Temperature is a physical quantity that characterizes the thermal state of matter. In thermodynamics, systems in thermal equilibrium have the same temperature; a temperature difference drives spontaneous heat transfer from a hotter body to a colder one under ordinary conditions. Temperature is distinct from energy: it does not measure the total energy contained in an object. Its scientific meaning rests on equilibrium, measurement, and the microscopic behavior of matter, rather than solely on sensations of hotness and coldness. (openstax.org)
Thermal equilibrium and thermodynamic definition
Two systems are in thermal equilibrium when thermal contact between them produces no net heat transfer. The zeroth law of thermodynamics states that if each of two systems is in thermal equilibrium with a third, they are in thermal equilibrium with each other. This relationship makes temperature measurement possible: a thermometer brought into equilibrium with an object can indicate their shared temperature. Thermal equilibrium concerns temperature specifically, whereas full thermodynamic equilibrium also requires the absence of other processes driving macroscopic change. (openstax.org)
Temperature is an intensive property: dividing a uniform equilibrium sample into smaller portions does not change their temperature. A more formal definition relates temperature to entropy and internal energy. For a simple system with fixed volume (V) and particle number (N),
[ T=\left(\frac{\partial U}{\partial S}\right)_{V,N}. ]
Here (U) denotes internal energy and (S) entropy. Temperature therefore describes how internal energy changes with entropy under specified constraints, rather than merely how much energy is present. (ocw.mit.edu)
Microscopic interpretation
Statistical mechanics connects temperature with the collective behavior of atoms and molecules. For a classical ideal gas in equilibrium, the mean translational kinetic energy per particle is
[ \left\langle E_{\mathrm{trans}}\right\rangle=\frac{3}{2}k_{\mathrm B}T, ]
where (k_{\mathrm B}) is the Boltzmann constant. Higher temperature corresponds to greater average translational energy, not to every particle having the same speed. Individual particles continually exchange energy through collisions. (nist.gov)
This relation is not a universal definition applicable unchanged to all materials. Molecules may also rotate and vibrate, while interactions contribute to internal energy. The number of available motions and their excitation influence how much energy a substance absorbs when its temperature rises. Thus, substances at the same temperature need not have equal internal energies, even when their particle numbers are equal. (nist.gov)
Units and temperature scales
The kelvin, symbol K, is the unit of thermodynamic temperature in the International System of Units. Its magnitude is defined by fixing the Boltzmann constant at exactly
[ k_{\mathrm B}=1.380649\times10^{-23}\ \mathrm{J,K^{-1}}. ]
This definition connects temperature measurement to a universal physical constant. Kelvin values are written without a degree sign: 300 K, not 300 °K. (nist.gov)
The Celsius scale uses the same interval size as the kelvin but a different zero point:
[ t_{\mathrm C}=T_{\mathrm K}-273.15. ]
The Fahrenheit scale is related by
[ t_{\mathrm F}=\frac{9}{5}t_{\mathrm C}+32. ]
A temperature difference of 1 K therefore equals 1 °C or 1.8 °F. Near standard atmospheric pressure, pure water freezes at approximately 0 °C and boils at approximately 100 °C; these temperatures depend on conditions and do not define the modern kelvin. (nist.gov)
Measurement and calibration
Thermometers infer temperature from a reproducible physical response. Contact instruments may use liquid expansion, electrical resistance, or a thermoelectric voltage. Platinum resistance thermometers are important reference instruments, while thermocouples support measurements over broad temperature ranges. Accurate contact measurement requires sufficient thermal equilibration and attention to the exchange of heat between the sensor and its surroundings. (bipm.org)
Non-contact instruments infer temperature from emitted electromagnetic radiation. Their operation draws on blackbody radiation, but real surfaces need not emit like ideal blackbodies. Surface emissivity and the instrument’s spectral response affect the inferred temperature. Such instruments allow measurements without inserting a probe into the object. (nist.gov)
Practical precision thermometry frequently uses the International Temperature Scale of 1990, or ITS-90. It specifies reference points and measurement procedures that make temperatures reproducible between laboratories. ITS-90 approximates thermodynamic temperature; small differences between the practical scale and thermodynamic temperature are studied and documented. Calibration supports metrological traceability, allowing results to be related to recognized references with stated uncertainties. (bipm.org)
Temperature, heat, and changes of state
Heat is energy transferred because of a temperature difference, not a substance stored inside a body. The heat capacity of a system describes how much energy is required to produce a specified temperature change under given conditions. Consequently, equal heat inputs can produce different temperature increases in different materials or different amounts of the same material. (openstax.org)
Energy transfer need not change temperature. During an equilibrium phase transition, such as melting at fixed pressure, added energy can alter the proportions of solid and liquid while temperature remains constant. Boiling and melting temperatures also depend on pressure, illustrating why a temperature value alone does not completely specify a material’s state. (openstax.org)
Low-temperature limit
Absolute zero is 0 K, equivalent to −273.15 °C. It represents the low-temperature limit of ordinary equilibrium systems, where their energy approaches its minimum possible value. Extrapolating ideal-gas behavior helped establish this concept, although real gases generally liquefy or solidify before that limit is approached. Absolute zero is not reached by ordinary cooling procedures; experiments instead attain progressively closer approximations. (openstax.org)