concept

temperature

Temperature is a physical quantity that measures the average kinetic energy of particles in a system.
14 related articles · 6 formulas · 3 who worked here

Description

Temperature is a statistical measure of the average kinetic energy of random particle motion. In thermodynamics, it determines the direction of heat transfer (from hot to cold). The Kelvin scale is tied to absolute zero, where thermal motion is minimal.

History

Quantitative measurements began with Galileo's thermoscope (1593). In 1714, Daniel Fahrenheit created a mercury thermometer and scale. Anders Celsius in 1742 proposed the centigrade scale. William Thomson (Lord Kelvin) in 1848 introduced the absolute scale. Ludwig Boltzmann statistically justified temperature via the Boltzmann distribution. Modern quantum thermometry achieves an accuracy of 10⁻⁶ K.

How it works

Temperature manifests through the Boltzmann distribution: the probability of a state with energy E is proportional to exp(-E/kT). Increasing T populates higher energy levels. Thermal radiation is described by Planck's law and Wien's displacement law. The velocity distribution of a gas is Maxwell-Boltzmann. Measurement: thermometers (liquid expansion), thermocouples (Seebeck effect), bolometers, pyrometers. The second law of thermodynamics forbids a perpetual motion machine, using temperature. Bekenstein-Hawking entropy relates black hole temperature to the horizon area.

In practice

Thermometer outside, refrigerator, smartphone processor, weather, cooking food — everywhere we control or measure temperature.

Fun fact

In space, far from stars, the temperature of the background radiation is only 2.7 K (−270 °C) — a remnant of the Big Bang.

Concept graph →

Formulas

$$J \propto T^\alpha$$
A quantity scales as a power of temperature.
What is in the formula
JvariableA generic physical quantity (e.g., current, stiffness)
TvariableTemperature — temperature kelvin
αvariableScaling exponent
j_c\proptot^α · 2606.31659
τ(f)=τ_c(\frac{f}{f_c})^α · 2607.00505
$$T_{\text{eff}} = \left( \frac{1}{\sigma} \int F_\lambda \, d\lambda \right)^{1/4}$$
Temperature of blackbody with same total flux.
What is in the formula
T_effvariableEffective temperature — temperature kelvin
F_lambdavariableSpectral flux density per unit wavelength — spectral flux density watt per metre cubed
lambdavariableWavelength — wavelength metre
sigmaconstantRelates total blackbody flux to temperature — stefan boltzmann constant = 5.670374419e-8 watt per metre squared per kelvin to the fourth
∫operatorIntegration over all wavelengths — integral
t_{\rmeff}=(\frac{1}{σ_{\rmsb}}\intf_{\rmp,surf,λ}dλ)^{1/4} · 2607.01316v1
$$T(R) \propto R^{-\alpha}$$
Temperature varies with radius as a power law.
What is in the formula
Tvariabletemperature — temperature kelvin
Rvariableradius (distance from center) — radius metre
αvariablepower-law index (positive for decreasing temperature outward)
t(r)=120{k}(r/{au})^{-3/7} · 2607.02660v1
$$T_{\mathrm{eq}} = T_* \sqrt{\frac{R_*}{2d}} (1-A)^{1/4}$$
Relates a planet's temperature to its star's properties and albedo.
What is in the formula
T_{\mathrm{eq}}variableEquilibrium temperature of the planet — temperature kelvin
T_*variableEffective temperature of the star — temperature kelvin
R_*variableRadius of the star — radius metre
dvariableDistance between the planet and the star — distance metre
AvariableBond albedo of the planet — albedo
t_{{eq}}=t_*\sqrt{\frac{r_*}{2a}}(1-a)^{1/4} · 2607.12017
$$\alpha = \frac{I_1}{I_2}$$
Ratio of two measured intensities.
What is in the formula
αvariableRatio of intensities — intensity ratio
I_1variableFirst intensity — intensity watt per metre squared
I_2variableSecond intensity — intensity watt per metre squared
α=i_0^{\bar{ν}_e}/i_0^{ν_e} · 2607.12558
$$T_{\text{rh}} \simeq \left(\frac{30}{\pi^2 g_*}\right)^{1/4} \sqrt{\Gamma M_P}$$
Temperature after inflation from decay rate and Planck mass.
What is in the formula
T_{\text{rh}}variableReheating temperature after inflation — temperature kelvin
g_*variableEffective number of relativistic degrees of freedom
\GammavariableInflaton decay rate — decay rate per second
M_PvariableReduced Planck mass — mass kilogram
\sqrt{}operatorTakes the square root of the argument — square root
\simeqoperatorIndicates approximate equality — approximate equality
t_{{rh}}\simeq(\frac{40}{π^2g_*})^{1/4}\sqrt{\gamma_φm_p} · 2607.23200v1

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