Thermometers
" A thermometric property
" Readings should be reproducible
" Construction easily duplicated
" Capable of reading T in a wide range
Thermometric systems
System Property
mercury-in-
Fixed Gas Volume Pressure
glass
Pt wire Resistance
thermometer
Thermocouple EMF
Helium Vapour Pressure
Paramagnetic Salt Magnetic
Susceptibility
Black Body Radiant Emission
Temperature scales
thermometric
property
Not good
Good
Might be OK
T
T1 T2
We need a type of thermometer,
independent of the properties of any
particular substance.
1
Constant-volume gas thermometer
mercury
reservoir
h
If the gas has a low
CV density
gas
T = kP
T
at constant gas volume
T to be measured
Bring gas & System to thermal equilibrium
Adjust reservoir to bring the meniscus to the
Constant Volume (CV) mark
Measure P
Constant-volume gas thermometer
Consider two systems, A and B
TA = kPA TB = kPB
P
TB PB
=
TA PA
We can compare the
0 273.15 K
T
temperature of the two
(-273.15 oC) (0 oC)
systems
In order to measure the
temperature, we need a
temperature scale
2
Temperature scale: the Triple Point of water
The phase diagram of water
P3 = 610Pa
T3 = 0.01oC
P
Patm
T3 = 273.15+0.01= 273.16 K
liquid
For water at standard pressure
solid
vapour
( )
TMP = 273.15K 0oC
T
Triple Point
( )
TBP = 373.15K 100oC
(P3,T3)
Calibration of the CV gas thermometer
T P
=
vapour
ice
T3 P3
P P
T = T3 = 273.16
P3 P3
water
For low gas densities, all gas
thermometers give the same
A triple-point cell
temperature for a given system,
irrespective of the gas used.
3
Temperature scales
Celsius temperature scale
TMP = 0 oC pure water freezing temperature
TBP = 100 oC pure water boiling temperature
Kelvin temperature scale
" Ideal gas scale
" Kelvin scale derived from the Second Lawof
Thermodynamics Ò! Material Independent
" Why is T3 = 273.16 K?
TBP
TBP -TMP =100 K
= 1.36609
TMP
(making temperature
(experiment)
difference of 1oC =1 K)
o
TMP = 273.15 K (0 C)
T3 = 273.15+0.01= 273.16 K
TBP = 373.15 K (100oC)
Practical thermometers
1. The constant-volume gas thermometer
P
T = 273.16
P3
Ideal behaviour at low density
Helium is most suitable
- liquifies at ~2.6 K
- does not diffuse through e.g. Pt
The primary standard
Cumbersome for practical applications
4
Practical thermometers
2. Platinum resistance thermometer
R(T)= R3(1+Ä…T + ²T2)
R3 can be calculated from the resistance at the water
triple point
Ä… and ² are empirical constants (determined by
different reference points)
Accurate and reproducible
Simple, stable and pure
Large T range (13.8  1234.9 K)
Empirical relationship: R(T) not known from first
principles
Practical thermometers
3. Thermocouples
2
µ (T ) = C0 + C1T + C2T +
metal A
C0, C1, C2 are constants, different for
T2
I
T1
each thermocouple: needs calibration
metal B
Reference junction
Rapid response (small mass)
Large T range (e.g. from -270 to +1234.9 oC for
chromel/alumel)
Precision Ä…0.2 oC (not so accurate as Pt resistance)
5
Practical thermometers
4. Radiation thermometer
Based on Planck's law for a blackbody radiator: the
spectrum of emitted radiation depends on T
Correction for real emitters (emissivity must be known)
Photoelectric detector compares spectrum with standard
For high T (>1100 oC)
Non-contact
Rapid response times (no need for thermal equilibration)
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