The Science of Measurement
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The Science of Measurement

A Historical Survey

Herbert Arthur Klein

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eBook - ePub

The Science of Measurement

A Historical Survey

Herbert Arthur Klein

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About This Book

`Klein is both a skilled reporter and a wide-ranging humanistic scholar. The book is popular and learned, witty and serious, literary and mathematical — always solid and entertaining.` — Los Angeles Times.
Although the topic of measurement might seem to lend itself to a dry-as-dust treatment, this book is just the opposite: an engrossing, easy-to-read study that treats a multifaceted topic with wit, imagination, and wide-ranging scholarship.
Metrology, the science of measurement, usually concerns itself with length, weight, volume, temperature, and time, but in this comprehensive work the topic also encompasses nuclear radiation, thermal power, light, pressure, sound, and many other areas.
Representing nearly ten years of research effort, The Science of Measurement is considered a definitive book on the concepts and units by which we measure everything in our universe. Nontechnical in its approach, it is not only completely accessible to the general reader but as entertaining and fun to read as it is informative and comprehensive.
` . . . not concerned only with problems of measuring the limits of space or the size of the proton. It is filled with interesting digressions. Not a book for daydreaming, but a book for the curious. Klein's survey of the units and concepts by which we measure everything in the universe helps us understand that universe much better.` — Boston Herald Advertiser

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Information

Year
2012
ISBN
9780486144979

IV

This Thermal Universe

. . . the most dynamic, distinctive, and influential creation of the western mind is a progressive science of nature.
—C. C. GILLISPIE,
The Edge of Objectivity (1960)

26

ON THE TRACK OF TEMPERATURE

Some say the world will end in fire . . .
—ROBERT FROST,
Fire and Ice



“The kelvin, the unit of thermodynamic temperature, is the fraction
e9780486144979_i0174.webp
of the thermodynamic temperature of the triple point of water.”
Thus is the International System’s temperature unit defined, since the adoption of Resolution Four at the Thirteenth General Conference on Weights and Measures in the autumn of 1967.
This definition establishes a unit, rather than a scale and its degree, to measure temperature. The previous definition, dating from the Tenth Conference, had not established a true unit, for it stated:
“The thermodynamic Kelvin degree is the unit of temperature determined by the Carnot cycle with the triple point of water defined as exactly 273.16° K.”
Today, for scientific purposes, temperature is measured by the kelvin unit, abbreviated simply as “K,” without any degree sign required or even permitted. Temperatures are constantly expressed in terms of degree Celsius (°C) and even degree Fahrenheit (°F), but these have become secondary, and the K is king.
Moreover, the K unit and its current definition can serve as a key to help unlock one of the most teasing and fascinating tangles of metrology. What is temperature? Above all, what is this particular type called in the definition “thermodynamic temperature”?
Humans are constantly aware of temperatures around them, in the vaguely qualitative way that our perceptions permit. Centuries ago began the slow struggle to work out systems and scales for quantifying temperatures. But even while progress was made in these directions, the nature of temperature remained obscure. In this chapter we shall seek to reveal enough of that essence of temperature to make clear why the kelvin unit exists today, and why it takes precedence over the other scales that still merit mention, because they are still in use around the world.

Temperature’s cryptic qualities—Temperature is a cryptic kind of physical variable. In the first place, it cannot be measured directly. Indirect and relative approaches must be employed. Our temperature-measuring devices—the thermometric mechanisms in actual use—depend on such consequences of temperature changes as the expansion of substances resulting from increasing temperature; the increased electrical resistance of substances resulting from increasing temperature; the changes of electromotive force (voltage) when junctions of unlike metals are subjected to changes of temperature; the velocity of sound waves in substances under various temperature conditions; and so on.
Literally dozens of different physical effects have been used or could conceivably be used as indirect indices of temperature changes. Yet the actual measurements are not measurements of temperature as such: they are measurements of the length of a column of mercury; of the resistance in ohms of a strip of metal; or the velocity of sound waves in some medium; and so forth. The numerical changes in such nontemperature physical variables are then interpreted as an index to the temperature level with which the sensing device or mechanism is in contact.
When two masses or systems of matter are placed in thermal contact, a form of energy called heat flows from the one at higher temperature into that at lower temperature. This energy transfer continues until the temperatures are equalized. The mass that was “hotter” has lost temperature; the mass that was “cooler” has gained temperature. The former temperature difference has been eliminated. Once that equilibrium is attained, no further net transfer of heat energy takes place.
Hence, temperature is a name for some condition in matter which determines the direction and extent of transfer of the kind of energy we call “heat.” Heat is one form of energy, but by no means the only form. The temperature of a body can be increased by allowing heat to flow into it from a warmer body next to it, but the temperature can be increased also by doing work on the body —as by pounding it, stirring it, rubbing it. Sending an electric current through the body may raise its temperature. Radiating its surface with infrared or light waves also may increase its temperature.
Each such change increases the body’s temperature and so increases the internal energy that it is able to share, in the form of heat, with other bodies—provided that the essential temperature difference exists. The measurement of the “heat content” of bodies goes on constantly. But the internal energy being measured did not necessarily enter those bodies in the form of heat, nor is it certain that it will all later leave those bodies in the form of heat.
Heat, in fact, should be used only with reference to the energy inflows and outflows that take place in consequence of temperature differences between the body in question and other bodies or systems of matter. Heat and temperature are thus virtually inseparable, but by no means identical.
Thermodynamics is the area of physical science concerned with relationships between the energy-in-motion called heat and the mechanical motions of sizable masses of matter. Thermometry might be called the measurement of the effect of these ever-shifting relationships on the tiniest particles or structures within matter.
The tiniest particles or structures within ordinary matter all around us are atoms and molecules, each molecule being an assemblage of two or more atoms. What do these atoms and molecules do in order to cause the mass of matter to show a change in temperature?
They move, on the average, more swiftly with each increase in temperature, and more slowly with each decrease in temperature. But that is an upside-down way to state it. In the first place, the thermodynamic temperature is proportional not to the average velocity of the atoms or molecules, but to the average motion energy per atom or per molecule, as the case may be.
Motion energy, usually called kinetic energy, increases in proportion to the square of the velocity of a moving object, big or little. Thermodynamic temperature increases in proportion to the average kinetic energy per atom or molecule composing the matter whose temperature is being measured.
Most substances around us are mixtures of atoms and molecules of widely different masses. For example, each atom of the mercury in a thermometer is far more massive than the molecules of oxygen, nitrogen, and other gases composing the air whose temperature that mercury is used to measure. Yet when the mercury is “at” the temperature of the surrounding air, the average kinetic energy of the mercury atoms must be neither greater nor less than the average kinetic energy of the oxygen molecules, the nitrogen molecules, and the rest of the less abundant molecules in the air.
Clearly, at any such equality of temperature the average or typical velocity of the more massive mercury atoms must be far less than the average velocity of the lighter oxygen molecules, and thus we must stress the energy per atom or molecule in preference to the average velocity per atom or molecule.
Temperature reflects the average disposable or transferable motion energy of the least or tiniest bits of which a substance is composed. It is the average energy-of-motion-per-smallest-component. Temperature is not the total of the kinetic energies in any mass of matter. If it were, the larger the aggregate mass, the higher its temperature would register. A 1-gram bit of iron at the boiling temperature of water (100° C) and a 100-kilogram chunk of iron also at 100° C are in equilibrium, thermally speaking. The big piece contains 100,000 times as many iron atoms as the small one, but in each the average kinetic energy per iron atom must be the same.
The word average, and its synonym mean, constantly appear in discussions of thermodynamic temperatures. At any instant some atoms will be moving faster than the average speed and others more slowly. Hence some have less kinetic energy than others, but they are so tiny, so numerous, and so constantly interacting that their energies are continually being redistributed. When a body of gas, of liquid, or of solid is found to be “at” a particular thermodynamic temperature, this means that everywhere within the space it occupies the average kinetic energy per molecule or atom is equal to that everywhere else.
Thermometric measuring devices always take averages of the kinetic energies of myriads of atoms or molecules. Temperature is indeed a statistical variable. It summarizes average, or representative, conditions among enormous numbers of individual and interacting components. A single atom or molecule cannot have a “temperature.” Indeed, millions or billions are involved in every meaningful temperature measurement.
Temperature, being a statistical average, is analogous to some social indices, such as “per capita income” in a large population. Some individuals have income many times that average, others have little or even no income. Yet it is possible to state that nation A has a higher per capita income than B; or a lower one; or even an identical one. An individual citizen of nation A or B has an annual income, just as a single atom at each instant has a kinetic energy. But no one citizen of A or B has a “per capita income,” and no single atom, or even few score atoms, can have a “temperature.”

Unmeasurable “temperatures”—Knowledge of the fact that thermodynamic temperature is directly proportional to the average motion energies of atoms or molecules in a large assemblage of matter is enormously enlightening and useful. It helps to understand why, in some highly unstable and swiftly changing states of matter, temperature cannot properly be measured at all. A certain stability and continuity is required in order to make possible the interactions and comparisons that yield numerical temperatures.
Atoms and molecules move in various ways within the containers or the shapes that confine them. The state best suited for illustrating the kinetic or motion theory of temperature is that of a gas. Its atoms and molecules fly about, every which way, constantly bumping into one another and into the walls of the confining receptacle. Each encounter results in a bouncing-away. followed a tiny instant later by a new collision.
Helium gas, composed of single atoms, comes about as close as any substance to the hypothetical “perfect gas.” Its atoms have a diameter of about 1.9 × 10—10 meter. This means that more than 5 billion of them would have to be lined up to attain a total length of just 1 meter. The colliding units are thus extremely tiny.
Also they are numerous almost beyond comprehension. The atomic mass of helium is 4. This means that 1 mole (gram molecular mass) of helium has a mass of 4 gram. The universal constant called Avogadro’s number tells us that 1 mole of any substance contains 6.022 2 × 1023 separate bits (atoms or molecules, as the case may be). This means that 1 gram of helium contains 1.505 5 × 1023 atoms, and 1 kilogram contains 1.505 5 × 1026 atoms.
With so many atoms in motion the numbers of collisions are enormous, and the frequency of the collisions is, at first, difficult to conceive. For example, in a volume of helium gas at standard atmospheric pressure (equivalent to about 14.7 lb/in2 or psi) and at the relatively cool temperature of freezing water (0° C or 273 K), the average number of collisions per atom is about 4,800 million (4.8 billion) per second.
The average velocity per atom is, under these conditions, about 1,202 meter per second (1.2 km/s). Thus, on the average, each atom travels only about 2.51 × 10—7 meter between successive collisions. In other words, in each meter of total travel, a helium atom averages about 4 million collisions and bouncing-away movements. A single helium atom travels, on the average, about 1,300 times its own diameter in distance between successive collisions.
A perfect gas would be one whose atoms were so small that they behaved like mere points of mass. Also it would be one whose atoms did not attract each other, no matter how closely squeezed together they were. No such perfect gas exists. But the hypothesis of the behavior of an imaginary perfect gas has helped to make the kinetic theory of temperature the useful tool that it is.
The atoms of a nearly perfect gas such as helium move in straight lines between collisions. These are called translational motions. The velocity of the atom is constant from one collision to the next. At any instant between collisions it has a definite kinetic energy, equal to one half the product of its mass times the square of its velocity.
The average of all these per-atom kinetic energies is the variable that is measured by the thermodynamic temperature figure. How does this work out in the case of helium gas at 1 atmosphere of pressure and at the freezing temperature of water (0° C)? The average velocity per atom, as stated above, is about 1,202 meter per second. Since about 1.505 5 × 1026 such atoms have a combined mass of 1 kilogram, the mass per atom is about 6.64 x 10—27 kilogram, and half of this mass times the velocity squared gives us an energy average of 4.8 × 10—21 joule per atom.
In other words, under these conditions the combined kinetic energies of about 210 million million million average helium atoms would together amount to 1 joule of energy.
The average energy of 4.8 × 10—21 joule per helium atom is a kinetic kind of way of expressing the meaning of a temperature of 0° C, which equals about 273 K. If we were to seal off a small volume of the helium gas at this pressure and temperature, and then warm it until its temperature had doubled, to 546 K, we would find that the average kinetic energy per atom likewise had doubled, rising from 4.8 to 9.6 × 10—21 joule.
And, even more interesting, if we measured the pressure at the doubled temperature, we should find th...

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