Echobel

Echobel, a siren-bard of The SI Guard, sings inside a copper sphere full of argon, and her note tells the temperature.

The Physics

In acoustic gas thermometry, the resonant frequencies of a gas-filled spherical cavity of known size give the speed of sound. For a dilute monatomic gas the speed of sound fixes k_BT per atom. Measurements of this kind at the triple point of water (NPL, LNE, INRiM and others) gave the most precise values of the Boltzmann constant before the 2019 redefinition.

c² = γk_BT/m

• c: speed of sound in the zero-pressure limit (m/s)
• γ: heat-capacity ratio, 5/3 for an ideal monatomic gas
• k_B: Boltzmann constant, 1.380 649 × 10⁻²³ J/K exactly
• T: thermodynamic temperature (K)
• m: mass of one gas atom (kg)

Since 20 May 2019 the kelvin is defined by fixing k_B exactly. Now that k_B is fixed, the same method works the other way round, as a primary thermometer.

Honest caveat: The formula holds for an ideal gas. Real argon has small pressure-dependent (virial) corrections, so measurements are taken at several pressures and extrapolated to zero. In that limit c depends on T and the atomic mass, not on pressure.

On the sticker

Echobel sings inside the glowing sphere resonator, with standing-wave rings around her. Printed text: ECHOBEL with the line c² = γkT/m. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.