Download Thermometry... a hot topic

Thermometry
Mike
Follows
... a hot topic
Temperature and how we measure it is one of the
most important and interesting areas of physics.
This is reflected in the huge number and variety
of thermometers that have been developed. In
this article, Mike Follows describes the surprising
range of thermometers available to scientists today.
M
any physical properties of materials
depend on temperature. Our biochemical
reactions work best at 37°C and we are
in serious danger if our body temperature strays
more than a couple of degrees either way. Being
able to record the global mean surface temperature
of the Earth is important in order to establish the
magnitude of global warming. We have even found
ways of working out how the temperature of the
Earth has changed over the last half a million years
as well as the temperature of distant stars and of
Outer Space itself.
Thermometer history
The thermometer has been more of a development
than a single invention. Philo of Byzantium (280 220 BC) was aware that air expands and contracts
with changes in temperature and described a
demonstration that was developed by Galileo
to become his air thermometer or thermoscope
in around 1600. This consisted of a glass bulb
containing air with a long tube extending downward
into a container of wine or other coloured liquid (see
figure 2). Engraving a scale on the tube converted
the thermoscope into the first thermometer.
Key words
temperature
thermometer
Kelvin scale
ideal gas
Air
Some definitions
The temperature of a substance is a measure of the
average kinetic energy of the constituent molecules
– the faster the molecules are moving or vibrating,
the hotter the body will feel. Temperature also
tells you the direction that heat or thermal energy
will flow; it flows down a thermal gradient from a
hotter body to a colder body. In the process, the
hot body will lose thermal energy to the cold body.
What is a thermometer?
The word thermometer comes from
the Greek thermos (meaning ‘hot’) and
metron (‘measure’). Figure 1 shows
a mercury-in-glass thermometer. As
with most thermometers, it comprises
a thermometric substance that
changes in response to temperature
(mercury expands on being heated)
as well as a means of converting this
physical change into a numerical value
(the visible scale marked on the glass).
Wine
Figure 2 A thermoscope – as the air is
heated, it expands and pushes the liquid
down the tube. On cooling, the air contracts
and atmospheric pressure pushes the liquid
back up the tube.
Figure 1 A mercury-in-glass thermometer
The Galilean thermometer (Figure 3) was
developed after Galileo’s death, based on
principles that he developed. Each glass
bulb is partially filled with a coloured
liquid and has a metal disc, engraved
with the temperature, suspended from
it. The bulbs are adjusted by varying the
mass of each metal disc so that they all
have slightly different densities. When
they are immersed in the column of
liquid paraffin, they will float if they are
less dense than the paraffin, and sink if
they are more dense.
– as the mercury gets warmer, it expands
Figure 3 A Galilean thermometer shows
and rises up the tube.
the temperature of its surroundings.
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If the temperature rises, the paraffin expands
and becomes less dense. One or more bulbs will
now be too dense to float, and will sink. (The
density of each bulb is fixed because neither its
mass nor volume changes with temperature.) The
temperature is then shown by the metal disc on a
bulb which is free-floating in the gap.
Galileo’s thermometer has the advantage that it is
not affected by changes in air pressure in the way that
his thermoscope was. The Galilean thermometer
uses paraffin because the density of water changes
very little in response to changes in temperature.
temperature range from about minus 260 °C to
1000 °C. Driven by the voltage between the ends of
the metallic resistor, the free electrons drift along.
However, increasing the temperature of the resistor
increases the vibration of the metal atoms. In turn,
this increases the number of collisions between the
atoms and the electrons, slowing them down. This
reduces the current – the resistance has increased.
Though the platinum resistance thermometer is
fairly reproducible, it is regarded as a secondary
thermometer as it needs to be calibrated against a
primary thermometer.
Ideal gases
Glowing
Many different thermometers followed but,
in 1780, Jacques Charles returned to the gas
thermometer. He showed that, for the same
increase in temperature, all gases exhibit the same
increase in volume. In a similar way, the pressure of
a gas increases as it is heated if its volume is fixed
– see figure 4.
Hot objects glow – they radiate light. We can use
this to find out the temperatures of hot objects,
even distant stars and deepest space.
When heated, the colour of metals pass through
red, orange and yellow. Eventually, they become
white hot when all the colours of the visible
spectrum are emitted. They also glow more brightly
because they are hotter and more thermal energy
is emitted.
Figure 5 shows how the spectrum of a hot object
changes as it is heated. In this graph:
• the x-axis shows the wavelength of the light
• the y-axis shows the intensity of the light.
You can see that, as the temperature increases, the
peak in the graph gets higher – more energy is being
radiated. At the same time, the peak moves to the
left, to lower wavelengths which are more energetic.
Figure 4 Measurements of the pressure of a gas show
that pressure increases linearly with temperature.
Notice that the graph in figure 4 can be extrapolated
to zero pressure. The graph intersects the horizontal
temperature axis close to minus 273.15 °C. This
is absolute zero and so the absolute temperature
scale was created. Sometimes called the Kelvin
scale, it is regarded as the fundamental measure
of temperature. The Celsius and Kelvin scales are
related by the equation:
K = °C + 273.15
Because the temperature can be calculated without
any unknown quantities, thermometers based on
an ideal gas are known as primary thermometers.
Going electrical
Gas thermometers are not very convenient or easy
to use so, in 1871, Sir William Siemens introduced
the Platinum Resistance Thermometer. This is
now widely used as a thermometer and covers the
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Figure 5 The spectrum of light radiated by a hot object
depends on its temperature. The peak wavelength
λmax (in m) is related to temperature T (in K) by the
equation λmax × T = 0.0029.
We can use this to find the temperature of a
distant object such as a star. A telescope can be
linked to a spectroscope that measures radiation
intensity across the electromagnetic spectrum.
The star’s temperature can be deduced from the
peak wavelength.
In 1964, Arno Penzias and Robert Wilson, two
radio astronomers, accidentally discovered the
cosmic background radiation, the afterglow of
the Big Bang. From its spectrum, we now know its
temperature to be 2.73 K – see figure 6.
The cricket as a thermometer
To many, the sound of chirping crickets is
synonymous with summer. Only the males
stridulate, which is the scientific term for
chirping, and they do this to attract a female.
Amos Dolbear noticed that the frequency
of chirping of the narrow-winged tree cricket
Oecanthus niveus depended on the prevailing air
temperature and, in 1897, he published his law
relating the temperature T to the number of
chirps per minute N:
T = 10 + (N - 40)/7
Figure 6 The spectrum of cosmic background
radiation, as measured by the COBE satellite. The line
shows that it corresponds to a temperature of 2.728 K.
© Nick Strobel www.astronomynotes.com
This is the equation of a straight-line graph.
Why does the chirping frequency increase with
temperature? Well, crickets are cold-blooded.
As the temperature rises, it becomes easier
to reach the activation energy required for
the chemical reactions that drive the muscle
contractions used to produce chirping, so they
happen more often.
Proxies
We can work out the Earth’s past temperature
and climate using proxy thermometers.
Dendrochronology is probably the best known
technique and uses the width of tree rings to
infer past climate. Wide tree rings correspond to
conditions that favour growth.
We can go back almost half a million years
using the ice cores that are being drilled out of
the Antarctic ice at Lake Vostok. Apart from the
measuring the concentration of greenhouse gases
like methane, isotopes of oxygen can also be
analysed. There are two important isotopes of
oxygen, 16O and the heavier 18O. Water molecules
with 16O atoms are lighter and evaporate more
easily. Water with 18O atoms is heavier and is rained
out more easily when the water vapour condenses.
In a colder world, more of the heavier water is
rained out before it reaches the poles so that polar
ice has a smaller fraction of the 18O isotope. This
can be used to infer past temperature – see figure 7.
This graph shows that the rate of chirping of
the snowy tree cricket Oecanthus fultoni shows
the same pattern as Dolbear’s crickets as the
temperature increases. Published by Thomas J.
Walker in the Annals of the Entomological Society
TJ Walker
of America in 1962.
Figure 7 Past temperature variations deduced from
oxygen-isotope measurements of an Antarctic ice core.
Ice formed 450 000 years ago was found at a depth of
over 3 km.
A male snowy tree cricket
Mike Follows teaches Physics
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