Temperature

The title of this article is ambiguous. For other meanings, see Temperature (disambiguation).

Temperature is a state variable of central importance in the macroscopic description of physical and chemical states and processes in science, technology and the environment. Temperature is an objective measure of how warm or cold an object is. It is measured with a thermometer. Its SI unit is the kelvin with the unit symbol K. In Germany, Austria and Switzerland, the unit degree Celsius (°C) is also permitted. The measured temperature can sometimes differ considerably from the perceived temperature.

If two bodies with different temperatures are brought into thermal contact, heat transfer takes place. As a result, the temperature difference decreases until the two temperatures have equalized. The heat always flows from the hotter to the colder body. When the temperatures are equal, thermal equilibrium prevails, in which heat exchange no longer takes place.

The microscopic interpretation of temperature arises in statistical physics, which assumes that any material substance is composed of many particles (usually atoms or molecules) that are in constant disordered motion and have an energy composed of kinetic, potential, and possibly also internal excitation energy. An increase in temperature causes an increase in the average energy of the particles. In the state of thermal equilibrium, the energy values of the individual particles are distributed statistically according to a frequency distribution whose shape is determined by the temperature (see - depending on the type of particle - Boltzmann statistics, Fermi-Dirac statistics, Bose-Einstein statistics). This picture is also applicable if we are not dealing with a system of material particles but with photons (see thermal radiation).

In the ideal gas, the total internal energy is given by the kinetic energy of all particles alone, where the average value per particle is proportional to the absolute temperature. The temperature unit kelvin is defined by specifying the proportionality factor and is thus directly linked to the energy unit joule. Before the revision of the International System of Units (SI) of 2019, the kelvin was still defined separately

The temperature is an intensive state variable. This means that it retains its value when the body under consideration is divided. In contrast, the internal energy as an extensive quantity has the properties of a quantity that can be divided.

Physical basics

Overview

All solids, liquids and gases consist of very small particles, the atoms and molecules. These are in constant disordered motion and forces act between them. By "disordered" in this context we mean, for example, that the velocity vectors of the particles of a body, relative to the velocity of its centre of mass, are distributed uniformly over all directions and also differ in their magnitudes. The mean value of the velocity magnitudes depends on the type of substance, the state of aggregation and, above all, the temperature. For solids, liquids and gases, the higher the temperature of a body, the greater the mean velocity of its particles. In general, this also applies to all other forms in which the particles can possess energy in a disordered manner, e.g. rotational movements, oscillations (this also includes lattice oscillations around their rest position in the crystal lattice of solid bodies). This illustrative connection already suggests that there is a lowest possible temperature, absolutezero, at which the smallest particles no longer move. Due to the uncertainty principle, however, complete motionlessness is not possible (zero-point energy).

A particular temperature that applies uniformly throughout the system exists only when the system is in a state of thermal equilibrium. Systems that are not in a state of equilibrium often consist of subsystems, each with its own temperatures, e.g. tap water and ice cubes in a glass, or the electrons and ions in a non-equilibrium plasma, or the degrees of freedom each for translation, rotation or vibration in an expanding molecular beam. If there is thermal contact between the subsystems, then the overall system will automatically strive towards a state of thermal equilibrium through heat exchange between the parts.

In theoretical terms, temperature is introduced as a fundamental concept by the fact that any two systems that are in thermal equilibrium with a third system are then also in thermal equilibrium with each other. This fact is also called the zeroth law of thermodynamics. Equality of temperatures means thermal equilibrium, i.e., there is no heat exchange even in the presence of thermal contact. The fact that a single state variable such as temperature is sufficient for deciding whether equilibrium exists can be derived from the zeroth law.

The sum of all energies of the disordered motions of the particles of a system and their internal potential and kinetic energies represents a certain energy content, which is called the internal energy of the system. The internal energy can be partially converted into ordered motion by means of a heat engine and then do work when a second system with a lower temperature is available. This is because only part of the internal energy can be used to convert it into work, while the rest must be given off as waste heat to the second system. According to the Second Law of Thermodynamics, there is a lower bound for this waste heat that is independent of the substances and types of processes used and is determined only by the ratio of the two temperatures. This was noticed by Lord Kelvin in 1848 and has been used to define the thermodynamic temperature since 1924. The same result is obtained if the state variable entropy is derived from the internal energy.

Almost all physical and chemical properties of substances are (at least weakly) dependent on temperature. Examples are the thermal expansion of substances, the electrical resistance, the solubility of substances in solvents, the speed of sound or the pressure and density of gases. In contrast, sudden changes in substance properties occur even with the smallest changes in temperature, when the state of aggregation changes or another phase transition occurs.

Temperature also influences the reaction rate of chemical processes in that this typically doubles for every 10 °C increase in temperature (van 't Hoff's rule). This also applies to the metabolic processes of living organisms.

Ideal gas

→ Main article: Ideal gas

The ideal gas is a model gas that is well suited for developing the basics of thermodynamics and properties of temperature. According to the model, the particles of the gas are point-like, but can still collide elastically against each other and against the wall of the vessel. Otherwise, there is no interaction between the particles. The ideal gas reproduces the behaviour of monatomic noble gases very well, but also applies to normal air to a good approximation, although polyatomic molecules can rotate or vibrate and therefore cannot always be simplified as point-like objects without internal degrees of freedom.

For the ideal gas, the temperature is proportional to the mean kinetic energy $\overline {E_{{\mathrm {kin}}}}$ of the particles

$\overline {E_{{\mathrm {kin}}}}={\tfrac {3}{2}}k_{{\mathrm {B}}}T$

Where is $k_{\mathrm {B} }$ the Boltzmann constant. So in this case, the macroscopic quantity temperature is linked to microscopic particle properties in a very simple way. Multiplied by the particle number , we get the total energy of the gas. Furthermore, the thermal equation of state applies to the ideal gas, which links the macroscopic quantities temperature, volume and pressure ,

$pV=Nk_{{\mathrm {B}}}T$ .

This equation was made the defining equation of temperature in the International System of Units in 2019 because, with the simultaneous numerical specification of the value of the Boltzmann constant, it contains only measurable quantities apart from T. The measurement specification takes into account that this equation is only approximately satisfied for a real gas, but holds exactly in the limiting case . $p\rightarrow 0$

Since the quantities ${\overline {E_{\mathrm {kin} }}},\ p,\ V$ cannot become negative, we can see from these equations that there must be an absolute zero temperature $T=0\,\mathrm {K} \ (=\;-273,15\,^{\circ }\mathrm {C} )$ must exist at which the gas particles would stop moving, and the pressure or volume of the gas would be zero. Absolute zero temperature really does exist, although this derivation is not valid because there is no substance that would remain gaseous to $T=0\,\mathrm {K}$ would remain gaseous. However, helium is still an almost ideal gas under atmospheric pressure at temperatures of a few K.

Temperature, heat and thermal energy

Sometimes the quantities temperature, heat and thermal energy are confused with each other. However, they are different quantities. Temperature and thermal energy describe the state of a system, temperature being an intensive quantity, but thermal energy (which can have different meanings) is often an extensive quantity. In ideal gases, temperature is a direct measure of the mean value of the kinetic energy of the particles. The thermal energy in its macroscopic meaning is equal to the internal energy, which is the sum of all kinetic, potential and excitation energies of the particles.

Heat, on the other hand, as a physical concept, does not characterize a single system state, but rather a process that leads from one system state to another. Heat is the change in internal energy minus any work done (see First Law of Thermodynamics). Conversely, if one assumes a certain amount of heat released or absorbed, then the process can lead to different final states with different temperatures depending on the process control (e.g. isobaric, isochoric or isothermal).

Temperature compensation

If two systems with different temperatures $T_{1},\;T_{2}$ are in a connection that allows heat transfer (thermal contact or diabatic connection), then heat flows from the hotter to the colder system and both temperatures approach the same equilibrium temperature $T_{G}$ . If no phase transitions or chemical reactions occur during this process, $T_{G}$ between the initial temperatures. $T_{G}$ is then a weighted average of $T_{1}$ and $T_{2}$ , where the heat capacities $C_{1},\;C_{2}$ of the two systems (if sufficiently constant) act as weight factors. The same end result also occurs when two liquids or two gases are mixed together (mixing temperature), e.g. hot and cold water. If phase transitions occur, the equilibrium temperature can also be equal to one of the two initial temperatures, e.g. 0 °C when cooling a warm drink with an unnecessary amount of ice cubes from 0 °C. In chemical reactions, the final temperature may also be outside the range , e.g. $[T_{1},\,T_{2}]$ below in the case of cold mixtures, above in the case of combustion.

Temperature in relativity

→ Main article: Relativistic thermodynamics

A thermodynamic equilibrium is first valid in the common rest system of both bodies. In the sense of special relativity, a system in thermodynamic equilibrium is therefore characterized by a rest system in addition to the temperature. Thermodynamic equations, however, are not invariant under Lorentz transformations. A concrete question would be, for example, what temperature is measured by a moving observer. The redshift of thermal radiation, for example, shifts the frequencies in Planck's radiation law in the ratio $\approx v/c$ and thus makes a radiating body appear colder as one moves away from it with velocity . In principle, the same problem already occurs when hot water flows through an initially cold pipe.

The temperature is represented as a time-like four-vector. Thus, in the system at rest, the three spatial coordinates are $0$ and the time coordinate is the usual temperature. To a moving system, one must convert using the Lorentz transformation. However, it is more convenient in the context of the equations of state, and therefore more usual, to use the inverse temperature, more precisely β $\beta ={\tfrac {1}{k_{{\mathrm {B}}}T}}$ , to be represented as a time-like four-vector.

To justify this, consider the 1st law, for reversible processes in the form

$\mathrm {d} S={\frac {1}{T}}\mathrm {d} U+{\frac {1}{T}}P\mathrm {d} V$ ,

and note that the energy of a moving system is greater by the kinetic energy than its internal energy , for $v/c\ll 1$ thus approximately

$E=U+{\frac {Mv^{2}}{2}}$

Where is the three-dimensional velocity. Therefore

$\mathrm {d} U=\mathrm {d} E-v\mathrm {d} v$ and

$\mathrm {d} S={\frac {1}{T}}\mathrm {d} E-{\frac {1}{T}}v\mathrm {d} v+{\frac {1}{T}}P\mathrm {d} V$ ,

in 4-dimensional notation therefore equals

$\mathrm {d} S=-\theta _{\mu }\mathrm {d} \mathbf {p} ^{\mu }+{\frac {1}{T}}P\mathrm {d} V$ ,

If $\mathbf {p} _{\mu }=(E/c,{\vec {p}})$ (with spatial momentum vector ${\vec {p}}$ ) the quadruple momentum and θ $\mathbf {\theta } _{\mu }=(-c/T,{\vec {v}}/T)$ is the inverse quad temperature.

In general relativity, spacetime is curved, so in general the thermodynamic limit is not well-defined. However, if the metric of spacetime is time-independent, i.e. static, a global temperature term can be defined. In the general case of a time-dependent metric, such as is the basis of the description of the expanding universe, state variables such as temperature can only be defined locally. A common criterion for a system to be at least locally thermal is that the phase space density satisfies the Boltzmann equation without scattering.

Temperature in quantum physics

In the field of quantum physics, temperature can be described by a disordered particle motion in which all possible forms of energy occur only if it is "sufficiently high". "Sufficiently high" here means that the energy $k_\mathrm{B} T$ is large compared to the typical distances between the energy levels of the individual particles in the given system. For example, the temperature must be well above 1000 K for molecular vibrations to be co-excited in diatomic gases such as N2, O2. For H2 molecules, excitation of rotation also requires temperatures above a few 100 K. Degrees of freedom which do not participate in the thermal motion at lower temperatures are called frozen. This is clearly expressed, for example, in the temperature dependence of the specific heat.

The theoretical treatment of thermodynamics in quantum physics is carried out exclusively with the methods of statistical physics (see quantum statistics, many-particle theory). In it, the temperature occurs exactly as in classical statistical physics in the exponent of the Boltzmann distribution and thus determines the form of the frequency distribution with which the particles assume the various energy states.

Temperature sensing and heat transfer

If two bodies of different temperatures are in thermal contact, then according to the zeroth law of thermodynamics energy is transferred from the warmer to the colder body until both have assumed the same temperature and are thus in thermal equilibrium. There may initially be temperature jumps between the two sides of the interface. There are three possibilities of heat transfer:

Heat conduction
Convection
Thermal radiation

Humans can only feel temperatures in the range between about 5 °C and 40 °C with the skin. Strictly speaking, it is not the temperature of an object touched that is perceived, but the temperature at the location of the thermoreceptors located in the skin, which varies depending on the strength of the heat flow through the skin surface (felt temperature). This has some consequences for the perception of temperature:

Temperatures above the surface temperature of the skin feel warm, those below feel cold.
Materials with high thermal conductivity, such as metals, lead to higher heat flows and therefore feel warmer or colder than materials with lower thermal conductivity, such as wood or polystyrene.
The perceived air temperature is lower when there is wind than when there is no wind (vice versa in extremely hot weather). The effect is described by the wind chill at temperatures < 10 °C and by the heat index at higher temperatures.
A slightly heated, tiled floor can be perceived as pleasantly warm when touched by bare feet, but cool when touched by hands. This is the case when the skin temperature on the hands is higher than on the feet and the temperature of the floor is in between.
Skin sensation cannot distinguish air temperature from superimposed thermal radiation. The same generally applies to thermometers; therefore, air temperatures, for example, must always be measured in the shade.
Lukewarm water is perceived differently by the two hands if they had previously been held in hot or cold water for a while.

Strictly speaking, this does not only apply to human sensation. In many technical contexts, too, it is not the temperature that is decisive, but the heat flow. For example, the earth's atmosphere has temperatures of more than 1000 °C in an area above 1000 km; nevertheless, no satellites burn up there, because the energy transfer is minimal due to the low particle density.

Questions and Answers

Q: What is temperature?

A: Temperature is how hot or cold something is.

Q: How can we measure temperature accurately?

A: To measure temperature more accurately, a thermometer can be used.

Q: What scale do most of the world use to record temperatures?

A: Most of the world uses degrees Celsius, sometimes called "centigrade" to record temperatures.

Q: In what countries are degrees Fahrenheit more often used?

A: Degrees Fahrenheit are more often used in the USA and some other countries.

Q: What scale do scientists mostly use to measure temperature?

A: Scientists mostly use kelvins to measure temperature because it never goes below zero.

Q: How do molecules move inside a material?

A: Scientifically, temperature is a physical quantity which describes how quickly molecules are moving inside a material. In solids and liquids the molecules are vibrating around a fixed point in the substance, but in gases they are in free flight and bouncing off each other as they travel.

Q: Are there any laws of physics related to gas temperatures, pressure and volume?

A: Yes, there is a law of physics that states that gas temperature, pressure and volume are closely related.