** Note: According to REACH Regulation 52005DC0020, we are required to sell mercury thermometers only to commercial customers. ***
The base unit of temperature is the Kelvin, abbreviated K. The Kelvin is 273.16ths of the thermodynamic temperature of the triple point of pure water. The triple point (= 273.16 K) describes the state of water in which it exists simultaneously in the solid, liquid, and gaseous phases. The triple point is 0.01 K higher than the melting point of water at an absolute pressure of 1013.25 mbar and is thus almost identical to it. In European countries, the Celsius scale is permitted as a legal temperature scale alongside the Kelvin scale. The unit is the degree Celsius, abbreviated °C. The Celsius scale is shifted by 273.15 K compared to the Kelvin scale, so that 0 °C corresponds to the melting point and 100 °C to the boiling point of pure water.
|
Conversions Kelvin and degrees Celsius |
|
|
T [K] = T - 273.15 [°C] |
t [°C] = t + 273.15 [°C] |
Basics:
Temperature plays an important role among the measured variables in meteorology. On the one hand, temperature has a significant influence on the course of meteorological processes, so that knowledge of the temperature of the air, but also of the ground and water, is an essential prerequisite for the analysis of meteorological events. On the other hand, a whole range of other measured variables (e.g., humidity, wind, radiation, pressure, etc.) can be obtained indirectly through temperature measurements. It is therefore not surprising that there are a considerable number of temperature measurement methods that allow extensive adaptation to the purpose of the respective measurement.
Although humans have a certain ability to distinguish between temperatures, this is not sufficient for a reasonably reliable temperature measurement. One must rely on indirect measurement methods, in which another quantity depends on the temperature in a sufficiently clear and reproducible manner. The most important and frequently used quantities of this type are
1. the extension of bodies:
2. gas thermometer,
3. Liquid thermometers (mercury, alcohol thermometers, Bourdon tubes),
4. Metal thermometer (bimetal).
5. the thermoelectric voltage
6. the electrical resistance
7. Metal wire thermometers and
8. Semiconductor thermometer.
In addition to these most commonly used temperature measurement methods, there are others that are more or less widespread and have also found their way into meteorological measurement technology, e.g.
- Measurement of surface temperature via terrestrial radiation and
- Temperature measurement using the rotation of the polarization plane of sugar solution filled in ampoules.
Given the variety of long-established temperature measurement methods, measuring air temperature appears to be a simple, easily manageable task. In reality, it is fraught with a number of sources of error, the complete elimination of which is generally impossible, and whose reduction often requires the payment of other types of errors. In this context, we will disregard the errors inherent in the measurement method itself, which also occur in non-meteorological temperature measurements, such as:
- aging,
- Adjustment errors,
- Transmission errors or
- Distilling over the thermometer filling.
It is assumed that the sensor such as
- thermometer ball,
- bimetallic strips,
- soldering point of the thermocouple,
- resistance body
is sufficiently homogeneously tempered and this temperature of the sensor can be correctly determined with the required accuracy.
Measurement principles
Mechanically
The measuring element is a circularly bent bimetallic spring clamped at one end, whose curvature changes under the influence of temperature changes. The free end transmits the signal to lever systems.
BR>
For remote transmission, measuring instruments with a liquid-filled sensor are used. In this case, the temperature-dependent expansion of the liquid in the sensor is transmitted to the Bourdon tube located in the housing, which transmits its deflection to the lever system.
Electronic
In electronic temperature measurement, a temperature-dependent resistor is usually used as the measuring element
(RTD = Resistive Temperature Detector). How much the resistance changes with temperature is determined by the
Temperature coefficient of the material is determined. Sensor materials are usually platinum and molybdenum with various
Nominal values and tolerance classes according to DIN EN 60751.
12.04.01 Air resistance thermometer Pt100
The inertia error
If a body - ie in particular the above-mentioned sensor - with the temperature -& is in air with the temperature -&\_, then due to the temperature difference -&--&\_ a current of sensible heat flows
(1) L = - α L (θ - θ L )
from the air to the body surface. It is positive if θ L > θ ie the air is warmer than the body. It is proportional to the temperature difference. L is the heat flow from the air to the body surface per unit time and area. In meteorology, it is measured in Wm 2 The coefficient α L is called heat transfer coefficient and is measured in Wm 2 K -1 specified. α L depends on the body shape, the type of flow and especially on the wind speed v, whereby often in good approximation α L ∼√v applies- For a cylinder with a diameter of 5 mm and a vertical flow, the following values can be used as an approximate guide for the size of a L take:
|
v |
0.1 |
0.2 |
0.5 |
1.0 |
2.0 |
5.0 |
10.0 |
ms -1 |
|
α |
15.7 |
2.1 |
35.0 |
49.5 |
70.0 |
110.7 |
156.5 |
W m -2 K -1 |
The exact value must be determined experimentally or mathematically in each individual case. If no further heat flows from the outside reach the body, this heat flows into the interior of the body and increases the body's temperature. To simplify further considerations, we assume that the thermal conductivity of the body is very good (metal), so that only insignificant temperature differences occur within the body and the body can be considered to have the same temperature everywhere. If C is the heat capacity of the body and F its surface area, then the heat flow flowing from the surface into the body can be expressed as B.
(2) B = [(C • dθ) / (F•dt)]
where dτ/dt is the temperature change per unit time (Ks -1 ). The somewhat complicated choice of sign stems from the fact that all heat flows to the surface are counted as positive, which will also be retained in later considerations.
In the absence of further heat flows as assumed above, (energy law)
( 3) L + B = 0
Inserting equations (1) and (2) into equation (3) gives
(4) - α L •(θ- θ L ) - (C/F)•(d θ / dt)= 0
or
(5)d θ / dt = - [(α •F) / C] • (θ- θ L ) -
If you add
(6) λ= {(α •F) / C]
This gives us the so-called Newton's law of cooling
(7) d θ / dt = -λ •(θ- θ L )
The differential equation (7) can be easily integrated
(8) ln = [(θ- θ L ) / (θ 0 - θ L )] = -λt
or
(9) θ =θ L + (θ 0 - θ L ) • e - λt
where $o is the temperature of the sensor at time t = 0.
In the case of sudden changes in air temperature, a thermometer initially indicates a different temperature and then asymptotically approaches the new air temperature without - strictly speaking - ever reaching it, since the second term of Eq. (9) only disappears for t → ∞. The time after which a thermometer has adjusted sufficiently accurately to the air temperature depends, in addition to the desired accuracy, primarily on λ. From Eq. (9), the physical meaning of the adjustment coefficient can be interpreted such that its inverse τ = 1/λ is the time after which the temperature difference between the thermometer and the air has decreased to 1/e times (1/e = 0.368) of the initial temperature difference. Depending on the intended use of a thermometer, one will therefore strive to establish the λ value.
The relationships described by Equation (6) provide a basis for this. It can be seen that λ is larger, the smaller the heat capacity of the sensor is. Furthermore, λ increases with increasing surface area F of the sensor. Assuming the same material and the same shape, C increases more strongly (3rd power) with the dimensions of the sensor than F (2nd power), so that the inertia increases with increasing size of the sensor. The influence of the sensor size on α L acts in the same direction. Here, too, alpha; L smaller for larger bodies. Finally, alpha; L . and thus λ increases with increasing ventilation.
For many meteorological measurements, one tries to minimize inertia as a source of error and therefore to increase λ. For example, minimum thermometers, whose filling volume (heat capacity) cannot be reduced due to the thicker capillaries (rods), have two elongated cylindrical vessels instead of a sphere. This increases the surface area F. The thermometers are often artificially ventilated (spinning thermometers, aspiration thermometers). Conversely, one relies on high inertia for thermometers used to measure soil and water temperature, as long as they are to adjust to the temperature of the medium in question (which is subject to much smaller temporal fluctuations) and can be read after being removed from the air.
If one wants to track rapid fluctuations in air temperature, one switches to thermocouples and resistance thermometers with freely stretched wires, because their heat capacity is significantly lower than that of even the thinnest glass thermometers, and their heat transfer coefficient is also higher under the same ventilation conditions. Of course, measurements with thermometers of this type also reveal the limits of a meaningful reduction in inertia. Air is by no means a body with a homogeneous temperature. Rather, due to the natural movement of air, sometimes warmer, sometimes colder air bodies drift past a fixed measuring point, so that a very dynamic measuring instrument will show a continuous rapid fluctuation in air temperature (up to 1 K and more), whereas for most applications, a reasonably smooth average value is desirable. Due to their inertia, our conventional thermometers automatically smooth out the "temperature gusts" to a degree suitable for most purposes.
The radiation error
The possibility of a tolerable compromise between suppressing irrelevant and detecting relevant influences on a thermometer's reading, as is possible with the "inertial error," does not exist with the second error in meteorological air temperature measurements, the "radiation error." To account for this error mathematically, the energy balance equation (3) of the sensor surface should be expanded to include a term that describes the solar and terrestrial radiation influences. Although the irradiation of a freely positioned thermometer by the sun is extremely one-sided, an average of the radiation quantities should again be used over the entire surface, and the radiation fluxes should be related to the unit of surface area.
In the solar range (about 0.3...3 (Am)) the thermometer is affected by solar radiation S and diffuse sky radiation D, as well as by solar reflected radiation from the ground and possibly also from neighboring bodies, and in the terrestrial range (about 3 ... 60 ^m) by atmospheric counter-radiation A and the thermal radiation from other bodies in the surroundings. According to the absorption coefficient of the surface for the solar (ε s ) and terrestrial (ε T ) range, a part is absorbed, the rest is reflected. The surface itself emits in the terrestrial range ε T • E = ε T - σ •T 4 where T is the absolute temperature of the surface and σ is the constant of the Stefan-Boltzmann radiation law (σ = 5.6697•10 -8 W•m -2 K -4 ). The sum of all these radiation fluxes, the radiation balance Q
(10) Q = ε s - (S + D) + ε T - (A - σ •T 4 )
enters as a new term in the energy balance equation (3).
In stationary equilibrium, when the temperature $ no longer changes under constant radiation conditions, B = 0 (see Eq. (2)). In this case,
(11) Q + L = 0.
Inserting L from Eq. (1) results in a relationship
(12) Q - α L -(θ - θ L ) = 0
It follows:
(13) θ= θ L (Q / α L )
The temperature θ of a sensor exposed to radiation therefore deviates from the air temperature θ L , and the more so, the larger the radiation balance Q, ie the energy input through the radiation processes, and the smaller the heat transfer coefficient aL is.
If one wants to measure the air temperature as free as possible from this radiation error, one must, on the one hand, strive to keep the radiation balance of the surface of the sensor small, and, on the other, ensure good ventilation. The aspiration thermometer, as used in the Assmann aspiration psychrometer, fulfills both requirements excellently. Here, the thermometer vessel is surrounded by two concentric, highly polished nickel-plated protective tubes. The outer tube largely keeps "extraneous" radiation away from the inner tube, whose temperature therefore differs only slightly from the air temperature. The inner tube, due to the nickel plating (ε t = 0.05) only results in a low exchange of radiation with the measuring sensor, which is also ventilated (v > 2 ms -1 ). Aspiration thermometers of this type, which of course can also have electrical sensors, are therefore by far the best method for measuring air temperature. Unfortunately, they cannot be used everywhere. The relatively strong ventilation current requires considerable quantities of air and therefore disturbs the natural conditions wherever there is strong temperature stratification, for example near the ground or in vegetation. In principle, an electrical drive for the fan is possible at measuring points that are difficult to access, but the question of power supply, especially for continuous operation (registration) in field experiments, presents considerable, often insurmountable difficulties. Last but not least, financial considerations play a decisive role in more extensive studies with many measuring points.
For many measurements, one must therefore make do with simpler radiation protection devices and accept the risk of errors. The most common form of radiation protection for meteorological measurements is the climate hut, which can be found at every meteorological station. In its basic form, which has undergone many modifications, it is a wooden casing with louvers as walls, a double roof and a double floor, which, like the louvered walls, allow the air to pass through. Inside, in addition to the extreme thermometers and the so-called hut psychrometer, there are also recording devices for temperature and humidity. Although the hut is painted white, it heats up noticeably above the air temperature, especially in weather with high radiation and little wind. Since both the wood of the hut and the glass of the thermometer behave almost like a blackbody in the range of terrestrial radiation (ε t = 1), the thermometer has a resulting radiation balance even in the absence of solar radiation. From Equation (10) follows:
(14) Q = A - E = σ•T H 4 - σ•T 4 =4•σ•T L • (θ H - θ) = α S • (θ H - θ)
where $h is the average temperature of the hut parts. The coefficient
(15) α S = 4 • σ •T L 3
(Wm -2 K -1 ) is called the radiation transfer coefficient. The following table provides an indication of its value:
|
θ H |
-10 |
0 |
10 |
20 |
30 |
°C |
|
α S |
4.1 |
4.6 |
5.1 |
5.7 |
6.3 |
W • m -2 • K -1 |
The energy balance equation (11) of the hut thermometer is therefore
(16)α S •(θ H - θ) - [α L • ( θ - θ L )] = 0
and gives the temperature of the thermometer
(17) θ = θ L +[ α S (α L • α S )]•( θ H - θ L )
Since as and aL are of the same order of magnitude, especially with poor ventilation, part of the hut's overheating is transferred to the thermometer via radiation. In addition, the air is also heated as it flows through the warmer blinds, so that #l in equation (17) is not the air temperature at the same height outside the hut. Errors of up to 2 K can certainly occur, although the average error usually remains noticeably below 1 K. Similarly, negative errors are possible at night when the hut's radiation balance is negative. Radiation shelters and other similar shielding reduce the radiation error but only inadequately eliminate it.
In the transient case, B does not vanish. The energy balance equation for the sensor surface is then
(18) Q + B + L = 0
or (19 ) Q - [(C • dθ) / (F • dt)] - α L • ( θ - θ L ) = 0 t
whatever you
(20) - [(C • dθ) / (F • dt)] - α L •(θ - (θ L + (Q/α L ))) = 0 _
can write.
Equation (20) corresponds completely to equation (4) in its structure and in the solution of the differential equation, if one replaces $L with the temperature #L+Q/aL modified by the radiation error. Thus, even in the unsteady case, a radiated thermometer behaves as if the air temperature were higher by the radiation error Q/aL.
If the sensor is in conductive contact with bodies of a different temperature—for example, through the thermometer shaft, holder, leads, etc.—heat can flow to the sensor, causing an error. This can be particularly significant with thermocouples. For conventional air temperature measurements, this effect is usually not significant. Wet thermometers give inaccurate readings in unsaturated air due to evaporative cooling. This effect can cause short-term errors (fogging).
Finally, it should be noted that completely eliminating radiation errors in air temperature measurements is not possible, except in the case where the air and the surroundings (walls) have the same temperature. All bodies undergo a greater or lesser radiation exchange with their surroundings, which influences body temperature. One can only attempt to reduce this influence to a tolerable level for the purpose of the problem, whereby the possible effort usually determines the limit of accuracy.
|
Minimum requirements for air temperature measurements for |
||
|
Measuring range |
resolution |
Required |
|
-60...60 °C |
0.1 K |
± 0.1 K |
* Accuracy is determined under laboratory conditions. T>