# Temperature (Thermodynamics)

The temperature of an ideal monatomic gas is related to the average kinetic energy of its atoms as they move. In this animation, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure. These room-temperature atoms have a certain, average speed (slowed down here two trillion fold).

Temperature is the measure of the average kinetic energy of the particles in a substance, which is related to how hot or cold that substance is.

Historically, two equivalent concepts of temperature have developed, the thermodynamic description and a microscopic explanation based on statistical physics. Since thermodynamics deals entirely with macroscopic measurements, the thermodynamic definition of temperature, first stated by Lord Kelvin, is stated entirely in empirical, measurable variables. Statistical physics provides a deeper understanding of thermodynamics by describing matter as a collection of a large number of particles, and derives thermodynamic (i.e. macroscopic) parameters as statistical averages of the microscopic parameters of the particles.

In statistical physics, it is shown that the thermodynamic definition of temperature can be interpreted as a measure of the average energy in each degree of freedom of the particles in the thermodynamic system. Because its temperature is seen as a statistical property, a system must contain a large number of particles for temperature to have a useful meaning. For a solid, this energy is found primarily in the vibrations of its atoms about their equilibrium positions. In an ideal monatomic gas, energy is found in the translational motions of the particles; with molecular gases, vibrational and rotational motions also provide thermodynamic degrees of freedom.

Temperature is a physical property that underlies the common notions of hot and cold. Something that feels hotter generally has a higher temperature, though temperature is not a direct measurement of heat. Temperature is one of the principal parameters of thermodynamics. If no net heat flow occurs between two objects, the objects have the same temperature; otherwise, heat flows from the object with the higher temperature to the object with the lower one. This is a consequence of the laws of thermodynamics.

Temperature is measured with thermometers that may be calibrated to a variety of temperature scales. In most of the world (except for Belize, Myanmar, Liberia and the United States), the Celsius scale is used for most temperature measuring purposes. The entire scientific world (these countries included) measures temperature using the Celsius scale and thermodynamic temperature using the Kelvin scale, which is just the Celsius scale shifted downwards so that 0 K[1]= −273.15 °C, or absolute zero. Many engineering fields in the U.S., notably high-tech and US federal specifications (civil and military), also use the Kelvin and Celsius scales. Other engineering fields in the U.S. also rely upon the Rankine scale (a shifted Fahrenheit scale) when working in thermodynamic-related disciplines such as combustion.

For a system in thermal equilibrium at a constant volume, temperature is thermodynamically defined in terms of its energy (E) and entropy (S) as:

$T \equiv \frac{\partial E}{\partial S}$

## Overview

Heating a body, such as a segment of protein alpha helix (above), tends to cause its atoms to vibrate more, and to cause it to expand or change phase.

Scientifically, temperature is a measurement of the average kinetic energy of the particles in a substance. The most immediate way in which we can measure this is by feeling it. However, this is unreliable because it is based upon the phenomenon of felt air temperature, which can differ at varying degrees from actual temperature. On the molecular level, temperature is the result of the motion of particles which make up a substance. Temperature increases as the energy of this motion increases. The motion may be the translational motion of the particle, or the internal energy of the particle due to molecular vibration or the excitation of an electron energy level. Although very specialized laboratory equipment is required to directly detect the translational thermal motions, thermal collisions by atoms or molecules with small particles suspended in a fluid produces Brownian motion that can be seen with an ordinary microscope. The thermal motions of atoms are very fast and temperatures close to absolute zero are required to directly observe them. For instance, when scientists at the NIST achieved a record-setting low temperature of 700 nK (1 nK = 10−9 K) in 1994, they used optical lattice laser equipment to adiabatically cool caesium atoms. They then turned off the entrapment lasers and directly measured atom velocities of 7 mm per second in order to calculate their temperature.

Molecules, such as O2, have more degrees of freedom than single atoms: they can have rotational and vibrational motions as well as translational motion. An increase in temperature will cause the average translational energy to increase. It will also cause, through equipartition, the energy associated with vibrational and rotational modes to increase. Thus a diatomic gas, with extra degrees of freedom rotation and vibration, will require a higher energy input to change the temperature by a certain amount, i.e. it will have a higher heat capacity than a monatomic gas.

The process of cooling involves removing energy from a system. When there is no more energy able to be removed, the system is said to be at absolute zero, which is the point on the thermodynamic (absolute) temperature scale where all kinetic motion in the particles comprising matter ceases and they are at complete rest in the “classic” (non-quantum mechanical) sense. By definition, absolute zero is a temperature of precisely 0 kelvins (−273.15 °C or −459.68 °F).

Contrary to other thermodynamic quantities such as entropy and heat, whose microscopic definitions are valid even far away from thermodynamic equilibrium, temperature being an average energy per particle can only be defined at thermodynamic equilibrium, or at least local thermodynamic equilibrium (see below).

As a system receives heat, its temperature rises; similarly, a loss of heat from the system tends to decrease its temperature (at the—uncommon—exception of negative temperature; see below).

When two systems are at the same temperature, no heat transfer occurs between them. When a temperature difference does exist, heat will tend to move from the higher-temperature system to the lower-temperature system, until they are at thermal equilibrium. This heat transfer may occur via conduction, convection or radiation or combinations of them (see heat for additional discussion of the various mechanisms of heat transfer) and some ions may vary.

Temperature is also related to the amount of internal energy and enthalpy of a system: the higher the temperature of a system, the higher its internal energy and enthalpy.

Temperature is an intensive property of a system, meaning that it does not depend on the system size, the amount or type of material in the system, the same as for the pressure and density. By contrast, mass, volume, and entropy are extensive properties, and depend on the amount of material in the system.

## Units

The basic unit of temperature (symbol: T) in the International System of Units (SI) is the kelvin (Symbol: K). The kelvin and Celsius scales are, by international agreement, defined by two points: absolute zero, and the triple point of Vienna Standard Mean Ocean Water (water specially prepared with a specified blend of hydrogen and oxygen isotopes). Absolute zero is defined as being precisely 0 K and −273.15 °C. Absolute zero is where all kinetic motion in the particles comprising matter ceases and they are at complete rest in the “classic” (non-quantum mechanical) sense (the relationship between temperature and average kinetic energy is restricted to gases, therefore, it does not apply to temperatures near absolute zero. So zero temperature does not mean that everything is at rest. It means, rather, that all atoms and molecules are in the ground state)[2]. At absolute zero, matter contains no thermal energy. Also, the triple point of water is defined as being precisely 273.16 K and 0.01 °C. This definition does three things: 1) it fixes the magnitude of the kelvin unit as being precisely 1 part in 273.16 parts the difference between absolute zero and the triple point of water; 2) it establishes that one kelvin has precisely the same magnitude as a one degree increment on the Celsius scale; and 3) it establishes the difference between the two scales’ null points as being precisely 273.15 kelvins (0 K = −273.15 °C and 273.16 K = 0.01 °C). Formulas for converting from these defining units of temperature to other scales can be found at Temperature conversion formulas.

In the field of plasma physics, because of the high temperatures encountered and the electromagnetic nature of the phenomena involved, it is customary to express temperature in electronvolts (eV) or kiloelectronvolts (keV), where 1 eV = 11,605 K. In the study of QCD matter one routinely meets temperatures of the order of a few hundred MeV, equivalent to about 1012 K.

For everyday applications, it's very often convenient to use the Celsius scale, in which 0 °C corresponds to the temperature at which water freezes and 100 °C corresponds to the boiling point of water at sea level. Because liquid cloud droplets commonly exist in the atmosphere at sub-zero temperatures, 0 °C is better defined as the freezing point of bulk water or the melting point of ice. In this scale a temperature difference of 1 degree is the same as a 1 K temperature difference, so the scale is essentially the same as the Kelvin scale, but offset by the temperature at which water freezes (273.15 K). Thus the following equation can be used to convert from degrees Celsius to kelvins.

$\mathrm{K = [^\circ C] \left(\frac{1 \, K}{1\, ^\circ C}\right) + 273.15\, K}$

In the United States, the Fahrenheit scale is widely used. On this scale the freezing point of water corresponds to 32 °F and the boiling point to 212 °F. The following conversion formulas may be used to convert between Fahrenheit (F) and Celsius (C) temperature values:

$C = \frac{5}{9} \left({F - 32}\right)$ and $F = \frac{9}{5}{C + 32}$.

See temperature conversion formulas for conversions between most temperature scales.