method

temperature measurement spectroscopy

Spectroscopy techniques for measuring temperature in gases, plasmas, and astronomical objects.
17 related articles · 3 formulas

Description

Temperature measurement spectroscopy is a set of techniques that use the light emitted, absorbed, or scattered by a substance to determine its temperature without direct contact. Instead of a thermometer, scientists analyze the spectrum of light — its intensity at different wavelengths — to infer how hot a gas, plasma, or distant star is. This is essential in environments where a physical probe is impossible, such as the interior of a fusion reactor, the atmosphere of a star, or the early universe.

History

The foundations were laid in the 19th century with the work of Gustav Kirchhoff and Robert Bunsen, who linked spectral lines to chemical elements and temperature. The quantitative use of spectral line ratios for temperature measurement developed in the early 20th century with the advent of quantum theory.

How it works

The key principle is that atoms and molecules emit or absorb light at specific wavelengths, and the relative strength of these spectral lines depends on temperature. For example, in a hot gas, more atoms are in excited states, so absorption lines from those states become stronger. By comparing the intensities of different lines, or by fitting the overall shape of a continuous spectrum (blackbody radiation), scientists can extract a precise temperature. In some advanced methods, like frequency-comb spectroscopy, a laser with a spectrum of equally spaced lines is used to measure absorption with extreme accuracy, allowing temperature mapping in gases and flames.

In practice

Used in astrophysics to determine stellar temperatures, in plasma physics to monitor fusion experiments, and in combustion research to map flame temperatures in engines and turbines.

Fun fact

The cosmic microwave background radiation, which fills the universe, is a perfect blackbody spectrum with a temperature of 2.725 Kelvin — measured so precisely that it reveals tiny variations of a few microkelvin, which are the seeds of galaxies.

Concept graph →

Formulas

$$S_a^{1/2} = \sqrt{\frac{4 k_B T k}{m^2 \omega Q}}$$
Spectral density of thermal acceleration noise depends on temperature and resonator properties.
What is in the formula
S_a^{1/2}variableSpectral density of acceleration noise (square root) — acceleration noise spectral density metre per second squared per root hertz
TvariableTemperature — temperature kelvin
kvariableSpring constant of the resonator — spring constant newton per metre
mvariableMass of the resonator — mass kilogram
ωvariableAngular resonance frequency — angular frequency radian per second
QvariableQuality factor of the resonator — quality factor
k_BconstantBoltzmann constant, relates thermal energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin
s^{1/2}_{a,th}=\sqrt{\frac{4k_btk_q}{m^2ω_{n,q}q_q}} · 2606.14738v1
$$T_B = \frac{F_\nu c^2}{2 k_B \nu^2 \Omega}$$
Brightness temperature relates flux density to source temperature.
What is in the formula
T_Bvariablebrightness temperature — brightness temperature kelvin
F_νvariablespectral flux density — spectral flux density watt per metre squared per hertz
νvariablefrequency — frequency hertz
Ωvariablesolid angle of the source — solid angle steradian
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
k_Bconstantrelates energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin
t_b=\frac{f_{ν}c^2}{2k_bν^2ω}>10^{12}{k} · 2606.04232v1
t_b\sim\frac{\varepsilon_{\rmrad}r^2mnγ_jc^3}{2k_bν^3t^2} · 2606.25035
$$\Delta\lambda = \frac{\lambda}{c} \sqrt{\frac{2k_B T}{m}}$$
Thermal motion broadens spectral lines via the Doppler effect.
What is in the formula
\Delta\lambdavariableLine broadening (full width at half maximum) — line width metre
\lambdavariableCentral wavelength of the spectral line — wavelength metre
TvariableTemperature of the emitting/absorbing gas — temperature kelvin
mvariableMass of the emitting/absorbing particle — mass kilogram
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
k_BconstantRelates thermal energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin
\sqrt{}operatorTakes the square root of the argument — square root
t_d=\frac{mc^2}{2k_bλ^2}\frac{δλ^2_{{fit}}-δλ^2_{{inst}}}{4\ln2} · 2606.06577v1

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