1. MACROSCOPIC THERMAL SCIENCES
OVERVIEW OF
MACROSCOPIC THERMAL SCIENCES
FUNDAMENTALS OF THERMODYNAMICS
▪ The First Law of Thermodynamics
▪ Thermodynamic Equilibrium and the Second Law
▪ The Third Law of Thermodynamics
THERMODYNAMIC FUNCTIONS AND PROPERTIES
▪ Thermodynamic Relations
▪ The Gibbs Phase Rule
▪ Specific Heats

2. IDEAL GAS AND IDEAL INCOMPRESSIBLE MODELS
▪ The Ideal Gas
▪ Incompressible Solids and Liquids
HEAT TRANSFER BASICS
▪ Conduction
▪ Convection
▪ Radiation

3. environment or surroundings
Fundamentals of Thermodynamics
Definitions of Thermodynamic Terms
constraints
system
(external forces)
parameters
constituent
environment or surroundings

4. property
quantities that characterize the behavior of a system at any instant of time. The property must be measurable and their values are independent of measuring device
spontaneous change of state
change of state that does not involve any interaction
between the system and its environment.
induced change of state
change of state through interaction with other system
in the environment
isolated system
a system which can experience only spontaneous
change of state

5. kinematics
study of the possible and allowed states of a system
dynamics
study of the time evolution of the state
equation of motion
relation that describes the change of state of a system
as a function of time
complete description often unknown
thermodynamic description: in terms of the end states and the modes of interaction (work and heat)
process
specified by the end states and the modes of interaction

6. reversible process
at least one way to restore both the system and its environment to their initial states
irreversible process
not possible to restore both the system and its environment to their initial states
steady state
a state that does not change as a function of time despite interactions between the system and other systems in the environment

7. The First Law of Thermodynamics
conservation of energy
Energy can be transferred to or from a system but
can be neither created nor destroyed.
energy balance for a system
for an infinitesimal change
kinetic energy, potential energy, internal energy

8. Thermodynamic Equilibrium and the Second Law
a state that cannot change spontaneously with time
unstable
metastable
stable :
thermodynamic equilibrium
state principle (stable-equilibrium-state principle)
Among all state of system with a given set of values of energy, parameters, and constituents, there exists one and only one stable-equilibrium state.
All properties are uniquely determined by the amount of energy, the value of each parameter, and the amount of each type of constituents

9. the second law
integrating factor
In an isolated system, entropy cannot be destroyed but can either be created (irreversible process) or remain the same (reversible process).
Entropy can be transferred from one system to another.

10. highest entropy principle
The entropy of the system is largest in the stable-
equilibrium state.
summary of the second law of thermodynamics
There exist a unique stable-equilibrium state for any system with given values of energy, parameters, and constituents.
Entropy is an additive property, and for an isolated
system, the entropy change must be nonnegative.
Among all states with the same values of energy,
parameters, and constituents, the entropy of the stable-equilibrium state is the maximum.

11. Internal energy (U): energy of a system with
volume (V) as its only parameter
r + 2 independent variables by the state principle
entropy: a property of the system
fundamental relations
definitions of temperature, pressure and chemical potential

12. Gibbs relation

13. The Third Law of Thermodynamics
Unique stable equilibrium state exists at zero absolute temperature (Nernst theorem).
spontaneous change of state
adiabatic availability
stable equilibrium state curve
lowest energy principle
Eg > 0: ground-state energy

14. Thermodynamic Relations
Thermodynamic Functions and Properties
Thermodynamic Relations
enthalpy
: characteristic function

15. Helmholtz free energy
Gibbs free energy

16. homogeneous state:
All subsystems are exactly identical to each other.
simple system:
a system that experiences only homogeneous states
for k equal-volume subsystems
intensive property: T, P, mj
extensive property: U, S, V, N

17. specific property
the ratio of an extensive property to the total amount of constituents (mass, mole, or number)
For a simple system,
Euler relation
Gibbs-Duhem relation
Euler relation for r = 1,
The chemical potential of a pure substance is specific Gibbs free energy.

18. The Gibbs Phase Rule
phase : collection of all subsystems that have the same values of all intensive properties
for a q-phase heterogeneous state
independent variables T, P, mi (i = 1, 2, 3, …, r)
Gibbs-Duhem relation
number of independent variable reduced to
Gibbs phase rule
r + 2: independent variables, q: number of equations
for a pure substance,
a single-phase state,
a two-phase state,
a three-phase state, T, P, m are all fixed: triple point

19. P – T diagram for a pure substance
S-L line
Critical point
Liquid
Solid
L-V line
Triple point
S-V line
Vapor T

20. T – v diagram for a material that expands upon melting
P＞Pc
P = Pc
S-L region
Temperature, T
(Tc,Pc)
L-V dome
P＜Pc
Liquid
Saturated Liquid
Saturated Vapor
Solid
Triple-point line
P＜Pt.p.
Sublimation
S-V region
Specific volume v

21. Specific Heats specific heat at constant volume
specific heat at constant pressure
heat reservoir
an idealized system that experiences only reversible heat interactions. For any finite amount of energy transfer, its temperature remains unchanged.
Specific heats are properties of a system
The specific heat at constant volume and the specific heat at constant pressure are defined as ~~~~
Specific heats are not defined for all equilibrium states.
For example, in two-phase state, the enthalpy varies without changing of temperature
So the specific heat approaches to infinity in these states.
For pure substance in a single phase, all properties can be expressed as function of T and P
This equation does not contain any information about the internal energy or the entropy.
However, we can use specific heat in addition to the equation of state to determine all intensive properties.

22. equation of state
For pure substance in a single phase, all properties
can be expressed as function of T and P. or

23. Ideal Gas and Ideal Incompressible Models
from molecular view,
intermolecular potential energy
associated with the forces between molecules and depends on the magnitude of the intermolecular forces and the position at any instant of time
molecular kinetic energy
associated with the translational velocity of individual molecules
intra-molecular energy (within the individual molecules)
associated with the molecular and atomic structure and related forces

24. The Ideal Gas intermolecular potential energy
Impossible to determine accurately the magnitude
because either the exact configuration nor orientation of the molecules is not known at any time or the exact intermolecular potential function.
Two situations which lead good approximations
At low or moderate densities: The molecules are relatively widely spread, so that two-molecules or two- and three- molecule interactions contribute to the potential energy.
At very low densities (high Temperature & very low pressure): Average intermolecular distance between molecules is so large that the potential energy may be assumed to be zero.
⇒ The particles would be independent of one another.
Ideal gas

25. equation of state
real Gas
compressibility factor
Z depends on the temperature & pressure.

26. real gas: affected by intermolecular force
Van der Waals
Virial
Beattie-Bridgman

27. Mayer relation
for ideal gas
perfect gas,
= constant

28. entropy

29. Incompressible Solids and Liquids
equation of state for incompressible solids and liquids
constant
constant

30. Heat Transfer Basics What is heat ? in a solid body
crystal : a three-dimensional periodic array of atoms
oscillation of atoms about their various positions of equilibrium (lattice vibration): The body possesses heat.
conductors: free electrons ↔ dielectics

31. vibration of crystals with an atom
longitudinal polarization vs. transverse polarization
us-1 us
us+1
us+2 s
s+1
s+2
s+3
s-1
us-1 us
us+1
us+2
us+3
the energy of the oscillatory motions:
the heat-energy of the body
more vigorous oscillations:
the increase in temperature of the body

32. Internuclear separation distance
in a gas
the storage of thermal energy:
molecular translation, vibration and rotation
change in the electronic state
intermolecular bond energy
average kinetic energy
kB = × J/K
Internuclear separation distance
(diatomic molecule)
Energy
dissociation energy for state 1
dissociation energy for state 2
electronic state 2
vibrational state
rotational state
electronic state 1
at T = 300 K,
air M = kg/kmol
= m/s

33. heat transfer
Heat transfer is the study of thermal energy transport within a medium or among neighboring media by
molecular interaction: conduction
fluid motion: convection
electromagnetic wave: radiation
resulting from a spatial variation in temperature.
energy carriers: molecule, atom, electron, ion, phonon (lattice vibration), photon (electro-magnetic wave)

34. continuum hypothesis
Ex) density
microscopic uncertainty
macroscopic uncertainty
local value of density
(3×107 molecules at sea level, 15°C, 1atm)

35. microscopic uncertainty
due to molecular random motion
macroscopic uncertainty
due to the variation associated with spatial distribution of density
In continuum, velocity and temperature vary smoothly. → differentiable
mean free path of air at STP (20°C, 1 atm)
lm = 66 nm,
bulk motion vs molecular random motion

36. local thermodynamic equilibrium
hot wall at Th
adiabatic wall L
adiabatic wall
gas
cold wall at Tc
a) lm << L : normal pressure
b) lm ~ L : rarefied pressure
c) lm >> L

37. governing equations
continuity eq.: mass conservation
for a fixed volume in space
Since V can be chosen arbitrary

38. in Cartesian tensor notation
incompressible flow or

39. momentum eq.: Newton’s 2nd law of motion
rate change of momentum = forces exerted on the body
forces
body force [N/m3]
surface force [N/m2]
stress tensor or

40. Momentum theorem

41. or
For a Newtonian fluid

43. For a constant m, l fluid
Stokes’ hypothesis
For an incompressible flow

44. energy eq.: 1st law of thermodynamics
: total energy
e : internal energy
rate equation or

46. total energy equation

47. Mechanical energy equation

48. Thermal energy equation
: viscous dissipation
If l = 0,

49. equation in terms of enthalpy hor

50. entropy equation

51. thermal energy equation in terms of temperature
First Tds equation
v : specific volume
Second Tds equation
Volume expansion coefficient
Isothermal compressibility

52. from first Tds equation
from entropy equation

53. from second Tds equation
from entropy equation

54. ideal gas

55. summary
with ideal gas assumption

56. Conduction Gases and Liquids Due to interactions of
atomic or molecular
activities
Net transfer of energy by
random molecular motion
Molecular random motion→ diffusion
Transfer by collision of random molecular motion
Solids
In non-conductors (dielectrics):
exclusively by lattice waves
In conductors:
translational motion of free electrons as well

57. Fourier’s law
heat flux
[J/(m2s) = W/m2]
k: thermal conductivity [W/m·K]
As Dx → 0,

58. Heat flux
vector quantity

59. temperature : driving potential of heat flow
heat flux : normal to isotherms
along the surface of T(x, y, z) = constant
T(x, y, z) = constant

60. Convection energy transfer due to bulk or macroscopic motion of fluid
bulk motion: large number of molecules moving
collectively
convection: random molecular motion
+ bulk motion
advection: bulk motion only

61. solid wall
hydrodynamic (or velocity)
boundary layer
thermal (or temperature)
boundary layer
at y = 0, velocity is zero: heat transfer only by molecular random motion

62. solid wall
When radiation is negligible,
h : convection heat transfer
coefficient [W/m2.K]
Newton’s Law of Cooling

64. Convection Heat Transfer Coefficient
not a property: depends on geometry and fluid dynamics
forced convection
free (natural) convection
external flow
Internal flow
laminar flow
turbulent flow

65. Thermal Radiation Characteristics
Independence of existence and temperature of medium
Ex) ice lens
black carbon paper
ice lens

66. 2. Acting at a distance
Ex) sky radiation
electromagnetic wave or photon
photon mean free path
ballistic transport
volume or integral phenomena
conduction
fluid: molecular random motion
free electron
solid: lattice vibration (phonon)
diffusion or differential phenomena as long as continuum holds

67. 3. Spectral and directional dependence
quanta
surface emission
history of path l il

68. Thermal radiation spectrum
ultra violet
0.4
infrared
0.7
thermal radiation
visible

69. Two points of view
Electromagnetic wave
Maxwell’s electromagnetic theory
Useful for interaction between radiation and matter
2. Photons
Planck’s quantum theory
Useful for the prediction of spectral properties of absorbing, emitting medium

70. Two distinctive modes of radiation
Thermal radiation through transparent media: surface radiation
Theoretical frame work
Solid state theory
Micro-physical properties
r, g, m
Optical constants n, k
EM theory
Transport theory q T
Surface radiative properties
e, r, a
Geometric integral eq.

71. 2. Thermal radiation in participating media:
gas radiation
Theoretical frame work
Quantum theory
Mie theory
Molecular or particle parameters
Radiation properties al, sl
Transport theory q T
Radiative Transfer Eq. (RTE)

72. Physical mechanism of absorption and emission
composition of radiating gas:
molecules, atoms, ions, free electrons
photon: basic unit of radiation energy
emission: release of photons of energy
absorption: capture of photons of energy
3 types of transition
bound-bound
bound-free
free-free

73. free-free transition
free-bound emission
free state
bound-free absorption EI
ionized energy E4
bound-bound emission E3
bound-bound absorption
bound state E2
E1 = 0
Energy transition for atom or ion

74. Bound-bound transition
When a photon is absorbed or emitted by an
atom or a molecule and there is no ionization
or recombination of ions or electrons
Magnitude of energy transition: related to
frequency of emitted or absorbed radiation
E3  E2 emission, E3 - E2 = hn a photon emitted with hn or
fixed frequency associated with the transition of energy level

75. E1  E2, E3, E4 absorption
in the form of spectral lines n an

76. an n Broadening Effect natural broadening
(Heisenberg uncertainty principle)
Doppler broadening
collision broadening
Stark broadening (strong electric field) n an

77. Carbon dioxide gas at 830 K, 10 atm

78. Transition of energy state
bound-bound transition
molecules:
rotational states
vibrational states
electronic states
atoms: electronic state

79. Internuclear separation distance
electronic state 2
vibrational state
Energy
dissociation energy for state 2
Transition between rotational levels in different electronic state
rotational state
Transition between rotational levels of same vibrational state in same electronic state
Transition between rotational levels in different vibrational states of same electronic state
dissociation energy for state 1
electronic state 1
Internuclear separation distance
(diatomic molecule)

80. Rotational transition within a given vibrational state:
associated energies at long wavelength 8 ~ 1000 mm
2) Vibration-rotation transition:
at infrared 1.5 ~ 20 mm
3) Electronic transition:
at short wavelength in the visible region 0.4 ~ 0.7 mm
Engineering industrial temperature:
vibration-rotation transition

81. 2. bound-free transition
sufficient energy of ionization or recombination
bound-free absorption (photoionization)
free-bound emission (photorecombination)
continuous absorption coefficient
3. free-free transition
in ionized gas (bremsstrahlung)

82. Scattering
Redirection of photons
reflection, refraction, diffraction
Elastic scattering (coherent)
Inelastic scattering
Isotropic scattering
Anisotropic scattering
Dependent scattering
Independent scattering

83. Scattering Regime
size parameter: pD/l
Rayleigh scattering:
molecular scattering pD/l << 1
Mie scattering:
Mie theory pD/l ~ 1
Geometric scattering:
principle of geometric optics pD/l >> 1

84. Intensity (spectral)
the amount of radiation energy streaming out through a unit area perpendicular to the direction of propagation ,
per unit solid angle around the direction w,
per unit wavelength around l,
and per unit time about t

85. solid angle: a region between the rays of a sphere and measured as the ratio of the element area dAn on the sphere to the square of the sphere’s radius
Rsinq
(steradian, sr) dq
dAn q R
ex) hemisphere: df f

86. spectral intensity: il l il dw dl f q dA
total intensity:

88. spectral radiative heat flux:q dA dw il
spectral radiative heat flux: dl l il
total radiative heat flux:

89. Emissive power fe qe dA
dwe
il,e
directional spectral emissive power
hemispherical spectral emissive power
hemispherical total emissive power

90. Blackbody radiation
Blackbody: a perfect absorber for all incident
radiation
black: termed based on the visible radiation, so
not a perfect description
b) Maximum emitter in each direction and at every
wavelength T
black T
non-black
c) Emitted intensity from a blackbody is invariant with
emission angle.

91. Simulated blackbody

92. Blackbody hemispherical spectral emissive power

93. Planck’s law
The Theory of Heat Radiation, Max Planck, 1901
spectral distribution of hemispherical
emissive power of a blackbody in vacuum
h: Planck constant
C0: speed of light in vacuum
k: Boltzmann constant

94. in a medium with a refractive index n:
n = 1 in vacuum and n = in air at room temperature over the visible spectrum

95. Blackbody spectral emissive powerlT
elb (W/m2.mm)
Blackbody spectral emissive power

96. Wien’s displacement law (1891)
lmax : the wavelength at which elb(l,T) is maximum lT

97. Blackbody total intensity and total emissive power
Stefan-Boltzmann’s law:
Stefan by experiment (1879):
Boltzmann by theory (1884):

98. Radiative Transfer Equation
Attenuation by absorption and scattering
Augmentation of intensity by emission
Augmentation of intensity by incoming scattering
Radiative Transfer Equation

99. Energy equation : summary
where