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![Page 1: How is temperature measured? T measurement is not based on a fundamental physical unit. Use a thermodynamic parameter (X) that varies in a known way with.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e245503460f94b12f4c/html5/thumbnails/1.jpg)
How is temperature measured?• T measurement is not based on a fundamental physical unit.
• Use a thermodynamic parameter (X) that varies in a known way with temperature.
• Measure its value at TWO fixed points of temperature and then interpolate and extrapolate.
X
Temp.
•
•
FP2FP1
X1
X2
Error!
Xm
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n.b.p. = normal boiling point
Ranges of various types of thermometer
V
P or V
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Reference Points for Older Temperature Scales
Daniel Fahrenheit (Danzig (Gdansk)1724)
Anders Celsius (Sweden, 1742)
Boiling point of water = 0 ºC !
Melting point of ice = 100 ºC!
Values were later reversed. Scale called “centigrade”
Ice, water and ammonium chloride mixture = 0 °F
Human body = 96 °F (now taken as 98.6 °F)
Two (or more) reference points result in errors when extrapolating outside of their range.
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)++1(= 20 BtAtRRt
For 0 ºC < t < 850 ºC
Pt Resistance Thermometer
Blundell and Blundell, Concepts in Thermal Physics (2006)
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Fixed temp.
(cold junction)
+ -Unknown temp.
(hot junction)
VSeebeck effect
Principle of Thermocouples
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Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094
Metals used for Thermocouples
Each type requires calibration against fixed points.
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Radiation energy density
Planck distribution law
T1∝max
infraredUV-Vis.
Spectral Distribution of Thermal Radiation
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4423
45
=15
2= TT
ch
kR
Stefan-Boltzmann equation:
Thermal Radiation
( )4=TPWTT
TPWRR
Compare radiation flux at an unknown temperature to the flux from a fixed point: triple point of water
SB constant
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Black Body Radiation from Au at its Melting Point
Used to calibrate pyrometers.
See presentation by Mark Owen at the Professional Training conference to hear about pyrometry at NPL.
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Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094
Fixed Temperature Reference Points
Melting points of metals and alloys
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xcTX =
Defining a Temperature Scale with a Single Fixed Point
X is a thermodynamic variable, Tx is the temperature at which it is measured, and c is a constant.
• Requires a linear (monotonic) relationship:
• Also requires a single fixed point. There are several possibilities!
• By international agreement* in 1954, the so-called “thermodynamic temperature scale” uses the triple point (TP) of water defined - not measured! - to be 273.16 K.
*Tenth General Conference on Weights and Measures
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•0.006
The Triple Point of Water
At the triple point of water: gas, solid and liquid all co-exist at a pressure of 0.006 atm.
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Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094
Cell for Establishing the Triple Point of Water
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Defining a Temperature Scale with a Single Fixed Point
K
T
cT
cT
XX x
TP
x
TP 16.273==
)(16.273=TP
x XX
T
We see that:
What thermodynamic variable should be measured to use the thermodynamic temperature scale?
So,
![Page 15: How is temperature measured? T measurement is not based on a fundamental physical unit. Use a thermodynamic parameter (X) that varies in a known way with.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e245503460f94b12f4c/html5/thumbnails/15.jpg)
( ) cTTP VnR ==
TPTP PP
KTK
TPP
16.273=⇒16.273
=
The Gas Scale of Temperature
Ideal gas law:
TP = 273.16KUnknown T
GasP, V
V and n are held constant.
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A constant-volume gas thermometer
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°C = K - 273.15Relationship between °C and K:
Defining the Kelvin and Celsius scales
Note that careful measurements find that at 1 atm. water boils at 99.97 K above the melting point of ice (i.e. at 373.12 K). 1 K is not exactly equal to 1 °centigrade!
“One Kelvin degree is 1/273.16 of the temperature of the triple point of water.”
Named after William Thomson (Lord Kelvin) who was a professor at the University of Glasgow.
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Proposed definition of the Kelvin
• Recognising that thermal energy is given by kT (where the Boltzmann constant is k = 1.38065 x 10-23 JK-1), the Kelvin could be defined simply as:
“The kelvin is the change of thermodynamic temperature that results in a change of thermal energy kT by 1.38065XX × 10−23 Joule.”
This definition requires a very precise measurement of k!
• Temperature scales have been refined as recently as 1990 (International Temperature Scale)
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Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094
R = NAk
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Measuring k with Brownian Motion
x rkT
tx
D6
=6
><=
2 is viscosity of fluid phase;
r is the particle radius
Random path
Sub-m polymer particles in water
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Third Law of Thermodynamics
Planck: The entropy of all systems is the same at 0K and may be taken to be zero.
A temperature of 0 K is unattainable in a finite number of steps.
Blundell and Blundell, Concepts in Thermal Physics (2006)