Temperature

Temperature is a physical quantity in thermodynamics plays a particularly important role. Your SI unit is the kelvin (K). In Germany, Austria and Switzerland, the unit is Celsius (° C ) is also permitted.

The temperature of a body featuring the possibility of making inner energy in form of heat. It is a material property ( intensive quantity obtained by dividing the same) during heat as an energy properties of a quantity has ( extensive quantity, which can be split). If two bodies of different temperature in contact, as long as heat flows from the body to the higher temperature to the body with the lower temperature until the two bodies at the same temperature; the final temperature does not lie outside the two initial temperatures. Many physical properties are directly dependent on the temperature and can therefore be used to determine the temperature. For reference, the law of Gay- Lussac for ideal gases is by the ratio of the volumes.

The temperature is in many areas of nature and technology is important. Almost all the physical and chemical properties of substances are at least weakly temperature dependent, for example, the electrical resistance or the density of what you make use of the fact for temperature measurements. Sometimes a small temperature difference makes a difference, changes in physical appearance and other phase transitions, see critical exponent. Temperature affects the metabolic processes of living organisms prevail. As part of the research to global warming, the influence of an increased concentration of greenhouse gases in the Earth's atmospheric temperature is investigated in detail.

The temperature sensitivity of the human being based not only on the temperature but also on the heat flow and the physical activity. The wind chill temperature is different in some cases considerably from the physical temperature.

• 4.1 Measurement of thermal contact
• 4.2 Measurement on the basis of thermal radiation

• 5.1 Empirical scales
• 5.2 scales with SI unit
• 5.3 scales without SI unit

Physical Basics

All solids, liquids and gases consist of very small particles called atoms and molecules. These are in constant irregular motion and forces acting between them. The velocities of the particles of the body are different. The average of the velocity values ​​of all particles of a stationary body depends on the type of substance, the state of aggregation, and especially the temperature. For solid, liquid and gaseous bodies, the higher is the temperature of a body, the greater the amount of his average velocity particles. This ideological context suggests that there is a lowest possible temperature, absolute zero point at which no longer move the smallest particles. Due to the uncertainty principle, however, a complete immobility is not possible ( zero point energy).

A uniform temperature is only for equilibrium systems defined ( thermodynamic equilibrium ). In systems that are not in the equilibrium state, a plurality of different temperatures are required for the description, such as the electron temperature and ion temperature in a non-equilibrium plasma or temperatures of translation, rotation, and vibration of a molecular beam expanding.

Ideal gas

The ideal gas is a model concept which is well suited to illustrate basic principles of thermodynamics and properties of temperature. According to the model, the particles of the gas are point-like, but can still elastically against one another and abut against the vessel wall. Otherwise there is no interaction between the particles. The ideal gas is a good approximation for gases with atoms as the smallest particles. Molecules can rotate or vibrate and therefore can not be simplified as point-like objects.

For an ideal gas, the temperature is proportional to the average kinetic energy of the particles

The Boltzmann constant. In this case, the macroscopic variable, temperature is related in a very simple manner with microscopic particle. Also applies to the ideal gas, the Ideal Gas Law, which is the macroscopic temperature, volume and pressure related

Wherein the particles of the system.

From these two equations we can conclude that an absolute zero temperature exists at which the gas particles do not move at all, so the average kinetic energy have zero. If the pressure is kept constant while reducing the temperature, the volume of gas is getting smaller and at zero temperature would the volume to zero, the gas would then be contracted to a point. On the other hand can be exploited the general gas equation, to determine the temperature for the measurement of volume and pressure. This is realized by the gas thermometer. These thermometers in contrast to other thermometers ranging from a two-point calibration, since the relationship of the variables is known and therefore they are used to calibrate other thermometers.

Temperature and heat

The temperature is sometimes confused with the warmth of a body. The heat or thermal energy, however, is a different physical size. Describes the state of the temperature of the system while heat characterizes the change of the heat energy, the change in the system state. The variation of the heat energy (e.g., isobaric or isochoric ) leads to various types of state changes for different changes in temperature. The respective ratio of heat change and change in temperature is called heat capacity.

Heat always moves from a higher temperature system to the lower system temperature when heat transfer between the systems is possible. This also results in a temperature compensation, wherein the heat transfer ends when the systems are in thermodynamic equilibrium, that is at the same temperature. The final temperature is dependent on the heat capacity of the systems involved. At a higher heat capacity of the same change of the heat results in a smaller change in temperature. This means that the final temperature during the mixing is of equal amounts of two substances with different heat capacities and initial temperature closer to the temperature of the substance with the higher heat capacity. An illustrative example is the comparison of water and air. Water has a much higher heat capacity than air, therefore, a bathtub full of hot water, a room much more heat than the same amount of air the same temperature.

Temperature in the theory of relativity

A thermodynamic equilibrium is distinguished from a rest frame. Thermodynamic equilibrium systems are therefore not invariant under Lorentz transformations, as can extract energy from, for example, of a uniformly flowing gas by means of a wind turbine. A system which is, in its rest system in thermodynamic equilibrium, this has the characteristic that by means of a wind turbine energy to be extracted is minimized. In terms of the special theory of relativity, a system in thermodynamic equilibrium is not only by the temperature also characterized by a relaxation system. To illustrate this, the temperature can be represented as a timelike four-vector. In a system so the three location coordinates and time coordinate to the usual temperature. However, it is in the context of state equations cheaper and therefore more common, the inverse temperature, represent more accurate than time-like four-vector.

In the general theory of relativity space-time is curved so that in general the thermodynamic limit is not well defined. If the metric of space-time independent of time, ie static, but a global concept of temperature can be defined. In the general case of a time-dependent metric, as it is for example based on the description of the expanding universe, the state variables can be defined as the temperature locally. A common criterion to ensure that a system is at least locally heat is that the phase space density satisfies the Boltzmann equation without scattering.

Temperature in quantum physics

The thermodynamic treatment of quantum systems is usually carried out using the methods of statistical mechanics. Especially in the context of quantum field theoretical systems while the density matrix plays an important role. However, since the density matrix of the canonical and grand canonical ensembles in the thermodynamic limit is infinite and thus loses its meaning, some effort is necessary for the correct treatment of these systems. In the axiomatic quantum field theory has been recognized that KMS states, which also include Gibbs states for finite volume systems, also for the thermodynamic limit can be defined and are suitable to calculate thermal expectation values ​​. In the standard theory, the problem is usually solved by a renormalization procedure.

Temperature sensitivity and heat transfer

When two bodies of different temperature in thermal contact, then as long as transmitted by the zeroth law of thermodynamics energy from a warmer to a colder body until both are in thermal equilibrium and the same temperature adopted. There are three possibilities of heat transfer:

Man can feel temperatures only in the area around 30 ° C. Strictly speaking, no one takes temperatures true, but the size of the heat flow through the skin surface, which is why it is also called a wind chill temperature. This has some consequences for the perception of temperature:

• Temperatures above the surface temperature of the skin feels warm, those below we feel as cold
• Materials with high thermal conductivity, such as metals, lead to higher heat fluxes and therefore feel warmer or colder than materials with lower thermal conductivity, such as wood or polystyrene
• The sensed temperature is lower than in wind with no wind. The effect is <0 ° C at temperatures described by the wind chill, and at higher temperatures due to the heat index.
• A slightly heated, tiled floor can be perceived as cool with bare feet as warm, with hands touching, however. This is the case when the temperature of the tiles between the temperature of the hands and feet is located.
• Skin sensates can not distinguish air temperature of superimposed thermal radiation. The same is true in general for thermometer; Therefore, for example, air temperatures must be always measured in the shade
• Same temperature is perceived by both hands as different if these previously exposed to different temperatures were

In fact, this applies not only to the human perception, and in many technical applications is not the temperature of meaning, but the heat flow. Thus, the Earth's atmosphere above 1000 km temperatures greater than 1000 ° C, but why burn up any satellites. Due to the small particle density, the energy transfer is minimal.

Temperature, thermal energy and the Zeroth Law of Thermodynamics

The formal characteristics of the temperature can be treated in thermodynamics. It refers to the temperature here as a native, intensive state variable. They can also be defined via the entropy S, as follows from the properties of this quantity that S is constant for all reversible changes of state without heat transfer Q:

With T as a state function. T is chosen so that a differential of a state function. After the Poincaré lemma is this necessary and sufficient

The ideal gas, the gas temperature satisfies this condition.

The statistical definition of temperature is Boltzmann:

Where:

• S is the entropy
• U is the internal energy
• The smoothed, averaged curve over that specifies how many ways the energy U can be distributed in the system itself; broken down into the smallest possible energy packets (see quantum ).
• Is Boltzmann's constant

In a very large collection of particles, and the presence of an ideal gas can be applied to Maxwell -Boltzmann distribution, and the temperature set as follows in sequence:

Where:

• M - mass of the particles
• - Average speed square

Temperature is thus a measure of the average non-directional, that is random, kinetic energy content (kinetic energy) of a collection of particles. The particles are in this case the air molecules and the molecules or atoms of a gas, a liquid or a solid. In statistical mechanics, the temperature is related to the energy per degree of freedom in connection. In the ideal gas of monatomic molecules are the three translational degrees of freedom per molecule and polyatomic gases can more rotational degrees of freedom are added.

For gases can this relationship between temperature and particle velocity according to the above relationship even specify quantitatively. A doubling of the temperature on the Kelvin scale leads to an increase of the ideal gases square average particle velocity by a factor of 2 ½ = 1.414. Two different gases have the same temperature as the product of the molar mass of individual gas and the square of the root mean square particle velocity is the same.

In thermal equilibrium, each degree of freedom of matter (physics) takes one of the temperature corresponding amount of energy ( movement, etc., potential energy, vibrations, electronic excitations). Exactly how much has to be calculated from the canonical distribution and is determined by the ratio of energy to temperature times Boltzmann constant kB. In the continuous (classical) kinetic energy this is exactly kBT / 2 The Boltzmann constant, resulting in a relationship between energy and temperature, is 11606.7 Kelvin per electron volt. At room temperature (300 Kelvin ) gives this 0.0258472 eV. The average kinetic energy of the particles in an ideal gas is ½ kBT for each of the three translational degrees of freedom, regardless of the molecular weight or molar mass. Because ½ mv2 = ½ kBT a particle is slower, the greater its mass, and in proportion to the square root of its mass. For ideal gases, mass increase and decrease speed same from each other, which leads to the law of Avogadro.

However, as the temperature of the thermal energy itself is only an average value within a many-body system and its relationship with the particle velocity can be derived also from the Maxwell - Boltzmann distribution:

The thermal equilibrium has an important property that leads to the formulation of the thermodynamics Zeroth law of thermodynamics.

If a system A to be located with a System B and B with a system C is in thermal equilibrium, then also A is in thermal equilibrium with C. The thermal equilibrium is therefore transitively, which makes it possible to introduce empirical temperature θ. This is defined so that two systems have exactly the same empirical temperature when they are in thermal equilibrium.

Measurement

Measurement by thermal contact

The temperature is measured here by means of thermometers or temperature sensors. The manufacturing a thermal contact requires sufficient heat conduction, convection or radiation equilibrium between measuring object ( solid, liquid, gas) and sensor. The measuring accuracy can be affected by unbalanced thermal radiation balance, air movement or by heat conduction along the sensor, for example. The measurement accuracy is theoretically limited by the random Brownian motion.

The temperature detection by thermal contact can be divided into four methods:

• Gas or liquid thermometer (eg traditional mercury or alcohol thermometer)
• Bimetallic thermometer

• Use of the temperature-dependent electrical resistance of conductors and semiconductors: (PTC ) and thermistor (NTC ), see also resistance thermometer
• Thermocouples supply voltages, depending on differences in temperature.
• Specific semiconductor circuits use the band gap to generate a proportional to absolute temperature voltage, see the bandgap reference.

• The temperature-dependent difference frequency different cut quartz resonators is to measure long-term stability and high resolution.
• The temperature dependent decay of the fluorescence of a luminescent material can be measured through an optical fiber.
• The fiber optic temperature measurement using the Raman effect in the optical fiber for locally resolved measurement of the absolute temperature on the entire length of the fiber.

• Seger cone ( shaped bodies that change their strength and thus its contour at a given temperature )
• Temperature measuring colors ( also thermochromic colors; color change at a certain temperature )
• Watch the softening, melting, annealing, or tarnish

Measurement based on heat radiation

The temperature of a contact surface can be determined by measuring the thermal radiation, provided that the emissivity is sufficiently accurately known. The measurement is carried out, for example, with a pyrometer or a thermographic camera.

Depending on the temperature to come besides, different wavelength ranges in question (see Stefan- Boltzmann law or Wien's displacement law ). At low temperatures bolometer, cooled microbolometer or semiconductor detectors are possible, at high temperatures uncooled photodiodes or the visual comparison of the intensity and color of the glow may be used ( tungsten filament pyrometer ).

On the right is a thermography; in this case a false-color representation of the radiation emission in the Middle infrared (about 5 ... 10 micron wavelength ) is produced which can be coupled by calibration in the form of a color scale on the temperature scale. The left are the reflection of radiation from the hot cup can be seen. Measurement error caused by this as well as in pyrometers

• Different or unknown emissivities of the measuring objects
• Reflections of external radiation on smooth surfaces
• Radiation of the air between the object and sensor

For minimization of all disturbing influences measurement accuracy and contrasts are to reduce possible differences in temperature of 0.01 K.

The non-contact temperature measurement based on heat radiation is also used for remote sensing and for determining the surface temperature of stars, assuming that the intrinsic radiation of the atmosphere is low enough. IR telescopes are therefore only useful on high mountains.

See also measuring instruments, metrology, measurement and temperature measurement category

Temperature scales and units

Empirical scales

An empirical temperature scale is an arbitrary determination of the magnitude of the temperature and makes it possible to specify the temperature with respect to a comparison value.

There are two methods to define a scale:

According to the first method, two fixed points are determined. These fixed points are conveniently found in nature and reproducible experiments values ​​. The distance between the fixed points is then divided equally by means of a temperature-dependent material or process properties: For example, the change in volume of mercury into 100 equal parts was divided in the Celsius scale, for the Fahrenheit scale, of the slightly different running volume change alcohol related.

In the second method, a fixed point, which is as previously defined by a material property (eg melting point of ice ) is sufficient. Now the distance ( scale mark to tick mark ) or the size of the unit must be set. A method that, despite some advantages could not be established, based on the change in volume of gases at constant pressure. As a unit of the temperature difference has been proposed by Rudolf plank corresponding to a change in volume by a factor of (1 1/ 273, 15). Such a logarithmic temperature scale extends to plus infinity to minus infinity. There is no absolute zero point is required, the determination of which is not exactly possible.

The most common temperature scales with their different characteristics are further tabulated below. Today's temperature scale is the " International Temperature Scale of 1990 " (ITS -90).

Scales with SI unit

The unit of thermodynamic temperature (symbol ) is the Kelvin with the unit symbol K. The Kelvin is an SI base unit. It is the 273.16te of the thermodynamic temperature of the triple point of water, in which co-exist its solid, liquid and gaseous phase. The zero point of the Kelvin scale is at absolute zero. The value 273.16 is chosen so because the triple point with a good approximation is 0.01 ° C and the absolute zero at -273.15 ° C.

The Celsius temperature (symbol or ) no longer exists according to its modern definition, the empirical temperature of the historic Celsius scale on, but is the thermodynamic temperature of the Kelvin scale with smaller numerical values ​​to 273.15:

The unit 'degree Celsius (° C) is a derived SI unit. The degree Celsius is identical to Kelvin. Temperature differences are given in K; the difference between two Celsius temperatures can also be specified in ° C. The numerical value is the same in both cases.

Scales without SI unit

In the U.S., the Fahrenheit scale with the unit degrees Fahrenheit ( unit symbol: ° F ) is still very common. The absolute temperature in Fahrenheit base with degrees Rankine ( unit symbol: ° Ra ) refers. The Rankine scale has zero as the Kelvin scale at absolute zero temperature, in contrast to this, however, the scale intervals of the Fahrenheit scale.

Temperature examples

In the following table some examples are mentioned temperatures. Specific material values ​​can be taken from articles such as boiling point and melting point. Other examples are temperature (temperature) listed in Article magnitude.