Thermodynamics (Lecture Notes Heat and Thermodynamics (7 th Edition by Mark W. Zemansky & Richard H. Dittman
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Chapter 1 Temperature and the Zeroth Law of Thermodynamics 1.1 Macroscopic Point of View If no matter crosses the boundary, = a closed system. If an exchange of matter, = an open system. Two points of view: Macroscopic: the human scale or larger. Microscopic: the molecular scale or smaller. Macroscopic Coordinates: (provide a macroscopic description of a system 1. No special assumptions (e.g., the structure of matter 2. Few in number (to describe the system 3. Fundamental (as suggested by our sensory perceptions 4. Directly measurable Including the macroscopic coordinate of temp. = Thermodynamics. 1.2 Microscopic Point of View A microscopic description of a system: 1. Assumptions 2. Many quantities 3. Mathematical models 4. Theoretical calculation = Statistical mechanics (Ch. 12 3
4 CHAPTER 1. TEMPERATURE AND THE ZEROTH LAW OF THERMODYNAMICS 1.3 Macroscopic VS. Microscopic Points of View = (Macroscopic description = Microscopic description ave 1.4 Scope of Thermodynamics Thermaodynamic systems: a gas, a vapor, a mixture (e.g., vapor and air, surface films, electric cells, wire resistors, electric capacitors, and magnetic substances. 1.5 Thermal Equilibrium and The Zeroth Law The 0 th law of thermodynamics: If A C and B C, A B. ( : thermal equilibrium 1.6 Concept of Temperature Isotherm: The locus of all points representing states in which a system is in thermal equilibrium with one state of another system. (See Fig. 1-3 = If (X 1, Y 1 (X 1, Y 1, (X 2, Y 2 (X 1, Y 1, (X 3, Y 3 (X 1, Y 1,, = Isotherm I. = If (X 1, Y 1 (X 1, Y 1, (X 2, Y 2 (X 1, Y 1, (X 3, Y 3 (X 1, Y 1,, = Isotherm I. The temperature of a system is a property that determines whether or not a system is in thermal equilibrium with other systems. 1.7 Thermometers and Measurement of Temperature (See Fig. 1-4 θ(x = a X (const. Y (1 See Fig. 1-5 (Triple-pt. cell θ T P = 273.16 K (2 (1 = θ(x T P = a X T P ( = a = 273.16 K X T P = θ(x = (273.16 K X X T P # (const. Y 1.8 Comparison of Thermometers In Table 1.1, = six thermometers. For a gas, = θ(x = (273.16 K P P T P (const. V.
1.9. GAS THERMOMETER 5 For a wire resistor, = θ(r = (273.16 K R R T P For a thermocouple, = θ(e = (273.16 K E E T P (const. tension. (const. tension. In Table 1.2, = choose a gas thermometers as the standard thermometer. 1.9 Gas Thermometer See Fig. 1-6. (The volume of the gas is kept constant. 1.10 Ideal-Gas Temperature Ideal-gas law: where P V = n R T, (1 n: the number of moles, R: the molar gas const., T : theoretical thermodynamic temp. (Sec. 7.7. Experiment: (T θ (1 = P V = n R θ P T P V = n R θ T P, θ T P = 273.16 K = θ = (273.16 K P P T P # (const. V (2 Measuring T : (at the normal boiling pt. of water 1. With the triple-pt. cell = P T P = 120 kpa (suppose. With steam, measure P NBP = θ(p NBP = (273.16 K PNBP 120. 2. Remove some of the gas = P T P, say, 60 kpa. Measure the new P NBP = θ(p NBP = (273.16 K PNBP 60. 3. Repeat the procedures 1 and 2. 4. Plot θ(p NBP P T P, = T = lim P T P 0 θ(p NBP = 273.16 K lim P T P 0 P P T P # (const. V (See Fig. 1-7.
6 CHAPTER 1. TEMPERATURE AND THE ZEROTH LAW OF THERMODYNAMICS 1.11 Celsius Temp. Scale θ( 0 C = T (K 273.15. e.g., θ NBP ( 0 C = T NBP (K 273.15 = 99.974 0 C }{{} # 373.124 1.12 Platinum Resistance Thermometry Range: 13.8033 1234.93 K ( 259.3467 961.78 0 C = R (T = R T P (1 + at + bt 2, a, b : consts. (empirical formula 1.13 Radiation Thermometry Blackbody radiation (> 1100 0 C 1.14 Vapor Pressure Thermometry Use 3 He or 4 He (isotopes of He. (0.3 5.2 K 1.15 Thermocouple E = c 0 + c 1 θ + c 2 θ 2 + c 3 θ 3, c is : consts. ( 270 1372 0 C 1.16 International Temperature Scale of 1990 (ITS-90 (See Table 1.3 ITS-90 = a set of defining fixed points measured with the primary gas thermometer + a set of procedures for interpolation between the fixed points using secondary thermometers. 1.17 Rankine and Fahrenheit Temp. Scales T (R = 9 5 T (K θ( 0 F = T (R 459.67 θ( 0 F = 9 5 θ(0 C + 32
Chapter 2 Simple Thermodynamic Systems 2.1 Thermodynamic Equilibrium mechanical equil. + chemical equil. + thermal equil. = thermodynamic equil. state 2.2 Equation of State For a closed system, the eq. of state relates the temperature to two other thermodynamic variables. e.g., (a gas = P V = nrt (very low pressure, or van der Waals eq.: P v = RT, v(= V/n: molar volume (or volume per mole, (P + a (v b = RT (higher pressure. v2 XYZ systems = Simple systems (e.g., a gas, 1-dim stretched wire, 2-dim. surface,... 2.3 Hydrostatic Systems E.g., a solid, a liquid, a gas, or a mixture of any two. = a P V T system The eq. of state, = V = func. of (T, P or V = V (T, P (1 or = P = func. of (T, V or P = P (T, V (2 7
8 CHAPTER 2. SIMPLE THERMODYNAMIC SYSTEMS or Exact differentials: = T = func. of (P, V or T = T (P, V (3 If dz is an exact differential of a func. of x and y, then ( ( z z dz = dx + dy, x y y x If P =const, (1 = dv = ( V T P ( V dt + P T dp, (4 = β = ( V/V T (coeff. of volume expansion, = β = 1 V If T =const, ( V T P (coeff. of volume expansion = B = P ( V/V (isothermal bulk modulus, = B = V ( P V T = κ = 1 V ( V P (2 = dp = ( P T (3 = dt = ( T P T (isothermal bulk modulus (isothermal compressibility V dt + ( P V V dp + ( T V T P dv, (5 dv, (6 (4 (6 = The dv, dp, and dt are differentials of actual functions. = exact differentials #. 2.4 Mathematical Theorems ( x 1 = ; y z ( y/ x z ( x y z ( y z x ( z = 1. x y e.g., a PVT system, ( = ( ( P V ( T V T T P P V = 1, = β = 1 V ( P = V T ( V T P & κ = 1 V ( V T ( T P P V = β κ # ( V P T,
2.5. STRETCHED WIRE 9 Therefore, (5 = dp = ( P T V dt + ( P V T dv = β κ dt 1 κv dv. If V = const, = dp = β κ dt, = P f P i dp = T f T i 2.5 Stretched Wire β κ, dt, = P f P i = β κ (T f T i # (V = const = a FLT system, F: tension (in N, L: length (in m, T : temp. (in K. If T = const, (within the limit of elasticity = F = k(l L 0, L 0 : the length at zero tension. (Hooke s law Since L = L(T, F, = dl = ( L T F dt + ( T F T df, If F = const, = α = 1 T ( L L (linear coeff. of exansion, = α = 1 L ( L T F (linaer coeff. of expansion If T =const, = Y = ( F/A ( L/L (Young s modulus, = Y = L A Since ( F L T = ( F T ( L T F ( F L T ( T F L = ( F L 2.6 Surfaces T (isothermal Young s mdulus = 1 L ( L T F = α A Y # = a γat system, γ: surface tension (in N/m, A: area (in m 2, T : temp. (in K. e.g., (1 For most pure liquids in equil. with their vapor phase,
10 CHAPTER 2. SIMPLE THERMODYNAMIC SYSTEMS = γ = γ 0 (1 T/T c n, γ 0 : the surface tension at 20 0 C, T c : critical temp., n: betw. 1-2. (2 A thin filem of oil on water, = (γ γ w A = a T, γ w : the surface tension of a clean water surface, a: a const. 2.7 Electrochemical Cell = a EZT system, E: emf (in Volts, Z: charge (in coulombs C, T : temp. (in K. Eq. of state, (by Exp. = E = E 20 + α(θ 20 0 + β(θ 20 0 2 + γ(θ 20 0 3, where E 20 : the emf at 20 0 C, θ: temp. in Celsius, α, β, γ: consts. 2.8 Dielectric Slab = an E PT system, where E: electric field (in V/m, P: tot. polarization emf (in C m, T : temp. (in K. Eq. of state, = P V = (a + b/t, a, b: consts. (for T > 10 K 2.9 Paramagnetic Rod = a HMT system, where H: magnetic field (in A/m, M: tot. magnetization (in A m 2, T : temp. (in K. Eq. of state, = M = CcH T, C c: Curie const. 2.10 Intensive and Extensive Coordinates Intensive coords. (indept of the mass:
2.10. INTENSIVE AND EXTENSIVE COORDINATES 11 e.g., P, F, γ, E, E, H, T, density(ρ,... Extensive coords. (propotional to the mass: e.g., V, L, A, Z, E, P, M, mass(m, U, S,... = extensive intensive = extensive
12 CHAPTER 2. SIMPLE THERMODYNAMIC SYSTEMS
Chapter 3 Work 3.1 Work If work is done on the system, = W > 0. If work is done by the system, = W < 0. 3.2 Quasi-Static Process quasi-static process (thermodynamics:: massless springs (mechanics or wires with no resistance (circuit 3.3 Work in Changing the Volume of a Hydrostatic System See Fig. 3-1 (quasi-static compression dw = F dx = P A dx, dv = A dx dw = P dv = W if = V f V i P dv (a quasi-static path i f i f, = W fi = V i V f P dv (a quasi-static path f i = W if # 13
14 CHAPTER 3. WORK 3.4 P V Diagram See Fig. 3-2 (a, (b, and (c. 3.5 Hydrastatic Work Depends on the Path See Fig. 3-3, i a f : W = 2P 0 V 0 i b f : W = P 0 V 0 i f : W = 3 2 P 0 V 0 = W is path-dependent. = W is not a state function. = W is an exact differential. 3.6 Calculation of P dv for Quasi-Static Processes Quasi-static isothermal expansion or compression of an ideal gas: = W = V f V i P dv, P V = nrt = V f V i nrt V dv = nrt V f V i dv V = nrt ln V f V i # Quasi-static isothermal increase of pressure on a solid: = W = P dv, dv = ( V P dp + ( V T T dt = κv dp P = P f P i κv P dp = κv P f P i P dp = κv 2 (P 2 f P 2 i #
3.7. WORK IN CHANGING THE LENGTH OF A WIRE 15 3.7 Work in Changing the Length of a wire dw = F dl, F = F(L, T, = W = L f L i F dl# 3.8 Work in Changing the Area of a Surface Film dw = γ da, = W = A f A i γ da# 3.9 Work in Moving Charge with an Electrochemical Cell dw = E dz, = W = Z f Z i E dz# 3.10 Work in Changing the Total Polarization of a Dielectric Solid dw = E dp, = W = P f P i E dp # 3.11 Work in Changing the Total Magnetization of a Paramagnetic Solid dw = µ 0 H dm, = W = µ 0 Mf M i H dm#
16 CHAPTER 3. WORK 3.12 Generalized Work See Table 3.1 (Work of simple systems 3.13 Composite Systems See Figs. 3-8 & 3-9. In general, a five-coords. system (Y, X, Y, X, and T, = dw = Y dx + Y dx = Choose T, X, and X as indept coords.
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18 CHAPTER 4. HEAT AND THE FIRST LAW OF THERMODYNAMICS Chapter 4 Heat and the First Law of Thermodynamics 4.1 Work and Heat 4.2 Adiabatic Work 4.3 Internal-Energy Function 4.4 Mathematical Formulation of the First Law 4.5 Concept of Heat 4.6 Difference Form of the Firat Law 4.7 Heat Capacity and its Measurement 4.8 Specific Heat of Water; the Calorie 4.9 Equation for a Hydrostatic System 4.10 Quasi-Static Flow of Heat; Heat Reservoir 4.11 Heat Conduction 4.12 Thermal Conductivity and its Measurement 4.13 Heat Convection 4.14 Thermal Radiation; Blackbody 4.15 Kirchhoff s Law; Radiation Heat 4.16 Stefan-Boltzmann Law
Chapter 5 Ideal Gas 5.1 Equation of State of a Gas 5.2 Internal Energy of a Real Gas 5.3 Ideal Gas 5.4 Experimental Determination of Heat Capacities 5.5 Quasi-Static Adiabatic Process 5.6 Rüchhardt s Method of Measuring γ 5.7 Velocity of a Logitudinal Wave 5.8 The Microscopic Point of View 5.9 Kinetic Theory of the Ideal Gas 19
20 CHAPTER 5. IDEAL GAS
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22 CHAPTER 6. THE SECOND LAW OF THE THERMODYNAMICS Chapter 6 The Second Law of the Thermodynamics 6.1 Conversion of Work into Heat and Vice Versa 6.2 The Gasoline Engine 6.3 The Diesel Engine 6.4 The Steam Engine 6.5 The Stirling Engine 6.6 Heat Engine; Kelvin-Planck Statement of the Second Law 6.7 Refrigerator; Clausius Statement of the Second Law 6.8 Equivalence of the Kelvin-Planck and Clausius Statements 6.9 Reversibility and Irreversibility 6.10 External Mechanical Irreversibility 6.11 Internal Mechanical Irreversibility 6.12 External and Internal Thermal Irreversibility 6.13 Chemical Irreversibility 6.14 Conditions for Reversibility
Chapter 7 The Carnot Cycle and the Thermodynamic Temperature Scale 7.1 Carnot Cycle 7.2 Examples of Carnot Cycles 7.3 Carnot Refrigerator 7.4 Carnot s Theorem and Corollary 7.5 The Thermodynamic Temperature Scale 7.6 Absolute Zero and Carnot Efficiency 7.7 Equality of Ideal-Gas and Thermodynamic Temperatures 23
24CHAPTER 7. THE CARNOT CYCLE AND THE THERMODYNAMIC TEMPERATURE SCALE
Chapter 8 Entropy 8.1 Reversible Part of the Second Law 8.2 Entropy 8.3 Principle of Carathéodory 8.4 Entropy of the Ideal Gas 8.5 T S Diagram 8.6 Entropy and Reversibility 8.7 Entropy and Irreversibility 8.8 Irreversible Part of the Second Law 8.9 Heat and Entropy in Irreversible Processes 8.10 Entropy and Nonequilibrium States 8.11 Principle of Increase of Entropy 8.12 Application of the Entropy Principle 8.13 Entropy and Disorder 8.14 Exact Differentials 25
26 CHAPTER 8. ENTROPY
Chapter 9 Pure Substances 9.1 P V Diagram for a Pure Substance 9.2 P T Diagram for a Pure Substance; Phase Diagram 9.3 P V T Surface 9.4 Equation of State 9.5 Molar Heat Capacity at Constant Pressure 9.6 Volume Expansivity; Cubic Expansion Coefficient 9.7 Compressibility 9.8 Molar Heat Capacity at Constant Volume 9.9 T S Diagram for a Pure Substance 27
28 CHAPTER 9. PURE SUBSTANCES
Chapter 10 Mathematical Methods 10.1 Characteristic Functions 10.2 Enthalpy 10.3 Helmholtz and Gibbs Functions 10.4 Two Mathematical Theorems 10.5 Maxwell s Relations 10.6 T ds Equations 10.7 Internal-Energy Equations 10.8 Heat-Capacity Equations 29
30 CHAPTER 10. MATHEMATICAL METHODS
Chapter 11 Open Systems 11.1 Joule-Thomson Expansion 11.2 Liquefaction of Gases by the Joule-Thomson Expansion 11.3 First-Order Phase Transitions: Clausius-Clapeyron Equation 11.4 Clausius-Clapeyron Equation and Phase Diagrams 11.5 Clausius-Clapeyron Equation and the Carnot Engine 11.6 Chemical Potential 11.7 Open Hydrostatic Systems in Thermodynamic Equilibrium 31
32 CHAPTER 11. OPEN SYSTEMS
Chapter 12 Statistical Mechanics 12.1 Fundamental Principles 12.2 Equilibrium Distribution 12.3 Significance of Lagrangian Multipliers λ and β 12.4 Partition Function for Canonical Ensemble 12.5 Partition Function of an Ideal Monatomic Gas 12.6 Equipartition of Energy 12.7 Distribution of Speeds in an Ideal Monatomic Gas 12.8 Statistical Interpretation of Work and Heat 12.9 Entropy and Information 33
34 CHAPTER 12. STATISTICAL MECHANICS
Chapter 13 Thermal Properties of Solids 13.1 Statistical Mechanics of a Nonmetallic Crystal 13.2 Frequency Spectrum Crystals 13.3 Thermal Properties of Nonmetals 13.4 Thermal Properties of Metals 35