
Temperature is a physical quantity that measures the average kinetic energy of particles in a system.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.
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.
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.
Thermometer outside, refrigerator, smartphone processor, weather, cooking food — everywhere we control or measure temperature.
In space, far from stars, the temperature of the background radiation is only 2.7 K (−270 °C) — a remnant of the Big Bang.
| J | variable | A generic physical quantity (e.g., current, stiffness) |
| T | variable | Temperature — temperature kelvin |
| α | variable | Scaling exponent |
| T_eff | variable | Effective temperature — temperature kelvin |
| F_lambda | variable | Spectral flux density per unit wavelength — spectral flux density watt per metre cubed |
| lambda | variable | Wavelength — wavelength metre |
| sigma | constant | Relates total blackbody flux to temperature — stefan boltzmann constant = 5.670374419e-8 watt per metre squared per kelvin to the fourth |
| ∫ | operator | Integration over all wavelengths — integral |
| T | variable | temperature — temperature kelvin |
| R | variable | radius (distance from center) — radius metre |
| α | variable | power-law index (positive for decreasing temperature outward) |
| T_{\mathrm{eq}} | variable | Equilibrium temperature of the planet — temperature kelvin |
| T_* | variable | Effective temperature of the star — temperature kelvin |
| R_* | variable | Radius of the star — radius metre |
| d | variable | Distance between the planet and the star — distance metre |
| A | variable | Bond albedo of the planet — albedo |
| α | variable | Ratio of intensities — intensity ratio |
| I_1 | variable | First intensity — intensity watt per metre squared |
| I_2 | variable | Second intensity — intensity watt per metre squared |
| T_{\text{rh}} | variable | Reheating temperature after inflation — temperature kelvin |
| g_* | variable | Effective number of relativistic degrees of freedom |
| \Gamma | variable | Inflaton decay rate — decay rate per second |
| M_P | variable | Reduced Planck mass — mass kilogram |
| \sqrt{} | operator | Takes the square root of the argument — square root |
| \simeq | operator | Indicates approximate equality — approximate equality |
















