Measurement of Temperature and Chemical Composition. Jones' Instrument Technology

190 Pages·1992·6.556 MB·English

by  B.E Noltingk (Eds.)

Fourth Edition
Jones'
Instrument
Technology
Volume 2
Measurement of
Temperature and Chemical
Composition
Edited by B E Noltingk
fsl U T T E R W O R TH
|*|E 1 N E M A N N
Butterworth-Heinemann Ltd
Linacre House, Jordan Hill, Oxford OX2 8DP
^ PART OF REED INTERNATIONAL BOOKS
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TOKYO TORONTO WELLINGTON
First published 1985
Reprinted 1987, 1992
© Butterworth-Heinemann Ltd 1992
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Applications for the copyright holder's written permission to
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British Library Cataloguing in Publication Data
Jones, E. B. (Ernest Beachcroft)
Jones' instrument technology - 4th ed.
Vol 2: measurement of temperature and chemical
composition
1. Measuring instruments
I. Title II. Noltingk, B. E. III. Jones, E. B.
(Ernest Beachcroft). Instrument technology
620'. 0044 QC100.5
ISBN 0 7506 0766 1
Library of Congress Cataloguing in Publication Data
Jones, E. B.
Jones' instrument technology - 4th ed.
Includes index.
ISBN 0 7506 0766 1
1. Mechanical measurements 2. Measurement of
temperature and chemical composition
I. Engineering instruments. I. Noltingk, B. E.
II. Jones, E. B. (Ernest Beachcroft). Instrument
technology
TA165.159674 1984 620'.0028 84-4273
Printed and bound in Great Britain by
Thomson Litho Ltd, East Kilbride, Scotland.
Contributors
Sir Claud Hagart-Alexander Bt., BA, MInstMC, DL,
had a long experience in instrumentation with ICI Ltd.
He is now a director of Instrumentation Systems Ltd.
The chapters on Chemical Analysis have been
contributed by a team from Central Electricity
Research Laboratories. Mr W. G. Cummings BSc,
CChem, FRSC, MInstE, MInstMC, was until recently,
head of the Analytical Chemistry Section, where Mr A.
C. Smith BSc, CChem, FRSC, MInstP, is now in
charge; Dr C K. Laird BSc, PhD, CChem, MRSC and
Dr K. Torrance BSc, PhD, also work in that Section.
Dr D. B. Meadowcroft BSc, PhD, MInstP, MICorrST,
is in the Materials Branch of C.E.R.L.
Preface
As in the first volume of this updated Instrument school put the subject on its curriculum - but only in
Technology, I must express my thanks to the con­ the classrooms: there were no pitches to play on and
tributors. They have, to a greater or lesser extent (but no balls to play with. Neither instrument technology
mainly greater), tolerated my cajoling them in two nor football can be well learned unless the
ways. First, to write at all. Secondly, to cover an agreed experimental is blended with the theoretical.
range of topics with an agreed thoroughness. I believe Instrument technology has been divided into four
that a useful book has emerged. I might especially volumes. It would have been impossibly bulky if it had
thank Mr Bill Cummings for applying his practical not! In the first volume we grouped the measurements
wisdom to helping define the areas of analytical of mechanical quantities. Here, in the second, we have
chemistry that needed to be dealt with in a modern two broad subjects of very wide interest, temperature
book on instrument technology. and chemical composition. They are both important
I am picking up a frequent theme of E. B. Jones, the for process control, but we have tried not to be tied too
original author, in underlining both the value of tightly to on-line instrumentation. Although the titles
technicians in today's technical industry and the need do not exactly correspond, it can be seen that between
for more of them. We hope that our book will play its them Volumes 1 and 2 of the new edition cover most of
part in their training and indeed in the training and the topics appearing in the old Volumes 1 and 2. The
understanding of many folk who need to have some new Volume 3 has several new subjects while Volume 4
knowledge of instrumentation. We have tried to tread deals with matters of general interest that stretch
a balanced path between the expounding of funda­ across the measurement of many different quantities,
mental science and the description of trivial practical justifying its title of Systems. More details can be seen
details. But with emphasis on the practical. I was once in the list of contents printed on page v.
told the story of a distant country where, yes, they were
very keen on football; their ministry of education BEN
decreed that there should be football lessons. So every 1985
1 Temperature measurement
C. HAGART-ALEXANDER
1.1 Temperature and heat be used or where the distances between the plant
measurement locations and the control room are very
1.1.1 Application considerations long it is usually better to use temperature trans­
mitters. These instruments use the same types of
Temperature is one of the most frequently used process
probes as other temperature measuring instruments.
measurements. Almost all chemical processes and
The transmitting mechanism is normally attached
reactions are temperature-dependent. Not infre­
directly to the probe. It may also have a local readout
quently in chemical plant, temperature is the only
facility as well as its transmitting function which is to
indication of the progress of the process. Where the
convert the measurement effect into a pneumatic or
temperature is critical to the reaction, a considerable
electrical signal suitable for transmission over long
loss of product may result from incorrect tempera­
distances' (See Volume 4 on transmitters.)
tures. In some cases, loss of control of temperature can
Temperature measurement effects are also used
result in catastrophic plant failure with the attendant
directly for simple control functions such as switching
damage and possibly loss of life.
on and off an electric heater or the direct operation of a
Another area where accurate temperature measure­
valve, i.e. thermostats.
ment is essential is in the metallurgical industries. In
the case of many metal alloys, typically steel and
aluminium alloys, the temperature of the heat treat­
1.1.2 Definitions
ment the metal receives during manufacture is a crucial
factor in establishing the mechanical properties of the For the understanding of temperature measurement it
finished product. is essential to have an appreciation of the concepts of
There are many other areas of industry where temperature and other heat-related phenomena.
temperature measurement is essential. Such applica­
tions include steam raising and electricity generation,
1.1.2.1 Temperature
plastics manufacture and moulding, milk and dairy
products and many other areas of the food industries. The first recorded temperature measurement was
Then, of course, where most of us are most aware of carried out by Galileo at the end of the sixteenth
temperature is in the heating and air-conditioning century. His thermometer depended on the expansion
systems which make so much difference to people's of air. Some form of scale was attached to his
personal comfort. apparatus for he mentions 'degrees of heat' in his
Instruments for the measurement of temperature, as records.
with so many other instruments, are available in a wide As with any other measurement, it is necessary to
range of configurations. Everyone must be familiar have agreed and standardized units of measurement.
with the ubiquitous liquid-in-glass thermometer. In the case of temperature the internationally
There is then a range of dial thermometers with the dial recognized units are the kelvin and the degree Celsius.
attached directly to the temperature measuring The definitions of these units are set out in Section 1.2.
element, i.e. local reading thermometers. Remote One must differentiate between heat and tem­
reading instruments are also available where the perature. The effect of temperature is the state of
measuring system operates the dial directly through a agitation, both oscillation and rotation of molecules in
length of metal capillary tubing. The distance between a medium. The higher the temperature of a body the
the sensing 'bulb' and the dial, or readout, of these greater the vibrational energy of its molecules and the
instruments is limited to about thirty metres. Where greater its potential to transfer this molecular kinetic
the temperature readout is required at a long distance energy to another body. Temperature is the potential
from the location of the sensing element there are two to cause heat to move from a point of higher tempera­
main options; either an electrical measuring technique ture to one of lower temperature. The rate of heat
such as a thermocouple or resistance thermometer can transfer is a function of that temperature difference.
2 Temperature measurement
1.1.2.2 Heat
Heat is thermal energy. The quantity of heat in a body
is proportional to the temperature ofthat body, i.e. it is
its heat capacity multiplied by its absolute
temperature.
Heat is energy and as such is measured in units of 100 °C
energy. Heat is measured in joules. (Before the inter­
national agreements on the SI system of units heat was
measured in calories. One calorie was approximately
4.2 joules.)
1.1.2.3 Specific heat capacity
Different materials absorb different amounts of heat to
produce the same temperature rise. The specific heat
capacity, or more usually the specific heat, of a
Figure 1.1 Increase of temperature during change of state of
substance is the amount of heat which, when absorbed a mass of water under conditions of constant energy input.
by 1 kg of that substance, will raise its temperature by
one kelvin
Specific heat capacity = J kg "l K "1
from water to steam. Once all the water has boiled to
1.1.2.4 Thermal conductivity steam the temperature will rise again but now at yet
another rate dependent on the specific heat of steam.
The rate at which heat is conducted through a body
This is illustrated in Figure 1.1.
depends upon the material of the body. Heat travels
The amount of heat required to convert a kilogram
very quickly along a bar of copper, for instance, but
of a substance from solid state to liquid state is the
more slowly through iron. In the case of non-metals,
'latent heat of fusion'.
ceramics or organic substances, the thermal con­
Likewise the 'latent heat of evaporation' is the
duction occurs more slowly still. The heat conductivity
amount of heat required to convert a kilogram of
is not only a function of the substance but also the form
liquid to vapour.
of the substance. Plastic foam is used for heat
insulation because the gas bubbles in the foam impede This levelling of temperature rise during change of
the conduction of heat. Thermal conductivity is state accounts for the constant freezing temperatures
measured in terms of: and constant boiling temperatures of pure materials.
The units of measurement of latent heat are joules per
energy x length kilogram:
area x time x temperature difference latent heat = J.kg-1
J.m
thermal conductivity =
m2.s.K 1.1.2.6 Thermal expansion
= J.m" .K" Expansion of solids When a solid is heated, it
increases in volume. It increases in length, breadth and
thickness. The increase in length of any side of a solid
1.1.2.5 Latent heat
will depend upon the original length / , the rise in
0
When a substance changes state from solid to liquid or temperature t, and the coefficient of linear expansion a.
from liquid to vapour it absorbs heat without change The coefficient of linear expansion may be defined as
of temperature. If a quantity of ice is heated at a the increase in length per unit length when the
constant rate its temperature will rise steadily until it temperature is raised 1 K. Thus, if the temperature of a
reaches a temperature of 0 °C; at this stage the ice will rod of length /, is raised from 0 °C to t °C, then the new
0
continue to absorb heat with no change of temperature length, l will be given by:
v
until it has all melted to water. Now as the heat
/ = / + / .ar = / (l+ar) (1.1)
continues to flow into the water the temperature will f 0 0 0
continue to rise but at a different rate from before due The value of the coefficient of expansion varies from
to the different specific heat of water compared to ice. substance to substance and the coefficients of linear
When the water reaches 100 °C the temperature rise expansion of some common materials are given in
will again level off as the water boils, changing state Table 1.1.
Temperature and heat 3
Table 1.1 Coefficients of linear expansion of solids made, and a the coefficient of expansion of the metal of
Extracted from Tables of Physical and Chemical Constants byt he scale.
Kaye and Laby (Longmans). The values given are per kelvin
A 1 mm division on the scale will therefore now
and, except where some temperature is specified, for a range
measure
about 20 degrees
\+a(t-t)mm (1.3)
2 l
Substance a {ppm)
An actual length / mm will therefore measure
2
Aluminium 25.5
Copper 16.7
(1.4)
Gold 13.9 \+CL(t-t)
2 x
Iron (cast) 10.2
The length will therefore appear to be smaller than it
Lead 29.1
Nickel 12.8 actually is. To make this error negligibly small,
Platinum 8.9 secondary standards of length are made of Invar, a
Silver 18.8 nickel steel alloy whose linear coefficient of expansion
Tin 21.4 is nearly zero.
Brass (typical) 18.9
Constantan (Eureka), Expansion of liquids and gases In dealing with the
60 Cu, 40 Ni 17.0
expansion of liquids and gases it is necessary to
Duralumin 22.6
consider the volume expansion, or cubical expansion.
Nickel steel,
Both liquids and gases have to be held by a container,
10% Ni 13.0
30% Ni 12.0 which will also expand, so that the apparent expansion
36% Ni (Invar) -0.3 to +2.5 of the liquid or gas will be less than the true or absolute
40% Ni 6.0 expansion. The true coefficient of expansion of a liquid
Steel 10.5 to 11.6 is equal to the coefficient of apparent expansion plus
Phosphor bronze, the coefficient of cubical expansion of the containing
97.6 Cu, 2 Sn, 0.2 P 16.8 vessel. Usually the expansion of a gas is so much
Solder, 2 Pb, 1 Sn 25
greater than that of the containing vessel that the
Cement and concrete 10
expansion of the vessel may be neglected in com­
Glass (soda) 8.5
Glass (Pyrex) 3 parison with that of the gas.
Silica (fused) -80° to0°C 0.22 The coefficient of expansion of a liquid may be
Silica (fused) 0° to 100 °C 0.50 defined in two ways. First, there is the zero coefficient
of expansion, which is the increase in volume per
degree rise in temperature, divided by the volume at
The increase in area with temperature, i.e. the 0°C, so that volume V at temperature t is given by:
t
coefficient of superficial expansion is approximately
V=V (l+ßt) (1.5)
twice the coefficient of linear expansion. The coefficient t 0
of cubic expansion is almost three times the coefficient where V is the volume at 0 °C and ß is the coefficient of
0
of linear expansion. cubical expansion.
In engineering practice it is necessary, especially in There is also the mean coefficient of expansion
large structures, to make allowance for thermal between two temperatures. This is the ratio of the
expansion. For instance bridges are built with increase in volume per degree rise of temperature, to
expansion joints. Many instruments are designed with the original volume. That is,
temperature compensation to accommodate thermal (L6)
expansion. Thermal expansion can be made use of for ^KS)
temperature measurement, as is dealt with in Section
1.3.
where V is the volume at temperature t and V is the
If great accuracy is required when measuring lengths t u t
volume at temperature t .
with a scale made of metal, allowance should be made 2
This definition is useful in the case of liquids that do
for the increase in length of the scale when its
not expand uniformly, e.g. water.
temperature is greater than that at which it was
calibrated. Owing to the expansion of the scale, a
length which was originally / at the temperature t at
t l9 1.1.2.7 Radiation
which the scale was calibrated, will have increased to /
2
where There are three ways in which heat may be transferred:
conduction, convection, and radiation. Conduction is,
/2 = /i[l+«('2-'i)] (1.2) as already covered, the direct transfer of heat through
Here t is the temperature at which the measurement is matter. Convection is the indirect transfer of heat by
2
4 Temperature measurement
the thermally induced circulation of a liquid or gas; in tp= 100 + 2.795 x 10~4(p-1.013 x 10~5)
'forced convection', the circulation is increased by a fan -1.334 x \0~9(p-1.013 x 105)2 (1.7)
or pump. Radiation is the direct transfer of heat (or
The temperature interval of 100 °C between the ice
other form of energy) across space. Thermal radiation
point and the steam point is called the fundamental
is electromagnetic radiation and comes within the
interval.
infrared, visible and ultraviolet regions of the electro­
magnetic spectrum. The demarcation between these
1.2.2 Kelvin, absolute or thermodynamic
three classes of radiation is rather indefinite but as a
temperature scale
guide the wavelength bands are shown in Table 1.2.
The earlier scales of temperature depended upon the
Table 1.2 Wavelengths of thermal radiation change with temperature of some property, such as
size, of a substance. Such scales depended upon the
Radiation Wavelength {fim) nature of the substance selected. About the middle of
the nineteenth century, Lord Kelvin defined a scale of
Infrared 100-0.8 temperature in terms of the mechanical work which
Visible light 0.8-0.4
may be obtained from a reversible heat engine working
Ultraviolet 0.4-0.01
between two temperatures, and which, therefore, does
not depend upon the properties of a particular
So far as the effective transfer of heat is concerned substance. Kelvin divided the interval between the ice
the wavelength band is limited to about 10 fxm in the and steam points into 100 divisions so that one kelvin
represents the same temperature interval as one Celsius
infrared and to 0.1 /im in the ultraviolet. All the
degree. (The unit of the Kelvin or thermodynamic
radiation in this band behaves in the same way as light.
temperature scale is the 'kelvin'.) The definition of the
The radiation travels in straight lines, may be reflected
kelvin is the fraction 1/273.16 of the thermodynamic
or refracted and the amount of radiant energy falling
temperature of the triple point of water. This definition
on a unit area of a detector is inversely proportional to
was adopted by the thirteenth meeting of the General
the square of the distance between the detector and the
Conference for Weights and Measures in 1967 (13th
radiating source.
CGPM, 1967).
It has also been established that an ideal gas obeys
the gas law PV = RT, where T is the temperature on the
1.2 Temperature scales absolute or kelvin scale and where P is the pressure of
the gas, V is the volume occupied and R is the universal
To measure and compare temperatures it is necessary gas constant. Thus, the behaviour of an ideal gas forms
to have agreed scales of temperature. These tem­ a basis of temperature measurement on the absolute
perature scales are defined in terms of physical scale. Unfortunately the ideal gas does not exist, but
phenomena which occur at constant temperatures. the so-called permanent gases, such as hydrogen,
The temperatures of these phenomena are known as nitrogen, oxygen and helium, obey the law very closely,
'fixed points'. provided the pressure is not too great. For other gases
and for the permanent gases at greater pressures, a
known correction may be applied to allow for the
1.2.1 Celsius temperature scale departure of the behaviour of the gas from that of an
The Celsius temperature scale is defined by inter­ ideal gas. By observing the change of pressure of a
national agreement in terms of two fixed points, the ice given mass of gas at constant volume, or the change of
point and the steam point. The temperature of the ice volume of the gas at constant pressure, it is possible to
point is defined as zero degrees Celsius and the steam measure temperatures on the absolute scale.
point as one hundred degrees Celsius. The constant-volume gas thermometer is simpler in
The ice point is the temperature at which ice and form, and is easier to use, than the constant-pressure
water exist together at a pressure of 1.0132 x 105 gas thermometer. It is, therefore, the form of gas
N.m~2 (originally one standard atmosphere = 760 thermometer which is most frequently used. Nitrogen
mm of mercury). The ice should be prepared from has been found to be the most suitable gas to use for
distilled water in the form of fine shavings and mixed temperature measurement between 500 and 1500 °C,
with ice-cold distilled water. while at temperatures below 500 °C hydrogen is used.
The steam point is the temperature of distilled water For very low temperatures, helium at low pressure is
boiling at a pressure of 1.0132 x 105 N.m-2. The used.
temperature at which water boils is very dependent on The relationship between the kelvin and Celsius
pressure. At a pressure p, N. m -2 the boiling point of scales is such that zero degrees Celsius is equal to
water t in degrees Celsius is given by 273.15 K
p
Temperature scales 5
f =7-273.15 (1.8) means for identifying any temperature within much
narrower limits than is possible on the thermodynamic
where t represents the temperature in degrees Celsius
scale.
and T is the temperature kelvin.
The defining fixed points are established by realizing
It should be noted that temperatures on the Celsius
specified equilibrium states between phases of pure
scale are referred to in terms of degrees Celsius, °C,
substances. These equilibrium states and the values
temperatures on the absolute scale are in kelvins, K, no
assigned to them are given in Table 1.4.
degree sign being used. For instance the steam point is
written in Celsius, 100 °C, but on the Kelvin scale
Table 1.4 Defining fixed points of the IPTS-68(1)
373.15 K.
Equilibrium state Assigned value of
1.2.3 International Practical Temperature Scale of International Practical
temperature
1968 (IPTS-68)
'6 8 ^6 8
The gas thermometer, which is the final standard of
reference, is, unfortunately, rather complex and Triple point of
cumbersome, and entirely unsuitable for industrial equilibrium hydrogen 13.81 K - 259.34 °C
Boiling point of
use. Temperature measuring instruments capable of a
equilibrium hydrogen
very high degree of repeatability are available. Use of
at pressure of
these instruments enables temperatures to be 33 330.6 kN.irT2 17.042 K -256.108 °C
reproduced to a very high degree of accuracy, although
Boiling point of
the actual value of the temperature on the thermo- equilibrium hydrogen 20.28 K - 252.87 °C
dynamic scale is not known with the same degree of Boiling point of neon 27.102 K - 246.048 °C
accuracy. In order to take advantage of the fact that Triple point of oxygen 54.361 K -218.789 °C
temperature scales may be reproduced to a much Boiling point of oxygen 90.188 K -182.962 °C
higher degree of accuracy than they can be defined, an Triple point of water(3) 273.16 K 0.01 °C
International Practical Temperature Scale was Boiling point of water(2)(3) 373.15 K 100 °C
adopted in 1929 and revised in 1948. The latest Freezing point of zinc 692.73 K 419.58 °C
Freezing point of silver 1235.08 K 961.93 °C
revision of the scale was in 1968 (IPTS-68) and this is
Freezing point of gold 1337.58 K 1064.43 °C
the scale used in this book. The 1948 scale is still used
in many places in industry. The differences between
temperatures on the two scales are small, frequently (1) Except for the triple points and one equilibrium hydrogen point (17.042 K) the
assigned values of temperature are for equilibrium states at a pressure p0=l
within the accuracy of commercial instruments. Table standard atmosphere (101.325kN.m"2).
1.3 shows the deviation of the 1948 scale from the 1968 In the realization of the fixed points small departures from the assigned
temperatures will occur as a result of the differing immersion depths of
revision.
thermometers or the failure to realize the required pressure exactly. If due
allowance is made for these small temperature differences, they will not affect the
accuracy of realization of the Scale.
Table 1.3 Deviation of IPTS-68 from IPTS-48 (2) The equilibrium state between the solid and liquid phases of tin (freezing point
of tin has the assigned value of 16 8 = 231.9681 °C and may be used as an alternative
to the boiling point of water.
'68 (°Q f6 8 4f 8 (3) The water used should have the isotopic composition of ocean water.
-200 0.022
-150 -0.013 The scale distinguishes between the International
0 0.000 Practical Kelvin Temperature with the symbol T and
68
50 0.010
the International Practical Celsius Temperature with
100 0.000
the symbol t the relationship between T and t is
200 0.043 68 68 6S
400 0.076 r = 7 -273.15K (1.9)
68 68
600 0.150
1000 1.24 The size of the degree is the same on both scales, being
1/273.16 of the temperature interval between absolute
zero and the triple point of water (0.01 °C). Thus, the
The International Practical Temperature Scale is interval between the ice point 0°C and the boiling
based on a number of defining fixed points each of point of water 100 °C is still 100 Celsius degrees.
which has been subject to reliable gas thermometer or Temperatures are expressed in kelvins below 273.15 K
radiation thermometer observations and these are (0°C) and degrees Celsius above 0°C.
linked by interpolation using instruments which have Temperatures between and above the fixed points
the highest degree of reproducibility. In this way the given in Table 1.4 can be interpolated as follows.
International Practical Temperature Scale is con­ From 13.81 K to 630.74 °C the standard instrument
veniently and accurately reproducible and provides is the platinum resistance thermometer. The ther-
6 Temperature measurement
mometer resistor must be strain-free, annealed pure Table 1.5 Secondary reference points (IPTS-68)
platinum having a resistance ratio W(T ) defined by
68 Substance Equilibrium Temperature
R(T ) state (K)
W(Ts) = 68 (1.10)
6 K(273.15K)
Normal hydrogen TP 13.956
where R is the resistance, which must not be less than Normal hydrogen BP 20.397
1.392 50 ohms at 7 = 373.15K, i.e. the resistance Neon TP 24.555
ratio 68 Nitrogen TP 63.148
Nitrogen BP 77.342
K(100°C) Carbon dioxide Sublimation
point 194.674
R(0°C)
Mercury FP 234.288
is greater than the ratio 1.3920 of the 1948 scale, i.e. the Water Ice point 273.15
platinum must be purer. Phenoxy benzine TP 300.02
Below 0 °C the resistance-temperature relationship Benzoic acid TP 395.52
Indium FP 429.784
of the thermometer is found from a reference function
Bismuth FP 544.592
and specified deviation equations. From 0°C to
Cadmium FP 594.258
630.74 °C two polynomial equations provide the Lead FP 600.652
resistance temperature relationship. This will be Mercury BP 629.81
discussed further in the section on resistance Sulphur BP 717.824
thermometers. Copper/aluminium
From 630.74 °C to 1064.43 °C the standard eutectic FP 821.38
instrument is the platinum 10 per cent rhodium/ Antimony FP 903.89
Aluminium FP 933.52
platinum thermocouple, the electromotive force-
Copper FP 1357.6
temperature relationship of which is represented by a
Nickel FP 1728
quadratic equation and is discussed in the appropriate
Cobalt FP 1767
section. Palladium FP 1827
Above 1337.58 K (1064.43 °C) the scale is defined by Platinum FP 2045
Planck's law of radiation with 1337.58 K as the Rhodium FP 2236
reference temperature and the constant c has a value Iridium FP 2720
2
0.014 388 metre kelvin. This will be discussed in the Tungsten FP 3660
section on radiation thermometers.
TP: triple point; FP: freezing point; BP: boiling point.
In addition to the defining fixed points the
temperatures corresponding to secondary points are
given. These points, particularly the melting or
freezing points of metals, form convenient workshop Table 1.6 Comparison of temperature scales
calibration points for temperature measuring devices
K °C °F °R
(see Table 1.5).
Absolute zero 0 -273.15 -523.67 0
Boiling point
o 90.19 -182.96 -361.33 162.34
Zero2 Fahrenheit 255.37 -17.78 0 459.67
1.2.4 Fahrenheit and Rankine scales Ice point 273.15 0 32 491.67
Steam point 373.15 100 212 671.67
These two temperature scales are now obsolescent in Freezing point
Britain and the United States, but as a great deal of of silver 1235.08 961.93 1763.47 2223.14
engineering data, steam tables etc. have been published
using the Fahrenheit and Rankine temperature a short
note for reference purposes is relevant.
is the temperature in Celsius and / the temperature in
Fahrenheit This scale was proposed in 1714. Its
Fahrenheit
original fixed points were the lowest temperature
obtainable with ice and water which was taken as zero. t = Uf-32) (1.11)
Human blood heat was made 96 degrees (98.4 on the
modern scale). On this scale the ice point is at 32 °F and
the steam point at 212 °F. There does not appear to be Rankine The Rankine scale is the thermodynamic
any formal definition of the scale. temperature corresponding to Fahrenheit. Zero in
To convert from the Fahrenheit to Celsius scale, if t Rankine is of course the same as zero kelvin. On the