Download FUNDAMENTALS OF THERMOMETRY PART I by Henry E

FUNDAMENTALS
OF
THERMOMETRY
PART
by
Henry
1: THE
E.
I
Sostmann
ABSOLUTE,
OR THERMODYNAMIC
KELVIN,
TEMPERATURE
Temperature
is a measure
of the hotness
of something.
be rational
(and
useful
between
people),
there
must
scale
of numerical
values
(the
most
familiar
of which
Centigrade
Scale),
and
on
devices
for
interpolating
temperature
scale
with
a real
Kelvin
Temperature
and
Second
laws
of
SCALE
For
a measure
to
be agreement
on a
is the
Celsius
or
between
the
defining
VdUfZS.
The
only
namic
First
absolute
is linear
establish
TKTS,
Zero,
by
its
as
Scale
(TKTS),
Thermodynamics.
or zero
Kelvin,
or
definition,
only
one
slope.
That
reference
273.15K,
or
basis
in
nature
which
can
The low
OK (without
nonzero
point
is
the
Thermody-
be deduced
limit
of the
from
the
TKTS
is
the
* mark),
and
since
it
reference
point
is needed
to
was
chosen,
in the
original
0-C.
O’C is a temperature
with
which
we all have
a common
experience.
It is
the temperature
at which
water
freezes,
or,
coming
from
the other
side,
ice melts;
at which
water
exists
under
ideal
conditions
as both
a liquid
and a solid
under
atmospheric
pressure.
In 1954 the reference
point
was
changed
to a much
more
precisely
reproducible
point,
O.Ol’C.
This
is
known
as the
triple
point
of water,
and
is the
temperature
at which
water
exists
simultaneously
as a liquid
and a solid
under
its own
vapor
pressure.
The triple
point
of water
will
be the subject.
of extended
discussion
important
in
a later
reference
article
in
this
series
point
in thermometry.
The unit
of temperature
temperature
interval
K, and
‘C or K (the
indicate
a temperature
1K or
l’C,
but
the
of
articles.
It
is
the
most
of the TKTS is the kelvin,
abbreviated
“K”.
The
‘C is identically
equal
to the
temperature
interval
latter
without
the
’ symbol)
may
be used
also
to
interval.
The
difference
between
1’C
and
2-C
is
temperature
1-C
= the
temperature
274.15K.
Measurements
of
temperature
employing
the
TKTS
directly
are
hardly
suitable
for
practicable
thermometry.
Most
easily
used
thermometers
are
not
based
on functions
of the
First
and
Second
Laws.
The
practicable
thermometers
that
will
be
discussed
later
in this
series
of
articles
depend
upon
some function
that
is a repeatable
and single-valued
analog
of, or consequence
of, temperature,
and they
are used
as
devices
of utilitarian
temperature
scales
(such
as the
Temperature
Scale)
which
are themselves
artifacts.
The main
the
realisation
of the
TKTS
is to establish
relationships
Thermodynamic
Scale
of
nature
and
the
practical
thermometers
of the
laboratory
or of industry,
so that
made
by non-thermodynamic
means
can be translated
into
TKTS,
and
rational
temperature
scales
can be constructed
related
to real&able
physical
phenomena.
There
points.
two or
ture
is
exist
in nature
a number
These
are physical
states
three
of the three
possible
constant.
of
in
what
which
phases
interpolation
International
purpose
between
for
the
scales
and
measurements
terms
of the
on a basis
are called
thermometric
some pure
material
simultaneously,
and
fixed
exists
in
tempera-
A two-phase
equilibrium
is represented
by the earlier
example
of the
freezing
point
of water,
or, more properly,
the coexistence
of liquid
and
solid
water.
For this
equilibrium
to represent
a constant
temperature,
O’C, pressure
must be specified,
and the
specification
is a pressure
of
1 standard
atmosphere,
10 1325 Pascal.
(A two-phase
fixed
point
at 1
standard
atmosphere
is called
the “normal”
point).
The variation
due to
pressure
from
the defined
temperature
of a liquid-solid
equilibrium
is
not
large
(which
is not
to say that
it may not
be significant).
The
freezing
point
of water
is reduced
approximately
O.OlK
for an increase
of pressure
of 1 atmosphere.
The variation
due to pressure
for a liquidvapor
equilibrium
is relatively
very
large.
A three-phase
equilibrium
is represented
by the triple
point
the coexistence
of liquid
and solid
water
under
its own vapor
at 0.Ol.C.
Because
all
three
possible
phases
are
determined
physical
state,
it is generally
possible
to realise
a triple
point
curately
than a two-phase
point.
This
may
be seen
from
the
Phase
Rule
of water,
pressure,
by the
more
ac-
of Gibbs:
P-C-2=F
where
P is an integer
equal
to the number
of phases
present,
C is the
number
of kinds
of molecule
present
(for an ideally
pure
material,
C =
1) and F is an integer
giving
the number
of degrees
of freedom.
Obviously,
for the two-phase
equilibrium
there
is one
degree
of freedom,
pressure,
and for the three-phase
equilibrium
F = 0; that
is, the temperature
is independent
of any other
factor.
Fig.1
illustrates
one,
two
and three-phase
equilibria.
la
2a
P=l
C=l
F=3
3a
P=2
C=l
F=2
P=3
C=l
F=O
Fig.
1: The Phase
Rule of Gibbs.
P = the number
of phases
C = the
number
of components
(1 for
a pure
material);
degrees
of
freedom.
la is uncontrolled.
lb is
a melt
point.
Ic is a triple
point.
A typical
since
the
(or rather
device
for
realizing
the
TKTS
is
vapor
pressure
of an ideal
gas
a statistical
mechanical
function,
same thing).
The
to be the
change
transfer
function
in pressure
of
A rudimentary
gas
illustrated
by using
low the
temperature
Celsius
Scale.
the
helium
gas
thermometer,
is a thermodynamic
function
which
for the purpose
is the
of a gas
a gas kept
change
in volume
of a gas
kept
at constant
to measure
accurately
change
in pressure
in volume,
constant-volume
gas
thermometers
than
constant-pressure
gas thermometers.
present;
F q the
or
freeze
thermometer
at constant
may be
volume,
chosen
or the
pressure.
Since
it is easier
than
it is to measure
change
are
more
common
in use
thermometer
is shown
in
it to show
that
the
zero
of the
normal
freezing
Fig
2. Its
operation
will
of the TKTS
is 273.15K
point
of water,
0’
on
be
bethe
Fig.
2 shows
a cylindrical
bulb
of constant
volume,
connected
by tubing
defined
as constant-volume,
to a U-tube
manometer.
A second
connection
to the
manometer
leads
to a reservoir
of mercury,
which
contains
a
plunger,
P, by means
of which
the column
height
of the manometer
may
be varied.
The constant-volume
bulb
and tubing
contain
an ideal
gas.
4
The bulb
is first
surrounded
by an equilibrium
mixture
of ice and water
(C, in Fig 2a). When the gas is in thermal
equilibrium
with the slurry
in
the bath,
the pressure
of the gas is adjusted
by moving
the plunger
so
that
both
columns
of mercury
in the U-tube
are at the same
height,
corresponding
to an index
mark
1.
2a
2b
Fig.2:
A rudimentary
gas thermometer.
B = mercury,
C = water
t ice (O-C),
(100’(Z),
P = a plunger
for adjusting
A = helium
gas.
D = water
t steam
mercury
level.
Next, the ice bath
is removed
and replaced
with a bath containing
boiling water,
or more
correctly,
an equilibrium
mixture
of liquid
and vapor
water
at a pressure
of 1 standard
atmosphere,
(D, in Fig 2b). As the
manometric
gas
is heated
by the
boiling
water
it expands,
and
the
mercury
in the manometer
is displaced.
The plunger
is actuated
to reposition
the surface
of the mercury
in the left leg at the index
mark
1,
restoring
the criterion
of constant
volume
in the closed
gas system,
a
condition
shown
in Fig 2b. However
the mercury
in the right,
open
leg
is not now at the
index
mark
1, but
measurably
higher.
In fact,
the
difference
in heights
indicates
that
the pressure
of the enclosed
gas at
the boiling
point
is 1.366099
times the pressure
at the freezing
point.
We
can then
calculate:
(100-c
- O’C)/(1.366099
- I)
= 273.15
Eq.2
5
and from
pressure
reduced
zero
this
we can understand
ratio
change
between
by
273.15
Celsius
or
is
Scale
reached
is
which
therefore
T = t
is
the
273.15K,
zero
TKTS.
The
zero
of
the
gas
constant
volume
the
TKTS and t is temperature
interval
and the
zero
to the
properties
of
thermometer
measurements
on the Celsius
of the TKTS
have
any
specific
sub-
can
be
expressed
P2
where
the
Ts
are
Scale,
and
the
TOs
= 01 - To) /
(‘5
- To)
temperatures
are
the
relationship
assumes
the
gas
thermometer
or the
volume
of the
on
zero
of
Eq.4
the
that
TKTS,
the
natural
temperature
Scale.
an ideal
gas.
The reader
reflects
Charles’
or Boyle’s
gas,
respectively,
be held
will
have
law,
if
constant.
gas is a gas
whose
behavior
can be predicted
exactly
from
Charles’
Law,
which
obeys
it through
all ranges
of temperature
sure,
and
where
the
relationship
between
concentration
(n/V),
temperature
and
(n/V)(T/P)
absolute
= I/R
commonly
written
pressure
observed
the
presAn ideal
Boyle’s
or
or presabsolute
is
Eq.5
= a constant
as
Eq.6
PV = nRT
where
R is the
gas constant,
identical
for all ideal
gases.
and is known
to about
30ppm.
A second
condition
is that
thus
the
internal
energy,
intermolecular
forces
acting,
depend
on the molecular
distances,
and
(6E
Unfortunately
is a large
/
in
equation
PI /
more
Celsius
Eq.3
All
This
that
sure
the
+ 273.15
on the
temperature
reference
of
of
as l/273.15
of the
if temperature
is
O’C,
an absolute
and
where
T is temperature
Scale.
Note that
the
been
defined
without
stance.
terms
the Celsius
degree
O’C and
1OO’C.
Thus
kelvin
intervals
below
6V)T
R = 0.082053,
there
be no
V, does
not
Eq.7
= 0
there
number.
is no real
ideal
gas,
Helium
comes
closest,
and
the
carbon
uncertainty
dioxide
of
varies
30ppm
most
6
widely
sures
possible
(or
the
from
ideality.
are
reduced,
to measure
change
However
real
reflecting
the
change
in
volume
of
gases
a
in
approach
reduction
pressure
a gas
at
ideality
in
density.
a gas
of
zero
volume)
as
at
the
their
Since
zero
pres-
it is not
pressure
requirement
for
an ideal
gas is approached
by making
a number
of measurements
at a
number
of pressures
and
extrapolating
to zero
pressure.
Such
a system
of measurements
is shown
in Fig.
3. Regardless
of the nature
of the gas,
all gas thermometers
at the same temperature
approach
the same reading
as the pressure
of the gas approaches
zero.
374.0
-
Fig3:
Pressure
pressures
at
Several
authors
ratios
of various
the condensation
have
proposed
gases
at various
point
of steam.
modifications
count
for
the
non-ideality
of real
gases.
of Clausius,
is the
virial
equation,
which
of the density
of the gas, and is written:
PV = nRT(1
where
the
nB,
+ --”
coefficients
etc.,
volume
virial
given
temperature.
mometry,
it
is
coefficient.
The departure
accurate
gas
n2Cv
+ ---“2
B,
n3Dv
+ ---“3
C, D, etc.,
from
the
ideal
One which
is a series
gas
are
law
is much
expansion
to
used,
in
ac-
that
terms
Eq.8
+...)
coefficients,
and
Over
the
usual
seldom
necessary
of real
gases
thermometry.
of
called
the
second,
third,
fourth,
are constants
for
a given
gas at a
range
of gas
densities
in gas
therto
go
beyond
the
second
virial
ideality
is
only
one
of
the
problems
of
A second
is the
purely
mechanical
matter
a real
connection
to convey
the
pressure
ter.
It is inconvenient
to locate
the bulb
thermostatted
enclosures,
2 to illustrate
enclosure,
and
a
common
of dead
space.
There
from
the bulb
to the
and the manometer
in
practice
each
carefully
thermostatted.
this
configuration.
Fig.
Fig.4:
Thermostatted
gas thermometer.
meter
and the gas bulb
are separately
temperature;
the (long,
perhaps
many
is not.
The
length,
price
which
paid
is that
goes
through
whose
temperature
and
compromise.
is
The
there
the
is a capillary
wall
of each
essentially
bulb
volume
is
4 is
to
use
two
must
be
manomethe same
separate
a modification
of
Fig.
The U-tube
manokept
at constant
meters)
capillary
tube,
generally
of
of the
two
thermostats
uncontrolled.
The
solutions
can
be made
as large
The temperature
distribution
as
some
and
are
care
possible
along
the
relative
to the capillary
volume.
capillary
length
can
be measured
at
suitable
intervals.
The
capillary
volume
can be kept
small
by providing
a capillary
of small
diameter,
but
not so small
as to introduce
thermomolecular
pressures
where
the tube
a correction
for
passes
through
a temperature
gradient,
or , conversely,
thermomolecular
pressure
can be made.
8
A third
obvious
problem
is that
als of construction.
An
that
only
the contained
ality
known
correction
in
the
system,
A fifth
relates
or impurities
required
is
including
that
to the
remaining
the
thermal
ideal
constant-volume
gas is subject
to
the whole
system
is subject
or estimated,
and for which
A fourth
gas
of
effects
from
to
for
gas
thermal
temperature
correction
the
of
expansion
changes,
which
must
be made.
gas
of sorption,
a less
than
the
head
column
in which
ideally
materi-
thermometer
assumes
expansion,
while
in re-
hydrostatic
the
of
must
pressure
of
be
the
itself.
impurities
in
clean
system,
the
are
gas,
ab-
sorbed
on the
walls
of the
bulb
and
other
parts
of the
thermometer
system
at the
reference
temperature,
desorbed
at a higher
temperature,
with
the effect
of elevating
the measured
gas pressure,
and then
reabsorbed
as the temperature
approaches
the
references
temperature.
Attention
to the
elimination
of sorption
has
resulted
in gas
thermometry
measurement
Gas
of
the
thermometry
menters
ner and
normal
has
for
some
Edsinger,
boiling
claimed
generations,
followed
the
point
of
attention
the most
by Schooley,
dards.
This
work
forms
much
of the
Practical
Temperature
Scale
of 1968
Scale
of 1990,
in an effort
to more
water
of
as
a
99.975-C!
number
recent
of whom
at the National
thrust
to replace
with
the International
closely
approximate
temperatures
in a practicable
Scale.
A concise
mometer
and
gas
thermometry
at the
NBS
is
should
be
consulted
by
anyone
interested
Schooley
provides
an example
of the
accuracy
of
fine
experi-
have
been
GuildBureau
of Stanthe
International
Temperature
thermodynamic
account
of the
gas
therand
given
by
Schooley,
in experimental
elegance.
and
precision
of this
work:
Fixed
Steam
point
Gas
therm
IPTS-68
Uncertainty
IC
IC
3
pt
99.975
231.924
419.514
231.9681
419.58
Tin pt
Zinc
pt
100.000
M.005
f0.015
io.03
With
the conclusion
of work
in preparation
for
ITS-90,
is considered
to be a finished
matter
at the NBS.
The
itself,
which
should
have
been preserved
as a national
ment,
is now
in the process
of dismemberment.
As a generality,
namic
values
methods
have
of
gas
the
been
thermometry
thermometric
used
largely
has
led the
fixed
points,
to
check
its
gas thermometry
gas thermometer
shrine
or monu-
development
of
and
a variety
accuracy
and
thermodyof other
consistency.
9
These
include
noise
portion
thermometry
of the
range
2: THE
INTERNATIONAL
On October
accepted
for
a
Practical
cession
acoustic
5,
thermometry,
and
of
the
OF
International
in
place
as
the
tr,O/‘C
= TgO/K
temperatures
-
are
thermometry,
appropriate
to
a
(ITS-90)
on
Weights
Committee
and
on
Measures
Thermometry
to replace
the
International
had replaced,
in turn,
a suc1927, etc.
The official
text
of
from
the official
the first
quarter
international
As in previous
“practical”
used
in the
title
of the
fined
as
each
Committee
the ITS-90,
in English
translation
lished
in Metrologia,
probably
in
and
1990
a recommendation
of its Consultative
new
“practical”
temperature
scale,
Temperature
Scale of 1968, which
of previous
Scales,
those
of 1948,
officially
gas
radiation
thermometry,
the temperature
Scale.
SCALE
1989,
dielectric-constant
legal
of
Scale
as
Scales
(although
the
new
Scale)
the
relationship
French,
1990.
of
word
will
The
be pubITS-90
is
1 January,
1990.
“practical”
to the TKTS
is
is
not
de-
273.15
defined
in
terms
of
the
equilibrium
states
of
pure
substances
(defining~
fixed
points),
interpolating
instruments,
and
equations
which
relate
the
measured
property
to T(90).
The
defining
fixed
points
and
the
values
assigned
to them
are
listed
in Table
1, and
the
values
which
were
assigned
on IPTS(68)
are listed
also,
for
comparison.
It is to be remembered
that,
while
the
Scale
values
assigned
to a fixed
point
may
have
been
changed,
the fixed
point
has the identical
hotness
it always
Several
had.
deep
From
cryogenic
0.65K
ranges
to
5.OK
are
using
provided.
a
These
helium
vapor
are:
pressure
interpolation
device
From
3.OK to the triple
volume
gas thermometer
point
of
neon
From
point
of
neon
4.2K
to
the
triple
(24.5561K)
with
4He
using
as
the
a constant-
thermometric
gas
From
3.OK
thermometric
to
the
gas
triple
point
of
neon
with
3He
or
4He
as
the
10
These
ranges
cialists,
and
thermometer
from
13.8033K
of
subranges.
slightly
The
are
probably
of interest
to only
a limited
number
of spewill
not be dealt
with
in detail
in this
paper.
The resistance
portion
of the
Scale
is divided
into
two
major
ranges,
one
to 0-C
and the other
from
O’C to 961,68’C,
with
a number
There
below
Scale
to
is
ranges
are
The
interpolations
platinum
resistance
the
resistance
a change
O’C,
and
one
range
O’C,
summarised
the
triple
in
which
embraces
specifically
Table
from
273.15K,
be strain
of these
the
as the
ratios
of
the
(PRTs)
at temperatures
point
of
water;
that
definition
of
IPTS(68)
(gallium
melt
W(234.3156K)
L 0.844235
(mercury
triple
WT(90)
-
where
WT(90)
the
reference
use
to
W,T(90)
is
the
(silver
Z 4.2844
T(90)
calculated
used
be
of
and
point)
from
of
point)
the
at
Eq.12
point
freeze
resistance
Eq.11
point)
freezing
the
made
of pure
platinum
of these
requirements
if
silver
must
also
Eq.13
resistance
ratio
relation-
Eq.14
= dWT(90)
is the observed
function,
and
resistance
of T(90)
is:
which
L 1.11807
temperature
+29.7646-C.
Eq.10
W(302.9146K)
W(1234.93K)
to
2.
as denominator.
The
PRT must
free;
it is considered
a measure
two constrains
are
met:
for
temperatures
-38.8344’
= RT(90)/R(273.16K)
and a PRT acceptable
meet this
requirement:
The
ship:
short
above
are
expressed
thermometers
at
WT(90)
third
slightly
value,
dWT(90)
W,T(90)
is the
is the
deviation
value
calculated
value
of the
from
spe-
cific
PRT from
the
reference
function
at T(90).
(The
reference
functions
represent
the characteristics
of a fictitious
“standard”
thermometer;
the
deviation
function
represents
the
difference
between
that
thermometer
and
an individual
real
thermometer).
The deviation
function
is obtained
by calibration
at the
specified
fixed
points,
and
its
mathematical
form
depends
THE
upon
RANGE
the
FROM
temperature
13.8033k
range
TO 273.16K
of
calibration.
11
The
reference
function
for
this
range
is
12
ln[WrT(90)]
= A,
where
the
If
PRT
the
+ K Ai{[ln(T(90)/273.16K)+1.5]/1.5)i
i=l
values
is
to
of
A,
and
Ai
be
calibrated
are
given
over
83.8058K
not
to
(-189.3442-C),
triple
the
entire
or
include
details,
the
primary
the
in
the
it must
be calibrated
at specified
fixed
tures
determined
by
vapor
pressure
mometers
will
most
likely
be calibrated
and
this
paper
will
of
general
interest
Kq.15
of
The
deviation
function
dW = aCW(T(90))
THE
RANGE
FROM
For the
freezing
range
point
WrT(90)
= C,
and
coefficients
the
I]
0-C
TO
from
O’C
of silver,
-
dWT(90)
+ c[WT(90)
-
II3
two
temperaSuch
therLaboratories,
that
the
laboratory
subranges
begin
at
requires
calibration
at the
triple
point
of mercury
(obtain
the
coefficients
a and
Eq.16
the
over
this
entire
range
must
be calibrated
at
and the freezing
points
of tin,
zinc,
aluminum
a, b and
c are
derived
from
the
tin,
zinc
the
and
and
-
the
freezing
function
is:
Ci are
11 + b[WT(90)
+ dCWt(90)
point
754.15)/4811i
specified
and the
reference
measurements
function
is
-
13.8033K,
to
Co and
= a[WT(90)
to
argon.
lllnW(T(90))
to 961.78-C,
the reference
9
+ I: Ci [(T(90)/K
i=l
temperature
deviation
down
961.76.C
aluminum
calibrations
respectively,
the deviation
of WT(90)
from
the
silver.
For
d = 0. The
Scale.
is:
+ blW(T(90))
The
PRT to be used
triple
point
of water
silver.
The coefficients
the
and also
at
thermometry.
by
National
but
assume
calibration
point
of
range,
points
gas
only
The
subrange
from
-189.3442’
to 273.16-C
triple
point
of
argon
(-189.3442’C),
the
38.8344-C)
and
the triple
point
of water
to
b.
text
below
-
of
water
Eq.17
in
the
coefficient
value
at
the
II2
- W(933.473KE2
text
of the
Scale.
d is derived
from
the freezing
point
of
freezing
point
Eq. 18
of
silver,
12
PRTs
may
be
terminating
ranges
of
calibrated
over
the
at the freezing
points
Eq. 18, the equation
is
jJoner
whole
range
For
the
dT(90)
For
still
limit
the
indium,
freezing
range
from
calibrations
point
of
dWT(90)
the
are
indium.
range
from
calibrations
the
are
equation
is
as
range
from
the
- a most
useful
calibrations
are
gallium
melting
dT(90)
= aCHT(90)
However
the
portion
0-c.
For
of
a
relatively
-
-
Scale
of
water
the
to
water
triple
function
II2
point
shorter
the
freezing
point
and
Eq.19
of
water
the
triple
function
to
the
freezing
point
is:
of
point
water
and
Eq.20
except
for
triple
point
range
for
function
O’C,
must
and
the
the
“Realising
the
melting
and
the
point
of
deviation
coefficients.
of mercury
to
near-environmental
and water
equation
is
the
melting
point
thermometry
triple
points
and
of
the
Eq.21
112
be calculated
from
Eq.17
polynomial
approximation
to +600-C,
accurate
-200’
thermometer
range
from
1.5mK below,
see the article
Isotech
Journal.
of
Eq.20
triple
point
of water
to
required
at these
points,
below
the
is:
11
11 + bCWT(90)
simple
point
at the
deviation
required
at the mercury
point,
and the deviation
reference
the
triple
required
at
The reference
-
same
the
triple
For
the
gallium,
For
the
gallium
from
are required
and tin. The
11 + bCWT(90)
= a[WT(90)
the
For
ranges
d=O
c=d=O
shorter
range
shorter
Coefficient
tin,
calibrations
points
of indium
= aCWT(90)
for
of aluminum
or zinc.
truncated
as follows:
Aluminum
Zinc
point
of
freezing
or
the
ITS(90)”
for
from
the
over
to 1mK
in
this
Eq.15
portion
for
the
above
the
resistance
above
O’C and
issue
of
the
13
The
temperature
radiation
is:
range
above
thermometer
as
L X(TYD)/LX(TYO(X)
the
freezing
interpolating
= (expCc2/
L X(T90)
and
XT90(X)]
LX(TSO(X))
ance
of a blackbody
TSO(X)
may be the
0.014388
m’K.
at
silver
3: THE
OF
1990
VALUE
The National
The
change
international
representations
was
made
standard
of
not
insignificant
various
national
resistors
following
Germany:
are
1)
-
1)
employs
the
a
relationship
Eq.22
OHM
of
the
because
resistance,
differences
laboratories,
which
were
adjustments
-
and
silver
the
spectral
concentrations
of radix
in vacuum
at TSO and at TSO(X).
gold
point
or the copper
point.
C2 =
wavelength
point,
the
THE
of
instrument,
/(eXP[C2/hT901
where
point
standard
also
the
quantum
Hall
permits
correction
in the value
due
to drift
kept
as
were
made
ohm
effect,
of the
assigned
to
over
years
National
standards
by England,
the
change
of
United
in
1990.
the
slight
new
but
the
ohm
by the
of the
standard
The
resistance.
States
and West
NPL
(England)
increased
the
value
of their
ohm
by
t1.61
ppm.
Thus
a perfectly
stable
1 ohm
resistor
calibrated
at
NPL
prior
to
January
1, 1990,
has a new
value
of 0.99999839
ohm.
A 10 ohm resistor
has a new
value
of 9.9999839
ohm.
1Q (NPL
1Q (NPL
NIST
ppm.
1990,
value
90)
89)
(United
A drift-free
has
a new
of
1Q (NBS
89)
ppm.
1990,
value
of
9.9999944
increased
89)
SO)
the
value
of
at NIST
A 10 ohm
their
ohm
prior
to
resistor
by
+I.69
January
1,
has a new
ohm.
so)
PTB
(West
A drift-free
has
a new
States)
(NPL
(NPL
1 ohm resistor
calibrated
value
of 0.99999831
ohm.
9.9999831
1~ (NIST
= 1.00000161Q
= 0.99999839Q
= 1.00000169s2
= 0.99999831Q
(NBS
(NIST
89)
90)
Germany)
increased
the
1 ohm resistor
calibrated
value
of 0.99999944
ohm.
ohm.
value
of their
ohm
by
to.56
at PTB prior
to January
1,
A 10 ohm
resistor
has a new
14
90) = 1.00000056
Q (PTB 89)
89) = 0.999999944
Q (PTB 90)
1~ (PTB
1Q (PTB
Other
laboratories
adjusted
the
ohm
(a decrease);
France,
+O.?lppm;
BIPM,
The
effects
mometer
on
the
calibration
calibrated
(for
example
follows:
t(89)
0-c
650-C
where
d(Q)
and d(t)
is
by
25.5249052)
is the decrease
the increase
in
= Ro
1 1 t a(tl
a and
13 are
given
is
= 24.994-C
The
change
in
thermometry.
It
ence
temperature
the
value
is unlikely
for
the
13 term
can
platinum
typical
(f or
90 Q
(USSR)
resistance
resistance
example
-0.15ppm
value
d(t)
25.52486
-0.00004
to.000393
85.28828
-0.00014
+0.001705
standards
but
real
at
85.28842~)
d(Q)
in resistance
measured
hotness
represented
by
ther-
for
the
O’C
are
as
the same
hotness
same
resistance.
as maintained
in most
resistance
dependance
therupon
as
(t68)
the
a
650-C
resistance
have
a small
The value
of resistance
tinue
to be. However
25-C
at
25.52490
85.28842
written
of
and
VNIIM
a standard
with
NIST
temperature,
(values
resistor).
1989,
NBS 89 Q
In addition,
practicable
mometry
laboratories
Rl
in
of
as follows:
tL92ppm.
be
to)
t
in
6(tl
- to)2l
the
calibration
conventionally
reported
Eq.23
report
at
for
25-C,
the
individual
and
will
con-
Eq.24
t(90)
of the
ohm
may
be significant
that
the difference
in the value
resistor
will
require
consideration.
in
precision
of the referCertainly
ignored.
************************************+***%%%%%%%%%%%%%%%%%%%%
In our
next
issue,
the
fixed
points
realising
them.
we
and
will
of
discuss
in detail
the
the
equipment
and
physical
operations
embodiment
involved
of
in
TABLE 1
15
FIXED POINTS OF THE IPTS-68
AND OF THE ITS(90)
AS ADOPTED BY CIPM, OCTOBER 5 1989
SUBSTANCE
STATE CELSIUS
TEMP.
IPTS-68
e-H2
Trip
-259.34
-259.3467
02
Trip
-218.789
-218.7916
Ar
Trip
-189.352
-189.3442
N2
Boil
-195.802
-195.794
Hg
Trip
-38.842
-38.8344
H20
Trip
0.01
Ga
Melt
29.772
29.7646
In
Freeze
156.634
156.5985
Sn
Freeze
231.9681
231.928
Zn
Freeze
419.58
419.527
Al
Freeze
660.46
660.323
Ag
Freeze
961.93
961.78
AU
Freeze
1064.43
1064.18
CU
Freeze
1084.88
1084.62
CELSIUS
TEMP.
ITS-90
0.01
Notes:
e-H2 represents
molecular
forms
Boiling,
Pa.
melt
hydrogen
and freeze
in
points
equilibrium
are
between
at 1 standard
the
ortho
atmosphere
and
para
= 101 325
TABLE 2
16
RANGES OF THE ITS-90
THE PURCHASEROF A CALIBRATION MUST STATE
THE RANGE REQUIRED*
LOW LIMIT
-259.3467
HIGH LIMIT
FIXED POINTS REOUIRED
0.01
e-H
(TP),
e-H2
(VP),
?TP), Ar (TP).
(TP). 50 (TP)
‘32
-218.7916
0.01
02
Ne (TP),
Hg
(TP),
Ar
(TP).
Hg (TP),
(TP),
b
OF’),
Hz0
H20
(TP)
-189.3442
0.01
Ar
0.01
29.7646
H$
0.01
156.5985
H20 (TP).
Ga (HP).
In (FP)
0.01
231.928
H20
(TP’),
Ga (HP),
Sn (FP)
0.01
419.527
H20
(TP).
Sn (FP),
Zn (FP)
660.323
H20 (TP),
(FP)
Sn (FP),
2n (FP),
Al
961.78
H20 (TP), Sn (FP),
(FP). A8 (FP)
Zn (FP),
Al
Hg (TP).
Ga (MP)
0.01
-38.8344
29.7646
(TP),
Ga (ME’)
H20 (TP).
pressure
determination,
(TP) = triple
point.
(VP) = a vapor
(MP)
= melting
freezing
point
at 1 standard
atmosphere,
standard
atmosphere
*The purchaser
may choose
to specify
-189.3442’
to +419.527’,
for example,
-200’
to +500’.
example,
(TP)
point
a combination
of several
or some extrapolation,
(FP)
at
=
1
ranges,
for
17
TABLE 3
THE COEFFICIENTS OF THE REFERENCE
The values of the coefficients
Eq. 15 and 17
FUNCTIONS
Ai and Ci of the reference
Eq.15
functions
of
Eq.17
CONSTANT OR
COEFFICIENT VALUE
CONSTANT OR
COEFFICIENT VALUE
A0
-2.135
Al
A2
3.183
-1.801
247 20
435 97
A3
A4
A5
0.717
0.503
-0.618
-0.053
0..280
272 04
440 27
993 95
323 22
213 62
0.107
-0.293
152 24
028 65
0.044
0.118
-0.052
598 72
686 32
481 34
A6
A?
A8
A9
A10
All
A12
347
co
29
Cl
c2
c3
c4
c5
c6
c7
c8
C¶
2.781
572
54
1.646
-0.137
-0.006
-0.002
0.005
0.001
-0.002
509 16
143 90
497 67
344 44
118 68
879 82
044 72
-0.000
0.000
461 22
457 24
TABLE 4
VALUES OF W,(t90)
AT THE RESISTANCE THERHOUETW FIXED POINTS
FIXED POINT Wr(T901
FIXED POINT iJr(T(90)
e-H2
(TP)
Ne UP)
02 (TP)
Ar (TP)
Hg (TP)
Hz0 (TP)
0.001
0.008
0.091
0.215
0.844
1.000
190
449
718
859
142
000
07
74
04
75
11
00
Ga (MP)
In
(MP)
Sn (FP)
Zn (FP)
Al (FP)
nP (FP)
1.118
1.609
1.892
2.568
3.376
4.286
138
801
797
917
008
420
89
85
68
30
60
53
18
FUNDAMENTALS
GAS
THERMOMRTRY,
THERMCMETRY
James
F.
especially
T. J.
OF
AND
Schooley,
on gas
Quinn,
THE
1, REFERENCES
THERMODYNAMIC
Th-o&y,
thermometry
Twnpm
PART
SCALE
CRC Press,
the NBS
at
a, Academic
Press,
London
F. Henning,
H. Maser,
Twnpucatuwn
&wag,
New
York,
3rd
edition
(1977).
German
pressure
thermometry
by W. Thomas
THE
INTERNATIONAL
t&&a
Preston-Thomas
06
19 68
TEMPERATURE
The
(~e:ev-i-&on
Raton,
and
I Metrologia
4oa
Poids
valuable,
Changea
.taomotive
Teddington,
York
(1986)
(1873)
Berlin
and
on
vapor-
P.wzc-GcaX
Tanpeaduae
12, 1 (1976)
tie
et
IPTS-68
and
Mesures,
Sevres,
but
will
be revised
e Scu&
The
Iti.awat.Lod
TempcauUu/t
official
text
of the
new
Scale,
and
it will
Metrologia
advises
that
it will
be published
1990).
1990
New
Springer-Verlag,
text;
fine
section
R.
E.
Bedford,
G.
Bonnier,
H.
Maas,
F.
Pavese,
appeoximetlng
.#LQ
I-tied
Temp wt.aauAe
BIMP,
when
published;
no
projected
date
is known.
unofficial
copies
of a late draft
indicate
that
this
will
THE
Florida
SCALE
Ira.tea~od
04 1975
Supp&mentcMy
Inbomon
Bureau
International
des
publication
continues
to be
date to include
ITS-90
Boca
06
be
in
the
EPT-76,
France.
This
at some
future
Techniquea
dolr
sceee
04
1990,
Our
reading
of
be of great
value.
1990
is the
title
of the
published
in Metrologia.
Vol. 27 No. 1 (February
OHM
Ln
tie
Vdue
04 the
UK
Force
and
Redistance,
England
(1989)
N.
Belecki
at
Imp&zmenting
Ohm, U.S.Department
V. Kose,
H.
WeCteagabe
Bundesanstalt
al,
the
Bachmair,
&e-w
PTB-E-35,
NIST
Technical
New
Rep~eaentetLon-6
of Commerce
(1989)
Neue
Re&xence
National
Note
S+and4nda
Physical
1263,
&.idl.h&Sn,
Braunschweig
FRG
Gu.id.a-f-ines
Vo-C-t
and
40’~
.the
Fe&t.egungen
blk
Physikalisch-Technische
d.-k
04
Iwoti
(1989)
06 &&QCLaboratory,
.the