Thermodynamic temperature Thermodynamic temperature is the absolute measure 1 Overview of temperature and is one of the principal parameters of thermodynamics. Temperature is a measure of the random submicroscopic Thermodynamic temperature is defined by the third law motions and vibrations of the particle constituents of of thermodynamics in which the theoretically lowest tem- matter. These motions comprise the internal energy of perature is the null or zero point. At this point, absolute a substance. More specifically, the thermodynamic tem- zero, the particle constituents of matter have minimal perature of any bulk quantity of matter is the measure motion and can become no colder.[1][2] In the quantum- of the average kinetic energy per classical (i.e., non- mechanical description, matter at absolute zero is in its quantum) degree of freedom of its constituent particles. ground state, which is its state of lowest energy. Thermo- “Translational motions” are almost always in the classical dynamic temperature is often also called absolute tem- regime. Translational motions are ordinary, whole-body perature, for two reasons: one, proposed by Kelvin, that movements in three-dimensional space in which particles it does not depend on the properties of a particular mate- move about and exchange energy in collisions. Figure 1 rial; two that it refers to an absolute zero according to the below shows translational motion in gases; Figure 4 be- properties of the ideal gas. low shows translational motion in solids. Thermodynamic temperature’s null point, absolute zero, is the temperature The International System of Units specifies a particular at which the particle constituents of matter are as close as scale for thermodynamic temperature. It uses the Kelvin possible to complete rest; that is, they have minimal mo- scale for measurement and selects the triple point of water tion, retaining only quantum mechanical motion.[3] Zero at 273.16K as the fundamental fixing point. Other scales kinetic energy remains in a substance at absolute zero (see have been in use historically. The Rankine scale, using Thermal energy at absolute zero, below). the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United Throughout the scientific world where measurements are States in some engineering fields. ITS-90 gives a practical made in SI units, thermodynamic temperature is mea- means of estimating the thermodynamic temperature to sured in kelvins (symbol: K). Many engineering fields in a very high degree of accuracy. the U.S. however, measure thermodynamic temperature using the Rankine scale. Roughly, the temperature of a body at rest is a measure of the mean of the energy of the translational, vibrational By international agreement, the unit kelvin and its scale and rotational motions of matter's particle constituents, are defined by two points: absolute zero, and the triple such as molecules, atoms, and subatomic particles. The point of Vienna Standard Mean Ocean Water (water with full variety of these kinetic motions, along with potential a specified blend of hydrogen and oxygen isotopes). Ab- energies of particles, and also occasionally certain other solute zero, the lowest possible temperature, is defined as types of particle energy in equilibrium with these, make being precisely 0 K and −273.15 °C. The triple point of up the total internal energy of a substance. Internal en- water is defined as being precisely 273.16 K and 0.01 °C. ergy is loosely called the heat energy or thermal energy in This definition does three things: conditions when no work is done upon the substance by its surroundings, or by the substance upon the surround- 1. It fixes the magnitude of the kelvin unit as being pre- ings. Internal energy may be stored in a number of ways cisely 1 part in 273.16 parts the difference between within a substance, each way constituting a “degree of absolute zero and the triple point of water; freedom”. At equilibrium, each degree of freedom will 2. It establishes that one kelvin has precisely the same have on average the same energy: k T /2 where k is B B magnitude as a one-degree increment on the Celsius the Boltzmann constant, unless that degree of freedom is scale; and in the quantum regime. The internal degrees of freedom (rotation, vibration, etc.) may be in the quantum regime 3. It establishes the difference between the two scales’ at room temperature, but the translational degrees of free- null points as being precisely 273.15 kelvins (0 K = dom will be in the classical regime except at extremely −273.15 °C and 273.16 K = 0.01 °C). low temperatures (fractions of kelvins) and it may be said that, for most situations, the thermodynamic temperature Temperatures expressed in kelvins are converted to de- is specified by the average translational kinetic energy of grees Rankine simply by multiplying by 1.8 as follows: the particles. T°R = 1.8TK, where TK and T°R are temperatures in 1 2 2 THE RELATIONSHIP OF TEMPERATURE, MOTIONS, CONDUCTION, AND THERMAL ENERGY kelvin and degrees Rankine respectively. Temperatures expressed in degrees Rankine are converted to kelvins by dividing by 1.8 as follows: TK = T°R⁄₁.₈. 1.1 Practical realization Main article: ITS-90 Although the Kelvin and Celsius scales are defined us- ing absolute zero (0 K) and the triple point of water (273.16 K and 0.01 °C), it is impractical to use this def- inition at temperatures that are very different from the triple point of water. ITS-90 is then designed to repre- sent the thermodynamic temperature as closely as pos- sible throughout its range. Many different thermometer designs are required to cover the entire range. These in- Fig. 1 The translational motion of fundamental particles of na- clude helium vapor pressure thermometers, helium gas ture such as atoms and molecules are directly related to temper- thermometers, standard platinum resistance thermome- ature. Here, the size of helium atoms relative to their spacing is ters (known as SPRTs, PRTs or Platinum RTDs) and shown to scale under 1950 atmospheres of pressure. These room- monochromatic radiation thermometers. temperature atoms have a certain average speed (slowed down here two trillion-fold). At any given instant however, a particu- For some types of thermometer the relationship between lar helium atom may be moving much faster than average while the property observed (e.g., length of a mercury column) another may be nearly motionless. Five atoms are colored red to and temperature, is close to linear, so for most purposes facilitate following their motions. a linear scale is sufficient, without point-by-point calibra- tion. For others a calibration curve or equation is re- temperature over the widest range. The heat capacity, quired. The mercury thermometer, invented before the which relates heat input and temperature change, is dis- thermodynamic temperature was understood, originally cussed below. defined the temperature scale; its linearity made readings correlate well with true temperature, i.e. the “mercury” The relationship of kinetic energy, mass, and velocity is 1 2 [4] temperature scale was a close fit to the true scale. given by the formula Ek = ⁄2mv . Accordingly, parti- cles with one unit of mass moving at one unit of velocity have precisely the same kinetic energy, and precisely the 2 The relationship of temperature, same temperature, as those with four times the mass but half the velocity. motions, conduction, and ther- Except in the quantum regime at extremely low tempera- mal energy tures, the thermodynamic temperature of any bulk quan- tity of a substance (a statistically significant quantity of 2.1 The nature of kinetic energy, transla- particles) is directly proportional to the mean average ki- tional motion, and temperature netic energy of a specific kind of particle motion known as translational motion. These simple movements in the three x, y, and z–axis dimensions of space means the par- The thermodynamic temperature is a measure of the ticles move in the three spatial degrees of freedom. The average energy of the translational, vibrational, and temperature derived from this translational kinetic en- rotational motions of matter's particle constituents ergy is sometimes referred to as kinetic temperature and (molecules, atoms, and subatomic particles). The full va- is equal to the thermodynamic temperature over a very riety of these kinetic motions, along with potential ener- wide range of temperatures. Since there are three trans- gies of particles, and also occasionally certain other types lational degrees of freedom (e.g., motion along the x, y, of particle energy in equilibrium with these, contribute and z axes), the translational kinetic energy is related to the total internal energy (loosely, the thermal energy) of the kinetic temperature by: a substance. Thus, internal energy may be stored in a number of ways (degrees of freedom) within a substance. When the degrees of freedom are in the classical regime ¯ 3 (“unfrozen”) the temperature is very simply related to the E = kBTk 2 average energy of those degrees of freedom at equilib- rium. The three translational degrees of freedom are un- where: frozen except for the very lowest temperatures, and their kinetic energy is simply related to the thermodynamic • E¯ is the mean kinetic energy in joules (J) and is pro- 2.2 The high speeds of translational motion 3 nounced “E bar” 2.2 The high speeds of translational mo- tion • kB = 1.3806504(24)×10−23 J/K is the Boltzmann Although very specialized laboratory equipment is re- constant and is pronounced “Kay sub bee” quired to directly detect translational motions, the resul- tant collisions by atoms or molecules with small parti- cles suspended in a fluid produces Brownian motion that • Tk is the kinetic temperature in kelvins (K) and is pronounced “Tee sub kay” can be seen with an ordinary microscope.