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Uncommon Measure: Acoustic Result Could Change Definition of Temperature

A new measurement of a fundamental physical constant marks a turning point in the quest to craft a perfect temperature scale



Courtesy of the National Physical Laboratory

The most accurate thermometer in the known universe sits in a rather nondescript white building in Teddington, England, on the campus of the U.K.’s National Physical Laboratory (NPL). It looks nothing like a slender tube filled with mercury or colored alcohol. Instead, it’s a copper vessel about the size of a large cantaloupe, filled with dilute ultrapure argon gas and studded with microphones and microwave antennas, precisely shaped by a diamond-tipped lathe so that its radius varies with an uncertainty of only about 12 atomic layers of copper. The purpose of this thermometer is not really to measure temperature, however. Rather, new results from this and other similar devices could soon allow scientists to redefine temperature completely and bring it in line with the meter and other standard international units of measurement.

What the device actually measures is the relation between energy, as measured in joules, and temperature, as measured in the international standard unit, the kelvin. This relation is expressed as the Boltzmann constant and, in a perfect world, would be the kelvin’s ideal physical basis. That it’s not is purely a historical accident born of the fact that most of our planet’s surface is covered with liquid water, a substance which conveniently changes to ice or vapor at well-known thresholds of temperature.

Because our standard conceptions of temperature are intimately linked to these phase changes of water, in principle we currently only know two temperatures exactly: absolute zero, the temperature at which atomic motion ceases, and 273.16 kelvins. That latter temperature is the so-called triple point of water, which can exist stably there as ice, liquid and vapor. In 1954 an international agreement defined the kelvin as 1/273.16 the difference between absolute zero and water’s triple point.

All thermometers around the world are ultimately calibrated against this triple-point temperature, which itself is calibrated using specially constructed triple-point cells filled with a carefully concocted mixture of water that has a certain, specific ratio of hydrogen and oxygen isotopes. (The international standards community refers to it as the Vienna standard-mean ocean water.) This system generally works quite well—a recent comparison of triple-point cells from across Europe revealed temperature variations between them of only some 20 millionths of a kelvin—but it begins to break down for temperatures far from water’s triple point, such as those found in cryogenic systems or within stars. Extremely low or high temperatures must be measured using standards such as the freezing point of copper or the electrical noise rippling through a resistor, all of which must be circuitously tied back to water’s triple point with varying amounts of uncertainty and approximation.

“It’s bonkers that the kelvin doesn’t directly relate temperature to energy,” says Michael de Podesta, an NPLmetrologist who leads the team responsible for the world-record thermometer. “It only happened this way because people started measuring temperature long before they knew what it actually was, before temperature was known to just be atoms and molecules buzzing around. Now that we know better and have the opportunity to correct it, we should.”

In pursuit of that goal, de Podesta and researchers at Cranfield University in the U.K. and the Scottish Universities Environmental Research Center spent the past five years building and refining their thermometer. It’s technically an “acoustic resonator”—when certain frequencies of sound are piped in through its microphones, it will ring like a bell. Comparing that sonic resonance with the vessel’s radius, which is measured via microwaves, de Podesta and his team can pin down the speed of sound within the gas-filled cavity, and thus the average speed at which the argon molecules are moving—that is, how much kinetic energy they contain. By doing all this while also holding the resonator’s temperature steady at 273.16 kelvins, at water’s triple-point, de Podesta and his team have made the most accurate measurement yet of the Boltzmann constant, pinning it at 1.38065156 (98) X 10-23 joules per kelvin. That “(98)” is a statistical measure of doubt about the two preceding digits and corresponds to an uncertainty of 0.7 part per million (ppm). The team’s findings are published July 11 in the journal Metrologia.

“This tells you how much of a change in energy corresponds to a temperature change of one degree,” de Podesta explains. “We hope that eventually by international agreement our measurements and others will ‘fix’ the Boltzmann constant so that forever after we define temperature as a certain number of joules per degree kelvin.”

Richard Davis, a metrologist and former top-level official at the International Bureau of Weights and Measures in Sèvres, France, notes that broader efforts are underway to tie other metric units to fundamental physical constants rather than arbitrary objects or materials, and says redefinitions could be officially enshrined as early as 2014. “The meter used to be defined by a platinum–iridium rod here in France, but since the 1980s it has been defined by the speed of light through a vacuum over a specific fraction of a second,” he says. “This was a case of the tail wagging the dog—we determined that fraction of a second to keep the meter unchanged. The redefinitions of the kilogram, the kelvin, the ampere and other units are coming next, but since the units themselves are not changing, this will be invisible to almost everyone except those who are working at the very highest levels of accuracy.”

Before any official change to the kelvin can take place, however, everyone must agree on the accuracy of the Boltzmann constant as measured by de Podesta and his collaborators. Groups in the U.S., China, France, Italy and Germany have projects to measure the constant. In particular, in 2010 Laurent Pitre at France’s national metrology lab, also using an argon-filled acoustic resonator, announced a Boltzmann measurement with an associated uncertainty of 1.24 ppm—0.54 ppm larger than de Podesta’s. The significant difference in uncertainty between these measurements is as yet unreconciled. Pitre declined to discuss his results for this article.

Michael Moldover, a metrologist at the National Institute of Standards and Technology in Gaithersburg, Md., who pioneered the first high-accuracy acoustic resonator measurements of the Boltzmann constant in 1988, praises the work of both de Podesta’s and Pitre’s groups but says that slow-simmering ire between the two fiercely competitive teams is now impeding scientific progress. “It’s been very difficult to get them to cooperate, but I’ve been pressuring them to because people need answers for this for the health of the field,” he says.

In the meantime, the global community of metrologists will continue their painstaking work, shaving ever-smaller uncertainties from their ever-more precise observations, bringing the standards by which our world is measured ever-closer to an elusive—and unattainable—ideal. Although practical applications of his group’s acoustic thermometry could emerge, such as the detection of impurities in natural gases, de Podesta admits that the frontiers of this quest have, for now, largely moved far beyond the practicalities of everyday life and into the lofty realm of aesthetics. “I like to think that this is a beautiful, elegant gift to the future that people will look back on and appreciate in 100 years,” he says. “Right now, no industrialists are beating my door down saying, ‘For God’s sake, do something about the kelvin!’ but we don’t know how this accuracy and precision might prove useful in the future. Right now, you don’t think twice about this stuff, and that’s because of people like me. We worry about these things so that you don’t have to.”

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