Temperature is a physical quantity that characterises thermal state and determines the direction of heat transfer between systems in thermal contact. When two systems are allowed to exchange energy and reach thermal equilibrium, they have the same temperature. Temperature is not identical to heat, thermal energy, or total internal energy.
At the microscopic level, temperature is related to the statistical distribution of energy among microscopic degrees of freedom, although the precise relationship depends on the system and the relevant form of energy. Temperature is measured using calibrated thermometers or other physical phenomena that vary predictably with thermal conditions. Common temperature scales include Celsius, Kelvin, and Fahrenheit, while the kelvin is the SI base unit for thermodynamic temperature.
The Kelvin scale is an absolute temperature scale whose zero corresponds to absolute zero, the limiting temperature at which a system approaches its lowest thermodynamically accessible energy state under appropriate conditions. Celsius and Kelvin have equal size increments, but their zero points differ by exactly 273.15 degrees under the modern definitions of the scales. Thus a temperature interval of one degree Celsius is equal in magnitude to an interval of one kelvin, while 0 degrees Celsius corresponds to 273.15 kelvin. Fahrenheit uses a different numerical scale and is still used in some countries and applications. Temperature conversion requires applying the correct scale relationship rather than simply treating numerical values from different scales as interchangeable.
Temperature measurement relies on thermometric properties that vary with thermal conditions. Traditional thermometers may use the expansion of a liquid, while modern instruments can use electrical resistance, thermoelectric voltage, semiconductor behaviour, gas properties, acoustic properties, or electromagnetic radiation. Resistance thermometers use predictable changes in electrical resistance, thermocouples generate a voltage related to temperature differences, and infrared thermometers infer temperature from emitted radiation under appropriate assumptions. Calibration establishes the relationship between an instrument indication and a reference temperature. Real thermometers have response times, finite resolution, calibration uncertainties, environmental sensitivities, and possible systematic errors, so the displayed value is always associated with limitations.
At the microscopic level, temperature is connected to the distribution of energy among particles and quantum states rather than simply being a direct measure of the average speed of every particle. In an ideal monatomic gas at equilibrium, temperature is proportional to the mean translational kinetic energy per particle, making kinetic energy an especially useful illustration. More complex systems contain rotational, vibrational, electronic, and other degrees of freedom that contribute to their thermal behaviour. Temperature is a statistical property and becomes particularly well defined for systems close to thermal equilibrium. Small systems, nonequilibrium systems, and systems containing multiple populations can require more specialised definitions because different components may not share a single common temperature.
Temperature determines the direction of spontaneous heat transfer between systems in ordinary thermal contact. Energy tends to transfer from a region of higher temperature to a region of lower temperature until thermal equilibrium is approached. This relationship is formalised by the zeroth law of thermodynamics and underlies the operation of thermometers. Temperature also affects material properties, chemical reaction rates, phase equilibria, electrical resistance, semiconductor carrier populations, magnetic behaviour, and mechanical dimensions. Because so many physical properties depend on temperature, temperature measurement is fundamental to laboratory science, industrial processing, weather observation, medicine, engineering, and environmental monitoring.
Temperature can vary spatially and temporally within a physical system. A solid object may have temperature gradients caused by uneven heating, cooling, or internal heat generation, while a fluid can contain layers or regions with different temperatures because of conduction, convection, radiation, or mixing. In engineering and fluid dynamics, local temperature fields can be described using temperature gradients that drive conductive heat transfer. In the atmosphere and oceans, temperature gradients influence density, circulation, weather, and climate processes. In stars and plasmas, temperature can differ between particle populations or between translational, rotational, vibrational, and other degrees of freedom, requiring careful definition of what temperature represents.
Temperature has several specialised meanings in physics. Negative absolute temperatures can occur in certain systems with bounded energy spectra and population inversion, but they are not simply colder than absolute zero; thermodynamically they can correspond to states that are effectively hotter than any positive temperature for the relevant system. Plasma temperatures may be expressed in energy units such as electronvolts because the thermal energy scale is directly useful for describing charged particle populations.
Effective temperature can be used in astrophysics for systems whose emitted radiation approximates a thermal spectrum even when the system is not a perfect blackbody. These examples demonstrate that temperature must always be interpreted in relation to the physical system and the definition being used.
Temperature is distinct from heat and thermal energy. Temperature describes thermal state, heat describes energy transferred because of a temperature difference, and thermal energy is commonly used to describe energy associated with microscopic thermal degrees of freedom. A large object and a small object can have the same temperature while containing very different amounts of thermal energy because their masses and material properties differ. Temperature also does not directly measure total internal energy because internal energy depends on the number of particles, composition, phase, interactions, and other variables. Correctly distinguishing these concepts is essential for understanding thermodynamics, calorimetry, heat transfer, phase changes, engines, refrigeration, and thermal measurement.
