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University Physics Volume 2

Chapter 3

University Physics Volume 2Chapter 3
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Table of contents
  1. Preface
  2. 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. 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

3.1

p 2 ( V 2 − V 1 ) p 2 ( V 2 − V 1 )

3.2

Line 1, ΔEint=40J;ΔEint=40J; line 2, W=50JW=50J and ΔEint=40J;ΔEint=40J; line 3, Q=80JQ=80J and ΔEint=40J;ΔEint=40J; and line 4, Q=0Q=0 and ΔEint=40JΔEint=40J

3.3

So that the process is represented by the curve p=nRT/Vp=nRT/V on the pV plot for the evaluation of work.

3.4

1.26 × 10 3 J . 1.26 × 10 3 J .

Conceptual Questions

1.

a. SE; b. ES; c. ES

3.

Some of the energy goes into changing the phase of the liquid to gas.

5.

Yes, as long as the work done equals the heat added there will be no change in internal energy and thereby no change in temperature. When water freezes or when ice melts while removing or adding heat, respectively, the temperature remains constant.

7.

If more work is done on the system than heat added, the internal energy of the system will actually decrease.

9.

The system must be in contact with a heat source that allows heat to flow into the system.

11.

Isothermal processes must be slow to make sure that as heat is transferred, the temperature does not change. Even for isobaric and isochoric processes, the system must be in thermal equilibrium with slow changes of thermodynamic variables.

13.

Typically CpCp is greater than CVCV because when expansion occurs under constant pressure, it does work on the surroundings. Therefore, heat can go into internal energy and work. Under constant volume, all heat goes into internal energy. In this example, water contracts upon heating, so if we add heat at constant pressure, work is done on the water by surroundings and therefore, CpCp is less than CVCV.

15.

No, it is always greater than 1.

17.

An adiabatic process has a change in temperature but no heat flow. The isothermal process has no change in temperature but has heat flow.

Problems

19.

p(V−b)=−cTp(V−b)=−cT is the temperature scale desired and mirrors the ideal gas if under constant volume.

21.

V + b p T – c T 2 = 0 V + b p T – c T 2 = 0

23.

74 K

25.

0.31

27.

pVln(4)

29.

a. 160 J; b. –160 J

31.


The figure is a plot of pressure, p, in atmospheres on the vertical axis as a function of volume, V, in Liters on the horizontal axis. The horizontal volume scale runs from 0 to 10 Liters, and the vertical pressure scale runs from 0 to 2 atmospheres. Four segments, A, B, C, and D are labeled. Segment A is a horizontal line with an arrow to the right, extending from 4 L to 10 L at a constant pressure of 2 atmospheres. Segment B is a vertical line with an arrow downward, extending from 2 atmospheres to 0.5 atmospheres at a constant 10 L. Segment C is a horizontal line with an arrow to the left, extending from 10 L to 4 L at a constant pressure of 0.5 atmospheres. Segment D is a vertical line with an arrow upward, extending from 0.5 atmospheres to 2 atmospheres at a constant 4 L.


W=900JW=900J

33.

3.53 × 10 4 J 3.53 × 10 4 J

35.

a. 1:1; b. 10:1

37.

a. 600 J; b. 0; c. 500 J; d. 200 J; e. 800 J; f. 500 J

39.

580 J

41.

a. 600 J; b. 600 J; c. 800 J

43.

a. 0; b. 160 J; c. –160 J

45.

a. 20 J; b. 90 J

47.

No work is done and they reach the same common temperature.

49.

54,500 J

51.

a. (p1–3V1)(V2−V1)+32(V22−V12)(p1–3V1)(V2−V1)+32(V22−V12); b. 32(p2V2−p1V1)32(p2V2−p1V1); c. the sum of parts (a) and (b); d. T1=p1V1nRT1=p1V1nR and T2=p2V2nRT2=p2V2nR

53.

a.

The figure is a plot of pressure, p in MegaPascals, on the vertical axis as a function of volume, V in Liters, on the horizontal axis. The horizontal volume scale runs from 0 to 6. The vertical pressure scale runs from 0 to 3. Two points, A at 2 Liters, 3 MegaPascals, and B at 6 Liters, and an unlabeled pressure, are shown and are connected by a curve. The curve is monotonically decreasing and concave up.

;
 b. W=4.39kJ,ΔEint=−4.39kJW=4.39kJ,ΔEint=−4.39kJ

55.

a. 4000 J; b. −4000 J; c. It does not depend on the process.

57.

a. 700 J; b. 500 J

59.

a. −3 400 J; b. 3400 J enters the gas

61.

100 J

63.

a. 370 J; b. 100 J; c. 500 J

65.

850 J

67.

pressure decreased by 0.31 times the original pressure

69.


The figure is a plot of pressure, p, in atmospheres on the vertical axis as a function of volume, V, in liters on the horizontal axis. The horizontal volume scale runs from 0 to 20, and the vertical pressure scale runs from 0 to 9. The data from the previous table is plotted as points and the equation y equals 8.4372 x to the minus 0.713 power is plotted as a curve. The points all lie on or very close to the curve.

;
γ=0.713γ=0.713

71.

106 K

73.

An adiabatic expansion has less work done and no heat flow, thereby a lower internal energy comparing to an isothermal expansion which has both heat flow and work done. Temperature decreases during adiabatic expansion.

75.

Isothermal has a greater final pressure and does not depend on the type of gas.

77.


The figure is a plot of pressure, p, in atmospheres on the vertical axis as a function of volume, V, in liters on the horizontal axis. The horizontal, V, axis runs from 1.0 to 2.0. The vertical, p, axis runs from 0 to about 40. Two isotherms are shown. One isotherm is for T equal to 500 K, with the pressure starting at about 40 atmospheres when the volume is 1.0 Liter and decreasing with volume to about 25 atmospheres at 2.0 liters. The second isotherm is for T equal to 300 K, with the pressure starting at about 25 atmospheres when the volume is 1.0 Liter and decreasing with volume to a little over 10 atmospheres at 2.0 liters. A third plot, labeled “Adiabatic” starts with the 500 K isotherm, at 1.0 L and about 40 atmospheres, and ends with the 300 K isotherm, at 2.0 L and just over 10 atmospheres.

Additional Problems

79.

a. WAB=0,WBC=2026J,WAD=810.4J,WDC=0;WAB=0,WBC=2026J,WAD=810.4J,WDC=0; b. ΔEAB=3600J,ΔEBC=374J;ΔEAB=3600J,ΔEBC=374J; c. ΔEAC=3974J;ΔEAC=3974J; d. QADC=4784J;QADC=4784J; e. No, because heat was added for both parts AD and DC. There is not enough information to figure out how much is from each segment of the path.

81.

300 J

83.

a. 59.5 J; b. 170 N

85.

2.4 × 10 3 J 2.4 × 10 3 J

87.

a. 15,000 J; b. 10,000 J; c. 25,000 J

89.

78 J

91.

A cylinder containing three moles of nitrogen gas is heated at a constant pressure of 2 atm. a. −1220 J; b. +1220 J

93.

a. 7.6 L, 61.6 K; b. 81.3 K; c. 3.63L·atm=367J3.63L·atm=367J; d. −367 J

Challenge Problems

95.

a. 1700 J; b. 1200 J; c. 2400 J

97.

a. 2.2 mol; b. VA=2.6×10−2m3VA=2.6×10−2m3, VB=7.4×10−2m3VB=7.4×10−2m3; c. TA=1220K,TB=430KTA=1220K,TB=430K; d. 30,500 J

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