Heat8Heat CapacitySpecific HeatCalorimetery
9 2a. Heat Capacity Heat is a form of energy that can be stored 9Heat is a form of energy that can be storedHeat Capacity: the amount of heat Q required to raise temperature of system by T=1SI Units: Joule/CExtensive quantity
10 2b. Specific Heat10Specific Heat is the (intensive) measure of heat capacity per unit (thermal) massJoseph Black (1760s) shows materials have different values of specific heatJoseph BlackMaterialJ/kg °Ccal/gm °CCopper3860.092Aluminum9000.215Air10500.251Ice22200.530Water41861.000
11 2c. Calorimetry First calorimeter used by Lavoisier & Laplace 1782 11First calorimeter used by Lavoisier & Laplace 1782Measure specific heat “c” of block of metal (mass M) by heating it to temperature Th, drop into mass “m” of cold water (Tc), measure final temperature T
12 3. Atomic Theory of Specific Heat 12Specific Heat of GasSpecific Heat of Solids, Dulong-Petit LawLow Temperature Behavior
13 3a. Specific Heat of a Gas13At constant volume*, heat added to a monatomic gas goes into random kinetic energy of molecules. All monatomic gasses have same specific heat per mole (R=gas constant) !For diatomic gasses, heat also goes into two axes of rotational kinetic energy. Each mode contributes (1/2)R per mole*If instead measured at constant pressure, the specific heat is more because energy goes into work of expanding the gas.
14 3b. Specific Heats of Solids 14Dulong & Petit Law (1819) show that many solids have the same specific heat if measured per mole (instead of per mass) of 25 J/mol CLater it was realized this is related to gas constant c=3RMaterialJ/kg °Cgm/molJ/mol °CAluminum90026.9824.3Copper38663.5524.5Silver236107.8725.5Tungsten134183.8424.6Lead128207.226.5
15 3c. Einstein and Debye Models 15Einstein (1907) and Debye (1912) show that specific heats all approach 3R at high enough temperatureAt low temperature go to zero (this prevents being able to go below absolute zero!)
16 3d. Einstein and Debye Models 16Einstein’s Model (1907) works well at intermediate and high temperatures, but not at low temperature.Debye’s Model (1912) works well at low temperature and high, but not in the middle.The Debye Temperature: TDAt low temperatures Debye shows that the specific heat increases with the cube of the temperature.
17 B. Heat Flow There are three mechanisms by which heat flows: 17There are three mechanisms by which heat flows:ConvectionConductionRadiation
18 1. Convection18Heat moved by physical flow of gas/liquid. Often creates “convection cells” (can be seen on surface of sun!).No good formula!
19 2. Conduction19(a) Phenomena: Heat in a solid is transported by collisions between electrons. Generally good conductors of electricity are also good conductors of heat because the electrons are free to move.Newton’s Law of CoolingLoss of heat is proportional to the difference in temperature of system to environment [R=thermal resistance]Temperature of system will follow an exponential decay law [C=heat capacity]
20 2c. Law of Thermal Conduction 20(c) Fourier’s Theory of thermal conductionHeat Flux: heat flow per time (Watts)=Q/tAmount of heat flow is inversely proportional to the “Thermal Resistance R” of the system (units of degree per Watt).Thermal resistance “R” depends upon geometry (length L, area A, hence its “extensive”) and the thermal conductivity “k” of the materialThTc
21 2c. Thermal Conductivity 21Thermal conductivity (intensive quantity!) of solids are better than liquids or gasses. In the latter, convection will usually dominate.Aluminum 240Water 0.57AirVacuum 0
22 3. Radiation22(a) Stefan’s LawEmissivityBlack Body Radiation Curve
23 3a. Josef Stefan’s Law 1879 Power (watts)=AT4 23Experimentally shows total output of light of a hot dense (black) body is proportional to 4th power of the temperature (in Kelvin)Power (watts)=AT4=5.67x10-8 Watts/(m2-K4)A=surface area1884 Ludwig Boltzmann (former student of Stefan) derives formula from thermodynamics.I was a guest speaker (Sept 2005) at the Josef Stefan Institute in Slovenia.
24 3a ii Measure Temperature of Sun 241604 Kepler proposes intensity of light drops of with square of distance (?)Charles Soret measures solar flux to be about 1400 Watts/m2 at surface of the earth.Stefan uses this to estimate temperature of sun to be 5700 K.
25 3b Leslie Cube Experiment (1804) 25A cube with different emissitivites on different faces. One usually shows that the “black” surface radiates better than “white” surface.
26 3bii Emissivity26A perfect “black body” will radiate according to Stefan’s law.Most systems are not perfect, and so we include a “fudge factor” called the “emissivity”: 0<e<1Further, the environment at temperature Te will radiate energy back into the system, so the rate at which system loses heat is:
27 3c.i. Wien’s Displacement Law 271893 shows that the “color” of black body is inversely proportional to temperatureWien’s constant =2,898,000 nm-KSo T=6000K gives =483 nm
28 3c.ii. Black Body Curve Willhelm Wien gets Nobel Prize 1911 28Willhelm Wien gets Nobel Prize 19111894 coins term “black body”The black body emits all colors, but where it peaks is described by Wien’s law
29 3.c.iii. Black Body Theory29Maxwell: hot atoms vibrate, acting like small antennas, radiating electromagnetic wavesWien tries to give theory to explain shape of curve, but it fails in IRRayleigh (1900) & Jeans (1905) have another theory, but it fails in UV, blowing up to infinite energy (the “ultraviolet catastrophe”).
30 3c.iv. Max Planck’s Theory 301900 Max Planck ad-hoc proposes that vibrations are “quantized”, i.e. come in steps of n=1, 2, 3, rather than continuous.Energy: E=nhf n=integer quantum number f=frequency of oscillation h is “Planck’s Constant h=6.626x10-34 Joule-Sec
31 3cv. Planck Radiation Law 31His theory exactly matched the experimental measurements of the black body radiation curvek = Boltzmann Constant (1.3810-23 Joule/Kelvin)
32 C. Phases of Matter Phases of matter Latent Heats of Phase Change 32Phases of matterLatent Heats of Phase ChangePhase Diagrams (PVT diagrams)
33 1. Phases There are 4 states of matter (called “Phases”) Solid Liquid 33There are 4 states of matter (called “Phases”)SolidLiquidGasPlasma (hot gas ionizes)
34 1b. Plasma34Superheating a gas, it will ionize (electrons separate from rest of atom) into a 4th state of matter called a “plasma”.
35 1c. Van der Waals equation 35Why are there phases of matter?Van der Waals (Nobel Prize 1910) modified gas equation predicts solid, liquid and gas phases.“a” represents attractive forces between molecules and “b” the volume of a mole of molecules.Johannes van der Waals
36 2. Latent Heats36Joseph BlackBlack (1761) measures the amount of heat it takes to change phase of water. Defines:Latent Heat of fusion (melt ice) is 80 cal/gmLatent Heat of vaporization (boil) 597 cal/gm
37 2b. Latent Heats-continued 37Some substances, n.b. dry ice (CO2), go straight from solid to gas, so we have a latent heat of “sublimation” (opposite process is “deposition”)Dry ice latent heat of sublimation is: 571 J/gmMuch better than using water ice (no melted water!)
38 3(a) PT Diagram for Pure Substance 38Triple Point: all 3 phases coexist.Above critical point it’s a “supercritcal fluid”, no distinction between gas and liquidClausius-Clapeyron equation tells us the slope of the phase change curve, where “L” is the latent heat, and v is change in volume per mole of phase transition.
39 PT Diagram for Water39Expands when freezes, hence ice under pressure will melt (ice skates!)Note from A to D the slope is negative!
40 PT Diagram for Helium40Helium: Has two different liquid states, hence two “triple points”
41 PVT diagram41Van der Waals equationPVT diagrams
43 Misc Notes 43 MCAT includes Van der Waals equation. Condensation vs evaporationEvaporation takes place at surface, boiling is throughout fluid.Regelation (melting under pressure of ice)Heat released by freezing, e.g. center of earth.Change of phase of hydrogen to a metal in jupiter and saturn (liquid or solid?)Ice III (what happened to Ice II ?), what conditions for change, glaciers?