NIST Explains the New Kelvin Definition

Reprinted with permission from the National Institute of Science and Technology website

Temperature is one of the most important and ubiquitous measurements in human life. For centuries, we have continuously improved on the systems, technologies, methods and units used to quantify and express it. Now, the definition of the kelvin (K)—the temperature unit of the International System of Units (SI), has been given a radically new definition. This redefinition was the result of 60 nations’ unanimous vote to revise the SI in November 2018.

In daily life, the kelvin temperature scale—named for the celebrated British physicist Lord Kelvin (1824–1907)—rarely makes an appearance. People are more familiar with the Fahrenheit and Celsius scales, which are used for most practical temperature measurements, such as in weather forecasts, food preparation, manufacturing, etc. Historically, both scales center around defined points such as the melting point of ice, the temperature of the human body or the boiling point of water.

The kelvin unit is not expressed in degrees like Celsius or Fahrenheit. It is used by itself to describe temperature. For example, “mercury loses all electrical resistance at a temperature of 4.2 kelvins.”

A change of one kelvin is the same amount of temperature change as one degree Celsius, but the kelvin scale is “absolute” in the sense that it starts at absolute zero, or what kelvin and other scientists called “infinite cold.” (0 K = -273.15°C = -459.67°F. Room temperature is about 70°F, 21°C or 294 K.)

A triple-point cell. Image: NIST

A triple-point cell. Image: NIST

The concept of an absolute temperature scale is powerful; it is different than simply relative temperature, in which objects are talked about being hotter or colder than something else. The absolute, thermodynamic temperature of an object provides information on how much average energy of motion (kinetic energy) its atoms and molecules have.

An important aside: According to classical, 19th-century physics, motion completely stops at absolute zero. But according to the quantum theory introduced in the 20th century, matter does have random motion at absolute zero, called “zero-point motion,” thanks to a quantum concept known as the Heisenberg uncertainty principle, which dictates that the position and momentum of an object cannot be known with complete certainty at the same time. The zero-point motion is not considered heat-driven (thermal) motion and thus is not part of the definition of thermodynamic, or absolute, temperature. At absolute zero the only motion that exists is quantum-mechanical zero-point motion.

The kelvin scale is used widely in science, particularly in the physical sciences. In everyday life, it is most often encountered as the “color temperature” of a lamp. An old-fashioned incandescent bulb, which puts out yellowish light, has a color temperature of about 3,000 K. Put another way, this means its yellowish spectrum closely resembles what a hot object at a 3,000 K temperature would naturally radiate. A lamp with a color temperature of 5,000 K to 5,600 K, which contains more blue light, is typically labeled “daylight” or “full spectrum” because the temperature of the surface of the sun is about 5,800 K. Many newly available LED lights fall within this range or go even higher.

Since 1954, the kelvin has been defined as “equal to the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water—the point at which water, ice and water vapor co-exist in equilibrium. That is a valuable common reference because, for a precise formulation of water at a specific pressure, the triple point always occurs at exactly the same temperature: 273.16 K.

Extrapolating from the water triple-point temperature to very high or very low temperatures is problematic; so, by international agreement, 21 other defining points are specified, ranging from the freezing point of helium to the freezing point of copper.

Now, however, the kelvin has been redefined in terms of the Boltzmann constant, which relates the amount of thermodynamic energy in a substance to its temperature. The new definition is:

The kelvin, symbol K, is the SI unit of thermodynamic temperature; its magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1.380649 × 10-23…J K-1[joules per kelvin].

If that seems like a mouthful, you wouldn’t be wrong! To best understand the context and significance of this historic redefinition, it’s helpful to learn more about the past, present and future of measuring temperature.

The Boltzmann constant (kB) relates temperature to energy. It is an indispensable tool in thermodynamics, the study of heat and its relationship to other types of energy. It’s named for Austrian physicist Ludwig Boltzmann (1844–1906), one of the pioneers of statistical mechanics. Statistical mechanics expands upon classical Newtonian mechanics to describe how the group behavior of large collections of objects emerges from the microscopic properties of each individual object.

Newton’s laws govern forces, masses and motions of objects or systems of objects. Newton’s laws are said to be deterministic: That is, someone who has a complete knowledge of the initial conditions of all the objects in a system can predict the future of the system accurately. That is how space missions can place robot landers at specific desired locations hundreds of millions of kilometers from Earth. It’s the same principle that allows expert billiards players to regularly win games.

But for a huge ensemble of objects, such as the billions of trillions of hot molecules propelling a piston in a steam engine (the dominant technology of Boltzmann’s era), there is no possible way to determine the state of each independent molecule: They are moving at different velocities with a range of different energies.

For example, air molecules at a room temperature of 25°C (300 K, or 77°F) are traveling at an average speed of about 500 meters per second (1,100 mph). But some are moving at 223 m/s, some at 717 m/s, and so forth, and they are all moving in different directions. Each individual property cannot be known.

The Maxwell-Boltzmann distribution shows the average speed and most probable speed of particles in a gas at a certain temperature. Image: Curt Suplee/NIST

The Maxwell-Boltzmann distribution shows the average speed and most probable speed of particles in a gas at a certain temperature. Image: Curt Suplee/NIST

Nonetheless, understanding the physics of heat engines and analogous systems demands some way to make mathematically useful statements about collections of enormous numbers of objects. Boltzmann and other scientists showed that it can be done in terms of statistics and probabilities—statistical mechanics. The collective thermodynamic properties of ensembles derive from the sum of the energies of each individual object. Interestingly, different energy values have different probabilities of occurring.

So how can the average energy content of a gas be calculated? Its energy is proportional to its thermodynamic temperature, and the Boltzmann constant defines what that proportion is: The total kinetic energy (E) in joules is related to temperature (T) in kelvins according to the equation E = kBT. For scale, one joule is the amount of energy expended by a 100-watt light bulb in 0.01 second, or a 1-watt bulb in one second.

Michael Moldover with an acoustic resonator he and his colleagues developed for making some of the world’s most accurate measurements of the Boltzmann constant. Image: NIST

Michael Moldover with an acoustic resonator he and his colleagues developed for making some of the world’s most accurate measurements of the Boltzmann constant. Image: NIST

The Boltzmann constant is thus expressed in joules per kelvin. In the new definition of the kelvin, the Boltzmann constant has an exact fixed value in joules per kelvin. The conditions are: the value obtained by at least one measurement method for kB has an uncertainty less than one part in a million; and that at least one fundamentally different type of measurement yields similar values with uncertainties less than three parts per million.

To date, the most accurate values of kB have been obtained by acoustic thermometry, which relies on the fact that the speed of sound in a gas is directly dependent on its temperature. NIST has a long history of making accurate measurements of the Boltzmann constant with this method.

Another leading technique is known as dielectric-constant gas thermometry (DCGT), in which researchers measure changes in a gas’s ability to respond to an electric field, known as its dielectric constant. The dielectric constant can depend sensitively on temperature and lead to accurate measurements of the Boltzmann constant.

NIST and other measurement science institutes are also employing several alternative methods such as Johnson Noise Thermometry (JNT) for measuring the Boltzmann constant. Recent JNT experiments at NIST have yielded a value for kB with an uncertainty of about 5 parts in a million. Many other new methods have been developed for measuring the Boltzmann constant, including optical measurements of helium gas.

In 2017, the world measurement science community met the requirements for giving the Boltzmann constant an exact value and redefining the kelvin. Acoustic thermometry, DCGT and JNT measurements from various research groups were used in a final determination of the Boltzmann constant for the redefinition of the SI in November 2018. Based on these data, the value of kB in a revised SI is 1.380649 x 10-23 J K-1.

While the kelvin is not presently based on a physical artifact, as the kilogram is for mass, its redefinition is just as momentous. The old definition based on the peculiar properties of a certain isotopic mixture of water, and not directly upon a universal constant of nature. Because it’s not possible to prepare two exactly identical formulations of this mixture, measurements of the kelvin were inevitably slightly different from setup to setup. Basing the kelvin on Boltzmann’s constant has put scientists on the same page, or more precisely on the same letter, k. This has enabled temperature measurements to be truly universal. ■