temperature

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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

The first thermometers were created in the 17th century by Galileo and Santorio. Later, Celsius and Fahrenheit devised convenient scales. Lord Kelvin in the 19th century proposed an absolute scale starting from zero.

How it works

When touching a hot radiator, heat flows to the hand: fast-moving particles of the radiator transfer energy to slow particles of the hand — temperatures equalize.

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

Temperature is an intensive thermodynamic quantity characterizing equilibrium state. The zeroth law of thermodynamics: two systems in thermal equilibrium with a third have the same temperature. Microscopically, in equilibrium, the average kinetic energy per degree of freedom is (1/2)k_B T (equipartition theorem). In statistical mechanics, 1/T = ∂S/∂U. The absolute scale is defined by the Carnot cycle. Practical scales (ITS-90) use fixed reference points. Extreme temperatures are measured by various physical principles.

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.

\langle E_k \rangle = \frac{1}{2} k_B T

⟨E_k⟩ — average kinetic energy, k_B — Boltzmann constant, k_B ≈ 1.381×10⁻²³ J/K, T — absolute temperature in kelvins

P_i \propto e^{-E_i/(k_B T)}

P_i — probability of the state, E_i — energy of the state, k_B — Boltzmann constant, T — temperature

\lambda_{\max} = \frac{b}{T}

λ_max — wavelength of maximum emission, b — Wien's constant, b ≈ 2.898×10⁻³ m·K, T — absolute temperature

j = \sigma T^4

j — radiant emittance per unit area, σ — Stefan-Boltzmann constant, σ ≈ 5.67×10⁻⁸ W·m⁻²·K⁻⁴, T — temperature

Open problems & fun facts

Definition of temperature in non-equilibrium systems (active media); Limits of quantum thermometry at ultra-low temperatures; Temperature of black holes and the information paradox (firewall); Measurement of temperature inside neutron stars via neutrinos

💡 The highest temperature in the laboratory is about 5.5 trillion degrees (at the LHC), 250,000 times hotter than the Sun's center. The record for cold is a few picokelvins, where atoms almost come to a stop.

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temperature

History

How it works

History

How it works

History

How it works

Open problems & fun facts

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