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  1. Preface
  2. Unit 1. Thermodynamics
    1. 1 Temperature and Heat
      1. Introduction
      2. 1.1 Temperature and Thermal Equilibrium
      3. 1.2 Thermometers and Temperature Scales
      4. 1.3 Thermal Expansion
      5. 1.4 Heat Transfer, Specific Heat, and Calorimetry
      6. 1.5 Phase Changes
      7. 1.6 Mechanisms of Heat Transfer
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 2 The Kinetic Theory of Gases
      1. Introduction
      2. 2.1 Molecular Model of an Ideal Gas
      3. 2.2 Pressure, Temperature, and RMS Speed
      4. 2.3 Heat Capacity and Equipartition of Energy
      5. 2.4 Distribution of Molecular Speeds
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 3 The First Law of Thermodynamics
      1. Introduction
      2. 3.1 Thermodynamic Systems
      3. 3.2 Work, Heat, and Internal Energy
      4. 3.3 First Law of Thermodynamics
      5. 3.4 Thermodynamic Processes
      6. 3.5 Heat Capacities of an Ideal Gas
      7. 3.6 Adiabatic Processes for an Ideal Gas
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 4 The Second Law of Thermodynamics
      1. Introduction
      2. 4.1 Reversible and Irreversible Processes
      3. 4.2 Heat Engines
      4. 4.3 Refrigerators and Heat Pumps
      5. 4.4 Statements of the Second Law of Thermodynamics
      6. 4.5 The Carnot Cycle
      7. 4.6 Entropy
      8. 4.7 Entropy on a Microscopic Scale
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  3. Unit 2. Electricity and Magnetism
    1. 5 Electric Charges and Fields
      1. Introduction
      2. 5.1 Electric Charge
      3. 5.2 Conductors, Insulators, and Charging by Induction
      4. 5.3 Coulomb's Law
      5. 5.4 Electric Field
      6. 5.5 Calculating Electric Fields of Charge Distributions
      7. 5.6 Electric Field Lines
      8. 5.7 Electric Dipoles
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    2. 6 Gauss's Law
      1. Introduction
      2. 6.1 Electric Flux
      3. 6.2 Explaining Gauss’s Law
      4. 6.3 Applying Gauss’s Law
      5. 6.4 Conductors in Electrostatic Equilibrium
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 7 Electric Potential
      1. Introduction
      2. 7.1 Electric Potential Energy
      3. 7.2 Electric Potential and Potential Difference
      4. 7.3 Calculations of Electric Potential
      5. 7.4 Determining Field from Potential
      6. 7.5 Equipotential Surfaces and Conductors
      7. 7.6 Applications of Electrostatics
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 8 Capacitance
      1. Introduction
      2. 8.1 Capacitors and Capacitance
      3. 8.2 Capacitors in Series and in Parallel
      4. 8.3 Energy Stored in a Capacitor
      5. 8.4 Capacitor with a Dielectric
      6. 8.5 Molecular Model of a Dielectric
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    5. 9 Current and Resistance
      1. Introduction
      2. 9.1 Electrical Current
      3. 9.2 Model of Conduction in Metals
      4. 9.3 Resistivity and Resistance
      5. 9.4 Ohm's Law
      6. 9.5 Electrical Energy and Power
      7. 9.6 Superconductors
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    6. 10 Direct-Current Circuits
      1. Introduction
      2. 10.1 Electromotive Force
      3. 10.2 Resistors in Series and Parallel
      4. 10.3 Kirchhoff's Rules
      5. 10.4 Electrical Measuring Instruments
      6. 10.5 RC Circuits
      7. 10.6 Household Wiring and Electrical Safety
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    7. 11 Magnetic Forces and Fields
      1. Introduction
      2. 11.1 Magnetism and Its Historical Discoveries
      3. 11.2 Magnetic Fields and Lines
      4. 11.3 Motion of a Charged Particle in a Magnetic Field
      5. 11.4 Magnetic Force on a Current-Carrying Conductor
      6. 11.5 Force and Torque on a Current Loop
      7. 11.6 The Hall Effect
      8. 11.7 Applications of Magnetic Forces and Fields
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    8. 12 Sources of Magnetic Fields
      1. Introduction
      2. 12.1 The Biot-Savart Law
      3. 12.2 Magnetic Field Due to a Thin Straight Wire
      4. 12.3 Magnetic Force between Two Parallel Currents
      5. 12.4 Magnetic Field of a Current Loop
      6. 12.5 Ampère’s Law
      7. 12.6 Solenoids and Toroids
      8. 12.7 Magnetism in Matter
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    9. 13 Electromagnetic Induction
      1. Introduction
      2. 13.1 Faraday’s Law
      3. 13.2 Lenz's Law
      4. 13.3 Motional Emf
      5. 13.4 Induced Electric Fields
      6. 13.5 Eddy Currents
      7. 13.6 Electric Generators and Back Emf
      8. 13.7 Applications of Electromagnetic Induction
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    10. 14 Inductance
      1. Introduction
      2. 14.1 Mutual Inductance
      3. 14.2 Self-Inductance and Inductors
      4. 14.3 Energy in a Magnetic Field
      5. 14.4 RL Circuits
      6. 14.5 Oscillations in an LC Circuit
      7. 14.6 RLC Series Circuits
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    11. 15 Alternating-Current Circuits
      1. Introduction
      2. 15.1 AC Sources
      3. 15.2 Simple AC Circuits
      4. 15.3 RLC Series Circuits with AC
      5. 15.4 Power in an AC Circuit
      6. 15.5 Resonance in an AC Circuit
      7. 15.6 Transformers
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    12. 16 Electromagnetic Waves
      1. Introduction
      2. 16.1 Maxwell’s Equations and Electromagnetic Waves
      3. 16.2 Plane Electromagnetic Waves
      4. 16.3 Energy Carried by Electromagnetic Waves
      5. 16.4 Momentum and Radiation Pressure
      6. 16.5 The Electromagnetic Spectrum
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  4. A | Units
  5. B | Conversion Factors
  6. C | Fundamental Constants
  7. D | Astronomical Data
  8. E | Mathematical Formulas
  9. F | Chemistry
  10. G | The Greek Alphabet
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
  12. Index

Check Your Understanding

2.1

We first need to calculate the molar mass (the mass of one mole) of niacin. To do this, we must multiply the number of atoms of each element in the molecule by the element’s molar mass.
(6mol of carbon)(12.0g/mol)+(5mol hydrogen)(1.0g/mol)+(1mol nitrogen)(14g/mol)+(2mol oxygen)(16.0g/mol)=123g/mol(6mol of carbon)(12.0g/mol)+(5mol hydrogen)(1.0g/mol)+(1mol nitrogen)(14g/mol)+(2mol oxygen)(16.0g/mol)=123g/mol
Then we need to calculate the number of moles in 14 mg.
(14mg123g/mol)(1g1000mg)=1.14×10−4mol.(14mg123g/mol)(1g1000mg)=1.14×10−4mol.
Then, we use Avogadro’s number to calculate the number of molecules:
N=nNA=(1.14×10−4mol)(6.02×1023molecules/mol)=6.85×1019molecules.N=nNA=(1.14×10−4mol)(6.02×1023molecules/mol)=6.85×1019molecules.

2.2

The density of a gas is equal to a constant, the average molecular mass, times the number density N/V. From the ideal gas law, pV=NkBT,pV=NkBT, we see that N/V=p/kBT.N/V=p/kBT. Therefore, at constant temperature, if the density and, consequently, the number density are reduced by half, the pressure must also be reduced by half, and pf=0.500atm.pf=0.500atm.

2.3

Density is mass per unit volume, and volume is proportional to the size of a body (such as the radius of a sphere) cubed. So if the distance between molecules increases by a factor of 10, then the volume occupied increases by a factor of 1000, and the density decreases by a factor of 1000. Since we assume molecules are in contact in liquids and solids, the distance between their centers is on the order of their typical size, so the distance in gases is on the order of 10 times as great.

2.4

Yes. Such fluctuations actually occur for a body of any size in a gas, but since the numbers of molecules are immense for macroscopic bodies, the fluctuations are a tiny percentage of the number of collisions, and the averages spoken of in this section vary imperceptibly. Roughly speaking, the fluctuations are inversely proportional to the square root of the number of collisions, so for small bodies, they can become significant. This was actually observed in the nineteenth century for pollen grains in water and is known as Brownian motion.

2.5

In a liquid, the molecules are very close together, constantly colliding with one another. For a gas to be nearly ideal, as air is under ordinary conditions, the molecules must be very far apart. Therefore the mean free path is much longer in the air.

2.6

As the number of moles is equal and we know the molar heat capacities of the two gases are equal, the temperature is halfway between the initial temperatures, 300 K.

Conceptual Questions

1.

2 moles, as that will contain twice as many molecules as the 1 mole of oxygen

3.

pressure

5.

The flame contains hot gas (heated by combustion). The pressure is still atmospheric pressure, in mechanical equilibrium with the air around it (or roughly so). The density of the hot gas is proportional to its number density N/V (neglecting the difference in composition between the gas in the flame and the surrounding air). At higher temperature than the surrounding air, the ideal gas law says that N/V=p/kBTN/V=p/kBT is less than that of the surrounding air. Therefore the hot air has lower density than the surrounding air and is lifted by the buoyant force.

7.

The mean free path is inversely proportional to the square of the radius, so it decreases by a factor of 4. The mean free time is proportional to the mean free path and inversely proportional to the rms speed, which in turn is inversely proportional to the square root of the mass. That gives a factor of 88 in the numerator, so the mean free time decreases by a factor of 2.2.

9.

Since they’re more massive, their gravity is stronger, so the escape velocity from them is higher. Since they’re farther from the Sun, they’re colder, so the speeds of atmospheric molecules including hydrogen and helium are lower. The combination of those facts means that relatively few hydrogen and helium molecules have escaped from the outer planets.

11.

One where nitrogen is stored, as excess CO2CO2 will cause a feeling of suffocating, but excess nitrogen and insufficient oxygen will not.

13.

Less, because at lower temperatures their heat capacity was only 3RT/2.

15.

a. false; b. true; c. true; d. true

17.

1200 K

Problems

19.

a. 0.137 atm; b. pg=(1atm)T2V1T1V21atm.pg=(1atm)T2V1T1V21atm. Because of the expansion of the glass, V2=0.99973V2=0.99973. Multiplying by that factor does not make any significant difference.

21.

a. 1.79×10−3mol;1.79×10−3mol; b. 0.227 mol; c. 1.08×10211.08×1021 molecules for the nitrogen, 1.37×10231.37×1023 molecules for the carbon dioxide

23.

7.84×10−2mol7.84×10−2mol

25.

1.87×1031.87×103

27.

2.47×107molecules2.47×107molecules

29.

6.95×105Pa;6.95×105Pa; 6.86 atm

31.

a. 9.14×106Pa;9.14×106Pa; b. 8.22×106Pa;8.22×106Pa; c. 2.15 K; d. no

33.

40.7 km

35.

a. 0.61 N; b. 0.20 Pa

37.

a. 5.88 m/s; b. 5.89 m/s

39.

177 m/s

41.

4.54×1034.54×103

43.

a. 0.0352 mol; b. 5.65×10−21J;5.65×10−21J; c. 139 J

45.

21.1 kPa

47.

458 K

49.

3.22×103K3.22×103K

51.

a. 1.004; b. 764 K; c. This temperature is equivalent to 915ºF915ºF, which is high but not impossible to achieve. Thus, this process is feasible. At this temperature, however, there may be other considerations that make the process difficult. (In general, uranium enrichment by gaseous diffusion is indeed difficult and requires many passes.)

53.

65 mol

55.

a. 0.76 atm; b. 0.29 atm; c. The pressure there is barely above the quickly fatal level.

57.

4.92×105K4.92×105K; Yes, that’s an impractically high temperature.

59.

polyatomic

61.

3.08×103J3.08×103J

63.

29.2°C29.2°C

65.

−1.6°C−1.6°C

67.

0.00157

69.

About 0.072. Answers may vary slightly. A more accurate answer is 0.074.

71.

a. 419 m/s; b. 472 m/s; c. 513 m/s

73.

541 K

75.

2400 K for all three parts

Additional Problems

77.

a. 1.20kg/m31.20kg/m3; b. 65.9kg/m365.9kg/m3

79.

7.9 m

81.

a. supercritical fluid; b. 3.00×107Pa3.00×107Pa

83.

40.18%40.18%

85.

a. 2.21×1027molecules/m3;2.21×1027molecules/m3; b. 3.67×103mol/m33.67×103mol/m3

87.

8.2 mm

89.

a. 1080J/kg°C1080J/kg°C; b. 12%12%

91.

2e/32e/3 or about 1.10

93.

a. 411 m/s; b. According to Table 2.3, the CVCV of H2SH2S is significantly different from the theoretical value, so the ideal gas model does not describe it very well at room temperature and pressure, and the Maxwell-Boltzmann speed distribution for ideal gases may not hold very well, even less well at a lower temperature.

Challenge Problems

95.

29.5 N/m

97.

Substituting v=2kBTmuv=2kBTmu and dv=2kBTmdudv=2kBTmdu gives
04π(m2kBT)3/2v2emv2/2kBTdv=04π(m2kBT)3/2(2kBTm)u2eu22kBTmdu=04πu2eu2du=4ππ4=104π(m2kBT)3/2v2emv2/2kBTdv=04π(m2kBT)3/2(2kBTm)u2eu22kBTmdu=04πu2eu2du=4ππ4=1

99.

Making the scaling transformation as in the previous problems, we find that
v2=04π(m2kBT)3/2v2v2emv2/2kBTdv=04π2kBTmu4eu2du.v2=04π(m2kBT)3/2v2v2emv2/2kBTdv=04π2kBTmu4eu2du.
As in the previous problem, we integrate by parts:
0u4eu2du=[12u3eu2]0+320u2eu2du.0u4eu2du=[12u3eu2]0+320u2eu2du.
Again, the first term is 0, and we were given in an earlier problem that the integral in the second term equals π4π4. We now have
v2=4π2kBTm32π4=3kBTm.v2=4π2kBTm32π4=3kBTm.
Taking the square root of both sides gives the desired result: vrms=3kBTmvrms=3kBTm.

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