Download Introduction - Temperature Scale

2003. 9.
이병주
포항공과대학교 신소재공학과
[email protected]
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction – Historical Background
Maxwell
· Newton → Classical Mechanics → Electromagnetism → Quantum Mechanics
· Lagrangian
· Rationalism
· Hamiltonian
· Time Reversible
· Experimental fact (산업혁명)
· Heat → Concept of Temperature
· PV work → Concept of Pressure
→ Thermodynamics
· Empirical Rule
· Time irreversible
· Thompson → Rumford
· Davy
· Mayor
· Carnot
· Joule
· Thomson → Kelvin
· Clausius
· Maxwell
· Gibbs
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - J. W. Gibbs
※ Expansion in scope has been made to embrace not only
thermal, mechanical and chemical effects, but also the
kinetic energy and the complete set of potentials energies:
gravitational, electrical, magnetic and body forces,
(with the exception of atomic energy).
※ J. Willard Gibbs, 1883
: On the Equilibrium of Heterogeneous Substances
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Microscopic vs. Macroscopic Point of View
· macroscopic : no special assumption on the structure of matter,
directly measured
· microscopic : assumption on the structure of matter (molecules),
unmeasurable.
can only be justified by comparing some
deduction with that from macroscopic
point of view.
· quantum mechanics
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Role of Thermodynamics
· Foundation of materials science
· Phase Diagrams, Chemical Reactions, Adsorption,
Capillarity effects and Electrochemistry, …, etc.
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Basic Terminology
· System / Surrounding (reservoir)
· State (Properties: description of state),
Change of state (properties) during a process
· Measurable and unmeasurable properties :
Unmeasurable property는 다른 측정 가능한 특성치로부터 결정
⇔ Property 간의 관계식 (EOS)
※ Thermodynamic systems,
thermodynamic properties,
thermodynamic relationships
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Terminology for System
· Unary / multicomponent
· Homogeneous / Heterogeneous
· Closed / Open
· Non-reacting / reacting
· Exchange of energies / No exchange
(※ Isolated)
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - State Function & Process Variable
· Thermodynamics State or State of Thermodynamic Equilibrium
Mechanical, Chemical and Thermal Equilibrium
Uniform and well defined thermodynamic coordinates
No tendency to change with time of thermodynamic coordinates
· path independence
→
 ∂V 
 ∂V 
dV = 
 dP + 
 dT
 ∂P  T
 ∂T  P
· Extensive and Intensive Properties
· Process variable (only have meaning for changing systems)
· work & heat
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Equation of State of an ideal gas
· Boyle’s law (1660):
· Charles’ law (1787):
P∝
1
V
→ PoV (T , Po ) = PV (T , P )
V ∝T →
V ( Po , To ) V ( Po , T )
=
To
T
PV PoVo
=
·
= constant = 1atm×22.414 liters ∕ 273.16 degree-mole
T
To
= 0.082057 liter-atm/degree-mole
· EOS of the ideal gas: PV = RT
▶ unit of Work
1atm = 76 cm of mercury = 76.0×13.595×980.665
= 1.013×106 dyne/cm2
1atm-liter = 1.013 × 102 joule
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Universal Equation of State for pure Substances
E u ( r ) = − Ec (1 + a * )e − a*
a = α ( r / re − 1)
*
1/ 2
 9 BΩ 

α = 
 Ec 
H. Rose, J.R. Smith, F. Guinea and J. Ferrante, Phys. Rev. B 29 (1984) 2963.
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Temperature Scale
▷ Thermal equilibrium and zeroth law of thermodynamics
▷ Temperature concept
the temperature of a system is a property that determines whether or not
a system is in thermal equilibrium with other systems.
▷ Gay-Lussac (1802):
thermal expansion coefficient of "permanent gases" is a constant.
α=
1
Vo
 ∂V 


T
∂
P

where Vo is the volume at 0.0(1) oC. α = 1/267.
· for ideal gas α = 1/273.16 → absolute zero of temperature, -273.16
▷ Measurement of Temperature
· thermometric property, X
· thermometric function, θ(X) ＝ aX
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Temperature Scale
Thermometers and thermometric properties
Thermometers
Gas (const. volume)
Electric resistor (const. tension)
Thermocouple (const tension)
Helium vapor (saturated)
Paramagnetic salt
Blackbody radiation
Thermometric properties
Pressure
Electric Resistance
Thermal Emf
Pressure
Magnetic susceptibility
Radiant emittance
Symbol
P
R
ε
P
χ
RB,λ
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Temperature Scale
Thermometer 마다 scale이 달라, 물의 삼중점을 제외한 나머지 온도에
대해서는 다른 값을 나타냄.
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Temperature Scale
저압에서 error가 작은 gas thermometer를 empirical temperature scale을
정의하기 위한 standard thermometer로 선정
▷ Gas thermometer의 발달 : 측정오차의 원인 분석 및 보완 과정
그림 Simplified constant-volume gas thermometer
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Temperature Scale
▷ Ideal-Gas Temperature, θ
Gas thermometer로 1기압 수증기의 온도를 재었을 때 그 온도는
thermometer에 사용된 gas의 종류에 따라 값이 약간씩 다르나,
PTP를 작게 하면 할수록 동일한 값에 수렴한다. (그림)
 P
θ = 273.16 lim 
PTP →0 P
 TP



(const. V)
※ 가장 적합한 gas로 Pt 용기 속으로 확산되지 않고, 비등점이 낮은 He 선정
→ 0.5 K 까지 측정 가능
※ It will be shown that in the temperature region in which a gas thermometer
may be used, the ideal gas scale and the Kelvin scale are identical.
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Temperature Scale
▷ Celsius Temperature Scale
Ideal Gas temperature scale과 크기가 같으나 물의 삼중점이 0.01oC 가
되도록 zero point 만 shifted 됨. ⇒ t(℃) ＝ θ(K) - 273.15
NMP of H2O
NBP of H2O
＝ 0.00℃
＝ 99.975℃
※ The only Celsius temperature which is fixed by definition is that of the triple point.
▷ Electric Resistance Thermometry
Platinum resistance thermometer : very accurate within the range -253 to 1200oC.
: Empirical formula RPt ＝ Ro (1 + At + Bt2)
⇒ A, B 항의 수가 늘어날수록 여러 개의 standard temperature 필요.
▷ Thermocouple
: Platinum+10%rhodium/platnum thermocouple: 0 to 1600oC.
: Empirical formula ε ＝ a + bt + ct2 + dt3
Byeong-Joo Lee
www.postech.ac.kr/~calphad
Introduction - Temperature Scale
Table Defining fixed points of the ITS-90 (International Temperature Scale)
Number
1
2
7
9
16
17
Temperature
T90/K T90/℃
3 to 5 -270.15 to 268.15
13.8033 -259.3467
83.8058 -189.3442
273.16 0.01
1337.33 1064.18
1357.77 1084.62
Substance(a) State(b) Wr (T90)
He
e-H2
Ar
H2O
Au
Cu
V
T
T
T
F
F
0.00119007
0.21585975
1.00000000
-
(a) All substances except 3He are of natural isotopic composition. e-H2 is hydrogen at the equilibrium concentration of the
ortho and para molecular forms.
(b) For complete definitions and advice on the realization of these various states. See "Supplementary Information for the
ITS-90". The symbols have the following meanings:
V : vapour pressure point
T : triple point (temperature at which the solid, liquid and vapor phases are in equilibrium)
G : gas thermometer point
M, F : melting point, freezing point (temperature, at a preassure of 101 325 Pa, at which the solid and liquid phases
are in equilibrium).
Byeong-Joo Lee
www.postech.ac.kr/~calphad