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## PowerPedia:Temperature

Lasted edited by Andrew Munsey, updated on June 14, 2016 at 10:05 pm.

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atoms relative to their spacing is shown to scale under 136 There was an error working with the wiki: Code[3] of pressure. These room-temperature atoms have a certain, average speed (slowed down here two trillion fold).]]

Temperature is a Physics property of a system that underlies the common notions of hot and cold something that is hotter has the greater temperature. Temperature is one of the principal parameters of There was an error working with the wiki: Code[4], the microscopic motions are the translational motions of the constituent gas particles.

Temperature is measured with There was an error working with the wiki: Code[5] to a variety of There was an error working with the wiki: Code[6]. Throughout the world (except for in the United States), the There was an error working with the wiki: Code[50] scale is used for most temperature measuring purposes. The entire scientific world (the U.S. included) measures temperature using the Celsius scale, and thermodynamic temperature using the There was an error working with the wiki: Code[51] scale. Many engineering fields in the U.S., especially high-tech ones, also use the Kelvin and Celsius scales. The bulk of the U.S. however, (its lay people, industry, There was an error working with the wiki: Code[52], and government) relies upon the There was an error working with the wiki: Code[53] scale. Other engineering fields in the U.S. also rely upon the There was an error working with the wiki: Code[54] scale when working in thermodynamic-related disciplines such as Combustion.

#### Overview

Intuitively, temperature is a measure of how hot or cold an object is. Microscopically, 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 There was an error working with the wiki: Code[7] achieved a record-setting cold temperature of 700 nK (1 nK = 10?9 K) in 1994, they used There was an error working with the wiki: Code[8] cool There was an error working with the wiki: Code[55] atoms. They then turned off the entrapment lasers and directly measured atom velocities of 7 mm per second in order to calculate their temperature.

There was an error working with the wiki: Code[56]s, 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 the energy associated with vibrational and rotational modes to increase. Thus a diatomic gas, with extra degrees of freedom like rotation and vibration, will require a higher energy input to change the temperature by a certain amount, i.e. it will have a higher There was an error working with the wiki: Code[57] 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 There was an error working with the wiki: Code[9] where all kinetic motion in the particles comprising matter ceases and they are at complete rest in the “classic? (non-Quantum mechanics) sense. By definition, absolute zero is a temperature of precisely 0&nbspThere was an error working with the wiki: Code[10] (?273.15 There was an error working with the wiki: Code[11] or ?459.67 There was an error working with the wiki: Code[12]).

#### Details

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The formal properties of temperature are studied in There was an error working with the wiki: Code[13] transformation, and the variation \delta S of its Entropy during this transformation.

:dS = \frac{\delta Q}{T}

Contrary to Entropy and heat, whose microscopic definitions are valid even far away from thermodynamic equilibrium, temperature can only be defined at thermodynamic equilibrium, or 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 There was an error working with the wiki: Code[14], There was an error working with the wiki: Code[15] (see heat for additional discussion of the various mechanisms of heat transfer).

Temperature is also related to the amount of There was an error working with the wiki: Code[58] and There was an error working with the wiki: Code[59] of a system. The higher the temperature of a system, the higher its internal energy and enthalpy are.

Temperature is an There was an error working with the wiki: Code[16], and depend on the amount of material in the system.

#### The role of temperature in nature

Temperature plays an important role in almost all fields of science, including physics, chemistry, and biology.

Many physical properties of materials including the There was an error working with the wiki: Code[17] (There was an error working with the wiki: Code[18]), There was an error working with the wiki: Code[19] heated to a temperature at which significant quantities of visible There was an error working with the wiki: Code[60] are emitted.

Temperature-dependence of the There was an error working with the wiki: Code[61] in air c, density of air ? and There was an error working with the wiki: Code[62] Z vs. temperature °C

{| class="wikitable"

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|T in °C || c in m/s || ? in kg/m³|| Z in N·s/m³

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| ?10 || 325.4 || 1.341 || 436.5

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| ?5 || 328.5 || 1.316 || 432.4

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| 0 || 331.5 || 1.293 || 428.3

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| 5 || 334.5 || 1.269 || 424.5

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| 10 || 337.5 || 1.247 || 420.7

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| 15 || 340.5 || 1.225 || 417.0

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| 20 || 343.4 || 1.204 || 413.5

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| 25 || 346.3 || 1.184 || 410.0

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| 30 || 349.2 || 1.164 || 406.6

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#### Temperature measurement

Main article: There was an error working with the wiki: Code[20].

Temperature measurement using modern scientific There was an error working with the wiki: Code[21]) and a scale both developed by There was an error working with the wiki: Code[22]. Fahrenheit's scale is still in use, alongside the There was an error working with the wiki: Code[63] scale and the There was an error working with the wiki: Code[64] scale.

##### Units of temperature

The basic unit of temperature (symbol: T) in the SI is the There was an error working with the wiki: Code[23] (Symbol: K). The Kelvin and Celsius scales are, by international agreement, defined by two points: There was an error working with the wiki: Code[24] water. Absolute zero is defined as being precisely 0&nbspK and ?273.15&nbsp°C. Absolute zero is where all There was an error working with the wiki: Code[25]) sense. At absolute zero, matter contains no Thermal energy. Also, the triple point of water is defined as being precisely 273.16&nbspK and 0.01&nbsp°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 There was an error working with the wiki: Code[65] scale and 3) it establishes the difference between the two scales’ null points as being precisely 273.15 kelvins (0&nbspK&nbsp= ?273.15&nbsp°C and 273.16&nbspK&nbsp= 0.01&nbsp°C). Formulas for converting from these defining units of temperature to other scales can be found at There was an error working with the wiki: Code[66].

In the field of There was an error working with the wiki: Code[67], because of the high temperatures encountered and the There was an error working with the wiki: Code[68] nature of the phenomena involved, it is customary to express temperature in There was an error working with the wiki: Code[69]s (eV) or kiloelectronvolts (keV), where 1 eV = 11,605&nbspK. In the study of There was an error working with the wiki: Code[70] one routinely meets temperatures of the order of a few hundred There was an error working with the wiki: Code[71], equivalent to about 1012 K.

For everyday applications, it is often convenient to use the There was an error working with the wiki: Code[26] and 100 °C corresponds to the There was an error working with the wiki: Code[72] of water at sea level. In this scale a temperature difference of 1 degree is the same as a 1&nbspK 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). In the United States, the There was an error working with the wiki: Code[73] scale is widely used. On this scale the freezing point of water corresponds to 32 °F and the boiling point to 212 °F.

See There was an error working with the wiki: Code[74] for conversions between most temperature scales.

##### Negative temperatures

:See main article: There was an error working with the wiki: Code[75].

For some systems and specific definitions of temperature, it is possible to obtain a There was an error working with the wiki: Code[76]. A system with a negative temperature is not colder than There was an error working with the wiki: Code[77], but rather it is, in a sense, hotter than There was an error working with the wiki: Code[78] temperature.

There was an error working with the wiki: Code[27] = 1 picokelvin (pK)

There was an error working with the wiki: Code[28] = 1 nanokelvin (nK)

There was an error working with the wiki: Code[29] = 1 microkelvin (µK)

There was an error working with the wiki: Code[30] = 1 millikelvin (mK)

There was an error working with the wiki: Code[31] = 1 kelvin

There was an error working with the wiki: Code[32] = 10 kelvins

There was an error working with the wiki: Code[33] = 100 kelvins

There was an error working with the wiki: Code[34] = 1,000 kelvins = 1 kilokelvin (kK)

There was an error working with the wiki: Code[35] = 10,000 kelvins = 10 kK

There was an error working with the wiki: Code[36] = 100,000 kelvins = 100 kK

There was an error working with the wiki: Code[37] = 1 megakelvin (MK)

There was an error working with the wiki: Code[38] = 1 gigakelvin (GK)

There was an error working with the wiki: Code[39] = 1 terakelvin (TK)

See There was an error working with the wiki: Code[79].

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#### Theoretical foundation of temperature

##### Zeroth-law definition of temperature

While most people have a basic understanding of the concept of temperature, its formal definition is rather complicated. Before jumping to a formal definition, let us consider the concept of Thermal equilibrium. If two closed systems with fixed volumes are brought together, so that they are in thermal contact, changes may take place in the properties of both systems. These changes are due to the transfer of heat between the systems. When a state is reached in which no further changes occur, the systems are in thermal equilibrium.

Now a basis for the definition of temperature can be obtained from the so-called There was an error working with the wiki: Code[80] which states that if two systems, A and B, are in thermal equilibrium and a third system C is in thermal equilibrium with system A then systems B and C will also be in thermal equilibrium (being in thermal equilibrium is a There was an error working with the wiki: Code[81] moreover, it is an There was an error working with the wiki: Code[82]). This is an empirical fact, based on observation rather than theory. Since A, B, and C are all in thermal equilibrium, it is reasonable to say each of these systems shares a common value of some property. We call this property temperature.

Generally, it is not convenient to place any two arbitrary systems in thermal contact to see if they are in thermal equilibrium and thus have the same temperature. Also, it would only provide an There was an error working with the wiki: Code[40].

Therefore, it is useful to establish a temperature scale based on the properties of some reference system. Then, a measuring device can be calibrated based on the properties of the reference system and used to measure the temperature of other systems. One such reference system is a fixed quantity of gas. The There was an error working with the wiki: Code[83] indicates that the product of the pressure and volume (P · V) of a gas is There was an error working with the wiki: Code[84] to the temperature:

:

P \cdot V = n \cdot R \cdot T

(1)

where 'T is temperature, n is the number of There was an error working with the wiki: Code[41]s of gas and R is the There was an error working with the wiki: Code[85]. Thus, one can define a scale for temperature based on the corresponding pressure and volume of the gas: the temperature in kelvins is the pressure in pascals of one mole of gas in a container of one cubic metre, divided by 8.31... In practice, such a gas thermometer is not very convenient, but other measuring instruments can be calibrated to this scale.

Equation 1 indicates that for a fixed volume of gas, the pressure increases with increasing temperature. Pressure is just a measure of the force applied by the gas on the walls of the container and is related to the energy of the system. Thus, we can see that an increase in temperature corresponds to an increase in the thermal energy of the system. When two systems of differing temperature are placed in thermal contact, the temperature of the hotter system decreases, indicating that heat is leaving that system, while the cooler system is gaining heat and increasing in temperature. Thus heat always moves from a region of high temperature to a region of lower temperature and it is the temperature difference that drives the heat transfer between the two systems.

##### Temperature in gases

For a There was an error working with the wiki: Code[42] are available, so molecular rotation or vibration must be included.

Particles of greater mass (say a There was an error working with the wiki: Code[43].

##### Temperature of the vacuum

The temperature of an object is proportional to the average kinetic energy of the molecules in it. In a pure There was an error working with the wiki: Code[86], there are no molecules. There is nothing to measure the kinetic energy of, and temperature is undefined. If a thermometer were placed in a vacuum, the reading would be a measurement of the internal temperature of the thermometer, not of the vacuum which surrounds it.

All objects emit There was an error working with the wiki: Code[87] radiation. Over time, a thermometer in a pure vacuum will radiate away thermal energy, decreasing in temperature indefinitely until it reaches the Zero-point energy limit.

In practice, there is no such thing as a pure vacuum since there will always be photons associated with the black body radiation of the walls of the vacuum. A thermometer orbiting the Earth can easily absorb energy from sunlight faster than it can radiate it away. This can lead to a dramatic temperature increase.

A thermometer isolated from solar radiation (in the shade of a larger body, for example) is still exposed to There was an error working with the wiki: Code[88]. In this case, the temperature will change until the rate of energy loss and gain are in equilibrium. At this point, the thermometer will have a temperature of 2.725 K, which is often referred to as the temperature of space.

##### Second-law definition of temperature

In the previous section temperature was defined in terms of the Zeroth Law of thermodynamics. It is also possible to define temperature in terms of the Second law of thermodynamics, which deals with Entropy. Entropy is a measure of the disorder in a system. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability. Consider a series of coin tosses. A perfectly ordered system would be one in which every coin toss would come up either heads or tails. For any number of coin tosses, there is only one combination of outcomes corresponding to this situation. On the other hand, there are multiple combinations that can result in disordered or mixed systems, where some fraction are heads and the rest tails. As the number of coin tosses increases, the number of combinations corresponding to imperfectly ordered systems increases. For a very large number of coin tosses, the number of combinations corresponding to ~50% heads and ~50% tails dominates and obtaining an outcome significantly different from 50/50 becomes extremely unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy.

We previously stated that temperature controls the flow of heat between two systems and we have just shown that the universe, and we would expect any natural system, tends to progress so as to maximize entropy. Thus, we would expect there to be some relationship between temperature and entropy. In order to find this relationship let's first consider the relationship between heat, work and temperature. A Heat engine is a device for converting heat into mechanical work and analysis of the There was an error working with the wiki: Code[89] provides the necessary relationships we seek. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, qH and the heat ejected at the low temperature, qC. The efficiency is the work divided by the heat put into the system or:

:

\textrm{efficiency} = \frac {w_{cy}}{q_H} = \frac{q_H-q_C}{q_H} = 1 - \frac{q_C}{q_H}

(2)

where wcy is the work done per cycle. We see that the efficiency depends only on qC/qH. Because qC and qH correspond to heat transfer at the temperatures TC and TH, respectively, qC/qH should be some function of these temperatures:

:

\frac{q_C}{q_H} = f(T_H,T_C)

(3)

There was an error working with the wiki: Code[44] states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between T1 and T3 must have the same efficiency as one consisting of two cycles, one between T1 and T2, and the second between T2 and T3. This can only be the case if:

:

q_{13} = \frac{q_1 q_2} {q_2 q_3}

which implies:

:

q_{13} = f(T_1,T_3) = f(T_1,T_2)f(T_2,T_3)

Since the first function is independent of T2, this temperature must cancel on the right side, meaning f(T1,T3) is of the form g(T1)/g(T3) (i.e. f(T1,T3) = f(T1,T2)f(T2,T3) = g(T1)/g(T2)· g(T2)/g(T3) = g(T1)/g(T3)), where g is a function of a single temperature. We can now choose a temperature scale with the property that:

:

\frac{q_C}{q_H} = \frac{T_C}{T_H}

(4)

Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in terms of temperature:

:

{efficiency} = 1 - \frac{q_C}{q_H} = 1 - \frac{T_C}{T_H}

(5)

Notice that for TC = 0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K. Since an efficiency greater than 100% violates the first law of thermodynamics, this implies that 0 K is the minimum possible temperature. In fact the lowest temperature ever obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 5 from the middle portion and rearranging gives:

:

\frac {q_H}{T_H} - \frac{q_C}{T_C} = 0

where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by:

:

dS = \frac {dq_{rev}}{T}

(6)

where the subscript indicates a reversible process. The change of this state function around any cycle is zero, as is necessary for any state function. This function corresponds to the entropy of the system, which we described previously. We can rearranging Equation 6 to get a new definition for temperature in terms of entropy and heat:

:

T = \frac{dq_{rev}}{dS}

(7)

For a system, where entropy S may be a function S(E) of its energy E, the temperature T is given by:

:

\frac{1}{T} = \frac{dS}{dE}

(8)

The reciprocal of the temperature is the rate of increase of entropy with energy.

#### Related

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Entropy

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Heat

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There was an error working with the wiki: Code[1], Wikipedia: The Free Encyclopedia. Wikimedia Foundation.

An elementary introduction to temperature aimed at a middle school audience

Why do we have so many temperature scales?

A Brief History of Temperature Measurement

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