Physics 5D - Heat, Thermodynamics, And Kinetic Theory

Physics 5D - Heat, Thermodynamics,and Kinetic TheoryHomework will be posted at the Phys5D website http://physics.ucsc.edu/ joel/Phys5D.Solutions are due at the beginning of class. Late homework will not be accepted since solutionswill be posted on the class website (password: Entropy) just after the homework is due, so thatyou can see how to do the problems while they are still fresh in your mind.DateTopicCourse ScheduleReadings1. Sept 30 Temperature, Thermal Expansion, Ideal Gas Law17.1-17.102. Oct 7Kinetic Theory of Gases, Changes of Phase18.1-18.53. Oct 14Mean Free Path, Internal Energy of Gases18.6-19.34. Oct 21Heat and the 1st Law of Thermodynamics5. Oct 28Heat Transfer; Heat Engines, Carnot Cycle6. Nov 4Midterm Exam (in class, one page of notes allowed)7. Nov 18The 2nd Law of Thermodynamics, Heat Pumps20.3-20.58. Nov 25Entropy, Disorder, Statistical Interpretation of 2nd Law20.6-20.109. Dec 2Thermodynamics of Earth and Cosmos; Overview of the Course10. Dec 11Final Exam (5-8 pm, in class, two pages of notes allowed)Copyright 2009 Pearson Education, Inc.Monday, September 30, 1319.4-19.919.10-20.2

Website for homeworks: http://physics.ucsc.edu/ joel/Phys5DCopyright 2009PearsonEducation, Inc.TextTextTextTextMonday, September 30, 13

Giancoli - Chapter 17Temperature, ThermalExpansion, and the Ideal GasLawCopyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-1 Atomic Theory of MatterAtomic and molecular masses are measured inunified atomic mass units (u). This unit isdefined so that the carbon-12 atom has a massof exactly 12.0000 u. Expressed in kilograms:1 u 1.6605 x 10-27 kg.Brownian motion is the jitterymotion of tiny flecks in water.Einstein showed in 1905 thatthis is the result of collisionswith individual watermolecules.Copyright 2009Pearson Education,Inc.TextTextTexttttttttttTextMonday, September 30, 13

17-1 Atomic Theory of MatterOn a microscopicscale, molecules insolids are held inplace by chemicalbonds, in liquidsthere are bonds butmolecules are ableto move, while ingases there areonly weak forcesbetween molecules.Copyright 2009Pearson Education,Inc.TextTextTexttttttttttTextMonday, September 30, 13solidsliquidsgases

Thermometers are instruments designed tomeasure temperature. In order to do this, theytake advantage of some property of matter thatchanges with temperature.Early thermometers:Thermometer chronology:Galileo thermoscope 1593Daniel Fahrenheit’salcohol thermometer 1709mercury thermometer 1714Copyright 2009Pearson Education,Inc.TextTextTexttttttttttTextMonday, September 30, 13Anders Celsius1742Lord Kelvin’sabsolute scale1848

17-2 Temperature and ThermometersCommon thermometers used today include theliquid-in-glass type and the bimetallic strip.Greater expansionwith increased TCopyright 2009 Pearson Education, Inc.Monday, September 30, 13!

180 Fahrenheit degrees17-2 Temperature and ThermometersTemperature is generallymeasured using either theFahrenheit or the Celsius /Kelvin scales.The freezing point of water is0 C, or 32 F; the boiling pointof water is 100 C, or 212 FTF F 32 F 1.8 TCTK TC 273.15 KAbsolute zero 0 KCopyright 2009 Pearson Education, Inc.Monday, September 30, 13 273.15 C

17-3 Thermal Equilibrium and theZeroth Law of ThermodynamicsTwo objects placed in thermal contact willeventually come to the same temperature.When they do, we say they are in thermalequilibrium.The zeroth law of thermodynamics says that iftwo objects are each in equilibrium with a thirdobject, they are also in thermal equilibrium witheach other.Copyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-4 Thermal ExpansionLinear expansionoccurs when an objectis heated.Here, α is the coefficient of linear expansion.Example: αAl 25x10-6, so if ΔT 100C, analuminum bar grows in length by a factor 1.0025Copyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-4 Thermal ExpansionVolume expansion is similar, except that it isrelevant for liquids and gases as well as solids:Here, β is the coefficient of volume expansion.For uniform solids, β 3α because each of the3 dimensions expands by the same factor α:ΔV l0 3 [(1 α ΔT)3 - 1] l0 3 3α ΔTneglecting terms of order (αCopyright 2009Pearson Education,Inc.TextTextTexttttttttttTextMonday, September 30, 13ΔT)2 .

17-4 Thermal Expansion}Copyright 2009 Pearson Education, Inc.Monday, September 30, 13Largerthan forsolids

Does a hole in a piece of metal get biggeror smaller when the metal is heated?A. Bigger, because the distance betweenevery two points expands.B. Smaller, because the surrounding metalexpands into the hole.Copyright 2009 Pearson Education, Inc.Monday, September 30, 13

Does a hole in a piece of metal get biggeror smaller when the metal is heated?A. Bigger, because the distance betweenevery two points expandsB. Smaller, because the surrounding metalexpands into the hole.Copyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-4 Thermal ExpansionExample 17-7: Gas tank in the Sun.The 70-liter (L) steel gas tank of a car isfilled to the top with gasoline at 20 C.The car sits in the Sun and the tankreaches a temperature of 40 C (104 F).How much gasoline do you expect tooverflow from the tank?Copyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-4 Thermal ExpansionExample 17-7: Gas tank in the Sun.The 70-liter (L) steel gas tank of a car isfilled to the top with gasoline at 20 C.The car sits in the Sun and the tankreaches a temperature of 40 C (104 F).How much gasoline do you expect tooverflow from the tank?Answer: The coefficient of volumeexpansion of gasoline is β 0.00095/ C,so the expansion of the gasoline isΔV β V0 ΔT (0.00095/ C) (70 L) 20 CCopyright 2009 Pearson Education, Inc.Monday, September 30, 13 1.3 L

17-4 Thermal ExpansionWater behaves differently from most other solids—itsminimum volume occurs when its temperature is 4 C.As it cools further, it expands, as anyone who leavesa bottle in the freezer to cool and then forgets about itcan testify.VolumeCopyright 2009 Pearson Education, Inc.Monday, September 30, 13Density

When water above 4 ºC is heated, thebuoyant force on an object of constantvolume immersed in it A. increases. B. is unchanged. C. decreases.Copyright 2009 Pearson Education, Inc.Monday, September 30, 13

When water above 4 ºC is heated, thebuoyant force on an object of constantvolume immersed in it A. increases. B. is unchanged. C. decreases, sinceGalileoThermometerFB weight of displaced fluiddecreasesCopyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-6 The Gas Laws and AbsoluteTemperatureThe relationship between the volume,pressure, temperature, and mass of a gas iscalled an equation of state.Boyle’s law: the volume of agiven amount of gas isinversely proportional topressure as long as thetemperature is constant.Robert Boyle (1627-1691)Founder of modern chemistryCopyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-6 The Gas Laws and AbsoluteTemperatureThe volume is linearlyproportional to thetemperature, as long as thetemperature is somewhatabove the condensationpoint and the pressure isconstant. Extrapolating, thevolume becomes zero at 273.15 C; this temperatureis called absolute zero.Guillaume Amontons, 1702Jacques Charles, 1787Joseph Gay-Lussac, 1808Copyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-6 The Gas Laws and AbsoluteTemperatureThe concept of absolute zero allows us todefine a third temperature scale—the absolute,or Kelvin, scale. This scale starts with 0 K atabsolute zero, but otherwise is the same as theCelsius scale. Therefore, the freezing point ofwater is 273.15 K, and the boiling point is373.15 K.Finally, when the volume is constant, thepressure is directly proportional to thetemperature.Gay-Lussac’s LawCopyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-7 The Ideal Gas LawWe can combine the three relations just statedinto a single relation:What about the amount of gas present? Ifthe temperature and pressure are constant,the volume is proportional to the mass m ofgas:Copyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-7 The Ideal Gas LawA mole (mol) is defined as the number ofgrams of a substance that is numericallyequal to the molecular mass of the substance:1 mol H2 has a mass of 2 g.1 mol Ne has a mass of 20 g.1 mol CO2 has a mass of 44 g.The number of moles (mol) in a certain massof material:Copyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-7 The Ideal Gas LawWe can now write the ideal gas law:where n is the number of moles andR is the universal gas constant.AmadeoAvogadroNote: PV has units of Force x Distance EnergyCopyright 2009 Pearson Education, Inc.Monday, September 30, 13

ConcepTest Nitrogen and Oxygen IWhich has more molecules—amole of nitrogen (N2) gas or a2) nitrogenmole of oxygen (O2) gas?3) both the sameMonday, September 30, 131) oxygen

ConcepTest Nitrogen and Oxygen IWhich has more molecules—amole of nitrogen (N2) gas or a2) nitrogenmole of oxygen (O2) gas?3) both the same1) oxygenA mole is defined as a quantity of gas molecules equal toAvogadro’s number (6.02 1023). This value is independent of thetype of gas.Monday, September 30, 13

ConcepTest Nitrogen and Oxygen IIWhich weighs more—a moleof nitrogen (N2) gas or a mole1) oxygenof oxygen (O2) gas?3) both the sameMonday, September 30, 132) nitrogen

ConcepTest Nitrogen and Oxygen IIWhich weighs more—a moleof nitrogen (N2) gas or a mole1) oxygenof oxygen (O2) gas?3) both the same2) nitrogenThe oxygen molecules have a molecular mass of 32, and thenitrogen molecules have a molecular mass of 28.Follow-up: Which one will take up more space?Monday, September 30, 13

17-8 Problem Solving with the IdealGas LawStandard temperature and pressure (STP):T 273 K (0 C)P 1.00 atm 1.013x105 N/m2 101.3 kPa.Determine the volume of 1.00 mol of anygas, assuming it behaves like an ideal gas,at STP.V RT/P (8.314 J/mol K) (273K) / (1.013x105 N/m2) 22.4 x 10-2 m3 22.4 LCopyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-8 Problem Solving with the Ideal Gas LawExample 17-12: Mass of air in a room.Estimate the mass of air in a room whosedimensions are 5 m x 3 m x 2.5 m high, at STP.Copyright 2009 Pearson Education, Inc.Monday, September 30, 13

17-8 Problem Solving with the Ideal Gas LawExample 17-12: Mass of air in a room.Estimate the mass of air in a room whosedimensions are 5 m x 3 m x 2.5 m high, at STP.Answer: The volume is 5 x 3 x 2.5 m3 37.5 m3 37500 LSince 22.4 L is one mole at STP, there are37500/22.4 1700 moles in the room. Sinceair is about 20% 02 and 80% N2, its averagemolecular mass is 0.2(32) 0.8(28) 28.8.Thus the mass of air in the room is 1700 x28.8g 48900 g 49 kgCopyright 2009 Pearson Education, Inc.Monday, September 30, 13

ConcepTest Ideal Gas LawTwo cylinders at the sametemperature contain the same gas.If B has twice the volume and halfthe number of moles as A, how doesthe pressure in B compare with thepressure in A?Monday, September 30, 131) PB PA2) PB 2 PA3) PB PA4) PB 4 PA5) PB PA

ConcepTest Ideal Gas LawTwo cylinders at the sametemperature contain the same gas.If B has twice the volume and halfthe number of moles as A, how doesthe pressure in B compare with thepressure in A?Ideal gas law: PV nRTor1) PB PA2) PB 2 PA3) PB PA4) PB 4 PA5) PB PAP nRT/VBecause B has a factor of twice the volume, it has a factor oftwo less the pressure. But B also has half the amount of gas,so that is another factor of two reduction in pressure. Thus, Bmust have only one-quarter the pressure of A.Monday, September 30, 13

17-8 Problem Solving with the IdealGas Law Volume of 1 mol of an ideal gas is 22.4 L If the amount of gas does not change: Always measure T in kelvins P must be the absolute pressureNote: absolute pressure gauge pressure 1 Atm1 Atm 101 kPa 14.7 psi 760 mmHg (torr)Copyright 2009 Pearson Education, Inc.Monday, September 30, 13