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Heat
Michael
Fowler,
Feeling and seeing temperature changes
Within some reasonable temperature range, we can
get a rough idea how warm something is by touching it. But this can be unreliable—if you put one
hand in cold water, one in hot, then plunge both of them into lukewarm water,
one hand will tell you it’s hot, the other will feel cold. For something too hot to touch, we can often
get an impression of how hot it is by approaching and sensing the radiant heat.
If the temperature increases enough, it begins to glow and we can see
it’s hot!
The problem with these subjective perceptions of
heat is that they may not be the same for everybody. If our two hands can’t
agree on whether water is warm or cold, how likely is it that a group of people
can set a uniform standard? We need to
construct a device of some kind that responds to temperature in a simple,
measurable way—we need a thermometer.
The first step on the road to a thermometer was
taken by one Philo of
Byzantium, an engineer, in the second century BC. He took a hollow lead sphere connected with a
tight seal to one end of a pipe, the other end of the pipe being under water in
another vessel.
To quote Philo: “…if you expose the sphere to
the sun, part of the air enclosed in the tube will pass out when the sphere
becomes hot. This will be evident
because the air will descend from the tube into the water, agitating it and
producing a succession of bubbles.
Now if the sphere is put back in the shade, that
is, where the sun’s rays do not reach it, the water will rise and pass through
the tube …”
“No matter how many times you repeat the
operation, the same thing will happen.
In fact, if you heat the sphere with fire, or
even if you pour hot water over it, the result will be the same.”
Notice that Philo did what a real investigative
scientist should do—he checked that the experiment was reproducible, and
he established that the air’s expansion was in response to heat being
applied to the sphere, and was independent of the source of the heat.
Classic Dramatic Uses of Temperature-Dependent
Effects
This expansion of air on heating became widely known in
classical times, and was used in various dramatic devices. For example, Hero of Alexandria describes a
small temple where a fire on the altar causes the doors to open.
The altar is a large airtight box, with a pipe leading
from it to another enclosed container filled with water. When the fire is set on top of the altar, the
air in the box heats up and expands into a second container which is filled
with water. This water is forced out
through an overflow pipe into a bucket hung on a rope attached to the door
hinges in such a way that as the bucket fills with water, it drops, turns the
hinges, and opens the doors. The pipe
into this bucket reaches almost to the bottom, so that when the altar fire goes
out, the water is sucked back and the doors close again. (Presumably, once the fire is burning, the
god behind the doors is ready to do business and the doors open…)
Still, none of these ingenious devices is a thermometer.
There was no attempt (at least none recorded) by Philo or his followers to make
a quantitative measurement of how hot or cold the sphere was. And the “meter” in thermometer means
measurement.
The First Thermometer
Galileo claimed to have invented the first
thermometer. Well, actually, he called it a thermoscope,
but he did try to measure “degrees of heat and cold” according to a colleague,
and that qualifies it as a thermometer.
(Technically, a thermoscope is a device making it possible to see
a temperature change, a thermometer can measure the temperature
change.) Galileo used an inverted
narrow-necked bulb with a tubular neck, like a hen’s egg with a long glass tube
attached at the tip.
He first heated the bulb with his hands then
immediately put it into water. He recorded that the water rose in the bulb the height
of “one palm”. Later, either Galileo or
his colleague Santorio Santorio put a paper scale next to the tube to read off
changes in the water level. This
definitely made it a thermometer, but who thought of it first isn’t clear (they
argued about it). And, in fact, this
thermometer had problems.
Question: what problems? If you
occasionally top up the water, why shouldn’t this thermometer be good for
recording daily changes in temperature?
Answer: because it’s also a
barometer! But—Galileo didn’t know about
the atmospheric pressure.
Torricelli, one of Galileo’s pupils, was the
first to realize, shortly after Galileo died, that the real driving force in
suction was external atmospheric pressure, a satisfying mechanical explanation
in contrast to the philosophical “nature abhors a vacuum”. In the 1640’s, Pascal pointed out that the variability
of atmospheric pressure rendered the air thermometer untrustworthy.
Liquid-in-glass thermometers were used from the
1630’s, and they were of course insensitive to barometric pressure. Meteorological records were kept from this
time, but there was no real uniformity of temperature measurement until
Fahrenheit, almost a hundred years later.
Newton’s Anonymous Table of Temperatures
The first systematic account of a range of
different temperatures, “Degrees of Heat”, was written by
Taking the freezing point of water as zero,
Newton found the temperature of boiling water to be almost three times that of
the human body, melting lead eight times as great (actually 327C, whereas
8x37=296, so this is pretty good!) but for higher temperatures, such as that of
a wood fire, he underestimated considerably.
He used a linseed oil liquid in glass thermometer up to the melting
point of tin (232°C). (Linseed oil doesn’t boil
until 343°C,
but that is also its autoignition temperature!)
Fahrenheit’s Excellent Thermometer
The first really good thermometer, using mercury
expanding from a bulb into a capillary tube, was made by Fahrenheit in the
early 1720’s. He got the idea of using
mercury from a colleague’s comment that one should correct a barometer
reading to allow for the variation of the density of mercury with
temperature. The point that has to be
borne in mind in constructing thermometers, and defining temperature scales, is
that not all liquids expand at uniform rates on heating—water, for example, at
first contracts on heating from its freezing point, then begins to expand at
around forty degrees Fahrenheit, so a water thermometer wouldn’t be very
helpful on a cold day. It is also not
easy to manufacture a uniform cross
section capillary tube, but Fahrenheit managed to do it, and demonstrated
his success by showing his thermometers agreed with each other over a whole
range of temperatures. Fortunately, it
turns out that mercury is well behaved in that the temperature scale defined by
taking its expansion to be uniform coincides very closely with the true
temperature scale, as we shall see later.
Amontons’ Air Thermometer: Pressure Increases
Linearly with Temperature
A little earlier (1702) Amontons introduced an air
pressure thermometer. He established
that if air at atmospheric pressure (he states 30 inches of mercury) at the
freezing point of water is enclosed then heated to the boiling point of water,
but meanwhile kept at constant volume by increasing the pressure on it, the
pressure goes up by about 10 inches of mercury.
He also discovered that if he compressed the air in the first place, so
that it was at a pressure of sixty inches of mercury at the temperature of
melting ice, then if he raised its temperature to that of boiling water, at the
same time adding mercury to the column to keep the volume of air constant, the
pressure increased by 20 inches of mercury.
In other words, he found that for a fixed amount of air kept in a
container at constant volume, the pressure increased with temperature by about
33% from freezing to boiling, that percentage being independent of the
initial pressure.
Thermal Equilibrium and the Zeroth Law of
Thermodynamics
Once the thermometer came to be widely used, more
precise observations of temperature and (as we shall see) heat flow
became possible. Joseph Black, a professor at the
As he wrote, “By the use of these instruments [thermometers]
we have learned, that if we take 1000, or more, different kinds of matter, such
as metals, stones, salts, woods, cork, feathers, wool, water and a variety of other
fluids, although they be all at first of different heats, let them be placed
together in a room without a fire, and into which the sun does not shine, the
heat will be communicated from the hotter of these bodies to the colder, during
some hours, perhaps, or the course of a day, at the end of which time, if we
apply a thermometer to all of them in succession, it will point to precisely
the same degree.”
We say nowadays that bodies in “thermal contact”
eventually come into “thermal equilibrium”—which means they finally attain the
same temperature, after which no further heat flow takes place. This is
equivalent to:
The Zeroth Law of Thermodynamics: If two objects are in thermal
equilibrium with a third, then they are in thermal equilibrium with each other.
The “third body” in a practical situation is just
the thermometer.
It’s perhaps worth pointing out that this trivial
sounding statement certainly wasn’t obvious before the invention of the
thermometer. With only the sense of
touch to go on, few people would agree that a piece of wool and a bar of metal,
both at 0°C,
were at the same temperature.
Measuring Heat Flow: a Unit of Heat
The next obvious question is, can we get more quantitative
about this “flow of heat” that takes place between bodies as they move towards
thermal equilibrium? For example,
suppose I reproduce one of Fahrenheit’s experiments, by taking 100 ccs of water
at 100°F,
and 100ccs at 150°F, and mix them together in an insulated jug so little heat
escapes. What is the final temperature
of the mix?
Of course, it’s close to 125°F—not surprising, but it does tell us
something! It tells us that the
amount of heat required to raise the temperature of 100 cc of water from 100°F to 125°F is exactly the same as the amount needed
to raise it from 125°F to 150°F. A series of such experiments
(done by Fahrenheit, Black and others) established that it always took
the same amount of heat to raise the temperature of 1 cc of water by one
degree, independent of the initial temperature of the water (provided
it’s between the freezing point and the boiling point).
This makes it possible to define a unit of
heat. Perhaps unfairly to
Fahrenheit,
1 calorie is the heat required to raise
the temperature of 1 gram of water by 1 degree Celsius.
(Celsius also lived in the early 1700’s. His
scale has the freezing point of water as 0°C, the boiling point as 100°C.
Fahrenheit’s scale is no longer used in science, but lives on in
engineering in the
Specific Heats and Calorimetry
The
specific heat of a substance is the heat required in calories to raise the
temperature of 1 gram by 1 degree Celsius.
As Fahrenheit continues his
measurements of heat flow, it quickly became evident that for different
materials, the amount of heat needed to raise the temperature of one gram by
one degree could be quite different. It
was natural to measure specific heats relative to that of water, the simplest
and most readily available substance for calorimetric experiments. There were
some surprises. For example, it had been widely thought before the measurements
were made, that one cc of Mercury, being a lot heavier than one cc of water,
would take more heat to raise its temperature by one degree. This proved not to be the case—Fahrenheit
himself made the measurement. In an
insulating container, called a “calorimeter” he added 100ccs of water at 100°F
to 100ccs of mercury at 150°F, and stirred so they
quickly reached thermal equilibrium.
Question: what do you think the final temperature was? Approximately?
Answer: The final temperature was,
surprisingly, about 120°F. 100 cc of water evidently “contained
more heat” than 100 cc of mercury, despite the large difference in weight!
The technique, called calorimetry, was widely used to find specific
heats of many different substances, and at first no clear pattern emerged. It was puzzling that the specific heat of
mercury was so low compared with water.
As the experiments progressed, it gradually became evident that heavier
substances, paradoxically, had lower specific heats.
A Connection With Atomic Theory
Meanwhile, this
quantitative approach to scientific observation had spread to chemistry. Towards the end of the 1700’s, Lavoisier
weighed chemicals involved in reactions before and after the reaction. This involved weighing the gases involved, so
had to be carried out in closed containers, so that, for example, the weight of
oxygen used and the carbon dioxide, etc., produced would accounted for in
studying combustion. The big
discovery was that mass was neither created nor destroyed. This had not been realized before because no
one had weighed the gases involved. It
made the atomic theory suddenly more plausible, with the idea that maybe
chemical reactions were just rearrangements of atoms into different
combinations.
Lavoisier also clarified
the concept of an element, an idea that was taken up in about 1800 by John
Dalton, who argues that a given compound consisted of identical molecules, made
up of elementary atoms in the same proportion, such as H2O (although
that was thought initially to be HO).
This explained why, when substances reacted chemically, such as the
burning of hydrogen to form water, it took exactly eight grams of oxygen for
each gram of hydrogen. (Well, you could also produce H2O2
under the right conditions, with exactly sixteen grams of oxygen to one of
hydrogen, but the simple ratios of amounts of oxygen needed for the two
reactions were simply explained by different molecular structures, and made the
atomic hypothesis even more plausible.)
Much effort was expended
carefully weighing the constituents in many chemical reactions, and
constructing diagrams of the molecules.
The important result of all this work was that it became possible to
list the relative weights of the atoms involved. For example, the data on H2O and H2O2
led to the conclusion that an oxygen atom weighed sixteen times the weight of a
hydrogen atom.
It must be emphasized,
though, that these results gave no clue as to the actual weights of atoms! All that was known was that atoms were too
small to see in the best microscopes. Nevertheless, knowing the relative
weights of some atoms in 1820 led to an important discovery. Two professors in
|
Element |
Specific Heat (cals/gm/degree C) |
Relative weights of the atoms |
Product of relative atomic weight and specific heat |
|
Lead |
0.0293 |
12.95 |
0.3794 |
|
Tin |
0.0514 |
7.35 |
0.3779 |
|
Zinc |
0.0927 |
4.03 |
0.3736 |
|
|
0.1880 |
2.011 |
0.3780 |
The significance of this, as they pointed out, was that the “specific heat”, or heat capacity, of each atom was the same—a piece of lead and a piece of zinc having the same number of atoms would have the same heat capacity. So heavier atoms absorbed no more heat than lighter atoms for a given rise in temperature. This partially explained why mercury had such a surprisingly low heat capacity. Of course, having no idea how big the atoms might be, they could go no further. And, indeed, many of their colleagues didn’t believe in atoms anyway, so it was hard to convince them of the significance of this discovery.
Latent Heat
One of Black’s experiments was to set a pan of
water on a steady fire and observe the temperature as a function of time. He found it steadily increased, reflecting
the supply of heat from the fire, until the water began to boil, whereupon the
temperature stayed the same for a long time.
The steam coming off was at the same (boiling) temperature as the water.
So what was happening to the heat being supplied? Black correctly concluded that heat needed to
be supplied to change water from its liquid state to its gaseous state, that
is, to steam. In fact, a lot of heat had
to be supplied: 540 calories per gram, as opposed to the mere 100 calories per
gram needed to bring it from the freezing temperature to boiling. He also discovered that it took 80 calories
per gram to melt ice into water, with no rise in temperature. This heat is released when the water freezes
back to ice, so it is somehow “hidden” in the water. He called it latent heat, meaning
hidden heat.
______________________________________________________________________________
Books I used in preparing this lecture:
A Source Book in Greek Science, M. R. Cohen and I. E. Drabkin, Harvard
university Press, 1966.
A History of the Thermometer and its Uses in
Meteorology, W. E. Knowles
Middleton, Johns
A Source Book in Physics, W. F. Magie,