Who invented the dilatometer?
Terms, devices, measurement and calculation
On this page you will find articles on the topic of "Density" - Definitions, hydrostatic liquid density measurement by determining the buoyancy of an exact sphere in a thermostatic measuring cell (IMETER M8)Correlations, influences and descriptions of the measurement methods partly with information on the relevant standards. On this On the other hand, we try to present everything that is essential in connection with the measurement of density. You can help us and point out corrections or missing items.
The density (Mass density, specific mass, density), Formula symbols ρ (rho), is the quotient of mass m and volume V. (ρ = m / V), i.e. "mass per volume". The density is the numerical value of the mass concentration. The legal unit is kg / m3, g / cm is also common3. The reciprocal of the density is called 1 / ρ specific volume (specific volume). Previously used and related terms in connection with density are: Tightness, Weights, Species weight and specific weight. The weights, symbol γ (gamma), is the quotient from the weight G and the volume V. of a body or a quantity of substance (γ =G / V). The specific gravity can be represented as the product of the density ρ of a body and the local acceleration due to gravity G, so: γ = ρ·G.Among the synonyms ρnDensity number, relativ density one understands the ratio of the mass of a body to the mass of an equal volume of a standard substance ρ0. The standard substance is mostly water at 4 ° C or mercury (ρn=ρ / ρ0). These locally realizable standard references circumvent the problem of the location dependence of the acceleration due to gravity, and the dimensionless numerical value is also comparable in all non-metric units in the world (specific gravity). The unit of specific gravity and specific gravity was p / cm3 (p = pond). If the acceleration due to gravity corresponds to the normal acceleration due to gravity, the values for density in p / cm³ and density in g / cm³ are the same. It should be mentioned that specific weightis still often used today as an equivalent term for density. The density is pressure and temperature dependent. The temperature dependency is expressed by the expansion coefficient, the pressure dependency by the compressibility or, in the case of solids, by the compression module. A precise specification of the density, especially for fluid substances, necessarily includes the specification of the associated temperature. The pressure dependency of the density in the fluctuation range of the normal pressure is - except for gases - insignificant.
2. Expansion coefficient
With increasing temperature, the volume of solid, liquid and gaseous substances increases, i.e. the density of the substances decreases with increasing temperature.
In Fig. 1, the clear dependence of density on temperature can be seen using the example of fuels. There are exceptions to the normal case, i.e. the fairly linear decrease in density with temperature. These include: water between freezing point and 4 ° C (anomaly of the water [Fig. 2, right]), special glass ceramics (e.g. Zerodur®), β-quartz, β-eucrypt, certain carbon fiber materials and spherical bodies with special morphology (► documented special case).
The cause of the thermal material expansion is the increasing space requirement of the particles with increasing temperature. In a physical formulation, the spatial expansion coefficient κ is:
κ = 1 /V.· DV./ dT
The value of κ (kappa) can be assumed to be sufficiently constant for rough calculations over a certain temperature interval. Teflon (PTFE) at 19 ° C is a classic exception in terms of linearity (see Figure 6 below). The coefficient κ is called correct cubic thermal isobaric expansion coefficient. In short, one speaks of cubic expansion coefficient or also from the room expansion coefficient. While κ is usually given for fluids, this is usually found for solids linear thermal isobaric expansion coefficient (α, alpha). The common unit for α is 10-6K-1. To this end, the equivalent expression is "µm · m-1· K-1 ", which means that temperature changes of one degree cause a change in length of α micrometers on a 1 meter long rod. For liquids, the thermal expansion is significantly greater, and the value is expressed as the spatial expansion coefficient κ in multiples of 10-5K-1 specified.The coefficient of thermal change in length (α) is often viewed in model calculations as being independent of spatial direction, temperature and pressure. α can, however, be dependent on the spatial direction (anisotropic) in the case of substances made up of ordered structures, as, incidentally, also the thermal conductivity.
In the case of table salt (NaCl), α is the same in all three spatial directions and is αx = αy = αz = 40 µm · m-1· K-1. With calcite (CaCO3) on the other hand, α is negative α in two spatial directionsx = αy = -6 µm · m‑1· K‑1 and in the third positive, αz = 26 µm · m‑1· K-1so that an expansion plus prevails. In the case of β-eucrypt (LiAlSiO4) with αx = αy = 7.8 and αz = -17.8 µm · m-1· K‑1, i.e. the negative expansion predominates; with aragonite (chemically also CaCO3) α is different in all three spatial directions: αx = 10, αy = 16, αz = 33 µm · m-1· K-1.
The linear expansion coefficient α for solids cannot therefore be given with certainty from α = κ / 3. Since (partially) crystalline, non-amorphous, stretched or stretched materials often have different α along an orientation (αx, αy, αz) than across to her. In the case of solids, "κ = 3α", as shown in the examples, is at least risky.
The entries listed in the tables on the right give an overview of the differences between these coefficients for solid and liquid substances. Apart from plastics, the value of κ is roughly an order of magnitude smaller for solids and about 3 to 10 times larger for gases than for liquids.
Fig.4: Temperature dependence of the expansion coefficients of the various fuels (see diagram in Fig. 1 above corresponding density curves) and n-dodecane as a comparison.
Liquid density table below: The information in the tables comes from various sources and is not guaranteed. (Density data largely from [Lit.12], measurements by IMETER on individual samples are marked with *; PDF document as a link.)
Fig.5: Water / salt water - expansion coefficients as a function of temperature - from density measurements on water with 3%, 2% and 1% table salt, tap water (from Augsburg) and pure water. The zero crossing indicates the temperature of the respective density maximum (i.e. the parabolic vertex in the density-temperature curve => Fig.2 and Fig.3).
Fig.5a: Temperature dependence of the cubic expansion coefficient in (a) bytyl rubber: The large value is typical for soft plastics. The decrease in temperature can be attributed to the increasing hardness (rubber elasticity).
|Rotating bimetal spirals (bimetal thermometer), flaking coatings and wandering adhesive film on glass panes, weathering and cracking are caused or favored by temperature changes when there is a difference in κ in material composites. For glasses is with the value κ the thermal shock resistance linked in such a way that the smaller κ is, deterrence is improved. For example, a device glass 20 has κ= 4.5 a thermal shock resistance of 190 K; Pyrex glass, on the other hand, achieves with κ= 3.2 at least 250 K. And quartz, κ= 0.5, can be quenched glowing in water. In so-called lava lamps, the effect of different expansion coefficients (of two immiscible liquids of similar densities) is very clear. The liquid is illuminated and heated from below by the lamp. The slightly denser and mostly colored lower phase has a higher coefficient of expansion and is pushed upwards in bubbles in the temperature-related convection current / density gradient, where it cools and sinks away from the heat source. Ocean currents, wind, weather, plate tectonics and volcanism represent convection currents, the cause of which is density differences in the amount of substance. The thermal expansion converts temperature differences into motion in the gravitational field.|
Wherever density differences no longer cause convection, some things no longer work; it is not possible to let a candle burn without gravity.
Solid density table: The information in the tables comes from various sources and is not guaranteed. In particular, the inconsistency of the values for κ and α in the literature should be noted. Measurements by IMETER on individual material samples are marked with *; PDF documentation as a link.
3. Compressibility, compression modulus
The compressibility (Χ) of liquids expresses their volume elasticity. The change in volume (i.e.V.) of a given volume (V.) is caused by a change in pressure (i.e.V.) causes: dV. = -Χ ·dp · V. The proportionality factor is Χ (Chi). The compressibility of liquids is low, so liquids are often assumed to be incompressible. This property becomes noticeable at high pressures or very precise measurements. Water has a compressibility of 0.5 GPa-1, Mercury 0.04 GPa-1, Diethyl ether 1.5 GPa-1, Pentane 2.5 GPa-1. For water 100m below the surface, the hydrostatic pressure (heavy pressure) (= Density * acceleration due to gravity * altitude, ρ · g · h) to a volume reduction of around 0.05%. In floating depths of 5 cm of the float during the hydrostatic density determination, 0.2ppm is achieved.
The speed of sound vs linked density ρ and compressibility Χ n.d.Gl. vs = [Χ ρ]1/2. (The compression module K for solids corresponds to the reciprocal of compressibility and can be derived from the elasticity constants E-modulus and Poisson's number µ be calculated: K = E./(3-6µ).)
While the density of gases and dripping liquids is a constant at the respective pressure (and temperature), which resets itself elastically after the effect of compression, other conditions can sometimes be found in solids. As metals are forged, the density of the material usually increases. In the case of non-purely elastic materials, such as the polystyrene foam EPS (Styropor®), this effect is noticeable - by simply adding permanent pressure points, which accordingly increase the density.
4. Density of mixtures, determination of the content
Density measurement has always been used to determine the content. For certain combinations of substances, often aqueous solutions, e.g. of sugar, alcohol (ethanol) and with appropriately measured scales for milk, must (must weight, Öchsle), battery acid (sulfuric acid in lead batteries) etc., spindles are widely used (hydrometers, hydrometers, see next Section). As a rule, the density of a mixture roughly corresponds to the proportions. The Mix density can be expressed for two components in a simple formula. With m1, the mass fraction of a component with the density ρ1 and m2, the mass fraction of the second component and the density ρ2, gives the total density ρGes the binary mix to:
ρGes = (m1+ m2) / (m1/ ρ1 + m2/ ρ2) = (m1+ m2) / (V1 + V2)
For table salt (NaCl) dissolved in water, the relationship only applies in the quality "π ·thumb", because the mixture or solution density at 10% NaCl is already almost 1.5% higher than it results from the simple formula. Im diagram (aboven) measurement data on the density of aqueous saline solutions for temperatures of 25 ° C and 50 ° C are shown (Data origin: Rogers, P. S. Z., Pitzer, K. S., J.Phys. Chem Ref. Data, 11, 15 (1982) and from the ►IMETER measurement ID7277.PDF). The deviation from the linear behavior can hardly be seen in the graphic, but it is clearly there. Mixtures or solutions of most liquids also do not behave linearly when measured precisely. Mixtures of acetic acid and water show an extreme picture (see diagram below). If accuracy is required in order to make definitive content determinations about the density or volume defects or enlargements (►Hexane / Cyclohexane.pdf), the circumstances must be clarified. This is done through exact density measurements on several defined mixtures and then allows a calibration function to be set up from density and mixture ratios. The following equation introduces a specific factor into the above ideal equation, the Mixing CoefficientsΦ12 :
ρGes = (m1+ m2) / (m1/(ρ1·Φ12) + m2/ρ2)
The mixing coefficient Φ12 : is however a function of the mixing ratio, which is determined from a concentration calibration. A corresponding measurement was carried out for the sodium chloride-water example. This gives the equation for the coefficient at 25 ° C:
Φ12 = 0,4601860 +0,8550176·ρGes -0,3144906·ρGes²
In those cases in which the concentration is to be determined from density measurement, a simpler formulation can also be used:
Or to predict the density as a function of the concentration, the equation determined from the measurement data
ρ [g / cm³] = ƒ (c [%]) = 0.9971057 + 6.96858E-3 · (c) + 2.03622E-5 · (c) ² (± 0.0001g / cm³)
be applied. The equations apply to the measured concentration range between 0.0138 and 10.1% or for mixture densities between 0.997171 and 1.069934g / cm³; IMETER automatically generates these relationships in a concentration measurement (see ►IMETER measurement IDN ° 7277.pdf).
Concentration determinations on mixtures three components (ternary mixtures) are also possible by density measurement. For example, the components sugar, water and ethanol for alcoholic fermentation or glycerine, propylene glycol and water as liquid for e-cigarettes could be determined in a wide range. However, this would require two density measurements. The measurements have to be carried out at different temperatures - and so the corresponding system of equations can be solved to determine the content. Accordingly, viscosity and surface tension, possibly with their temperature coefficients, can be used to physically determine the constituents of higher mixtures.
in the diagram (Fig.8) the exception to the rule is shown: mixtures of acetic acid and water. With a density above 1.04g / cm³, two different concentrations can be assigned to a density value (cf. ►Messung IDN ° 7575.pdf, ►Messung IDN ° 7576.pdf).
(The cause of the abnormal behavior becomes clear when the mass% is converted into mol%. With the molar ratio 1: 1 - at about 70% acetic acid - the density maximum occurs. The closest packing corresponds to the 1: 1 molecular ratio. - A little magic trick: you take a transparent vessel that is divided in the middle with a partition, put acetic acid in one half and the same amount of 50% vinegar in the other and in both compartments there is a lot of e.g. SAN polymer granulate [or another substance with a density of about 1.05g / cm³ that does not mind the acid]. The granulate lies in the vessel parts on the bottom, because the density of the solid is greater. Then you pull out the partition and the granulate begins to float) .
The vinegar-water special case is interesting from a metrological point of view for testing sensors and measuring devices. Because for one and the same density, e.g. 1.05g / cm³ (25 ° C), there are two different concentrations: surface tensions and viscosities. Corresponding display devices and their cross-sensitivities to density can be checked - and vice versa.
If it is precisely determined, the density is a highly precise measure of concentration for almost all binary mixtures. Other methods, chromatographic or spectroscopic, are nowhere near as precise as can be achieved by density measurement. In order to be able to carry out concentration calibrations correctly, determination methods are required that have no cross-sensitivity to surface tension and viscosity, because these properties also change.
5. Density determination methods
Density meters are called density meters, sometimes called densimeters. The density measurement with a Densitometer however, concerns e.g. the blackening and color density - that is, another densityart. To determine the Mass density A number of devices and methods are in use: hydrometers, pycnometers, hydrostatic weighing, the vibration measuring device along with less common ones such as the levitation method and the density gradient column, which are used in particular for solids.
5.1. Areometer (spindle, countersunk spindle, lowering balance, hydrometer)
The hydrometer, probably already known in antiquity, was (re) invented by Roberval in 1670.
Nowadays it is mostly an air-filled hollow glass body, the lower end of which is weighed down by a certain amount of lead shot, sand or mercury. At the top, the hollow body ends in a narrow, cylindrical neck on which a measured scale is attached. The deeper the hydrometer is immersed in the liquid, the lower the density. A set of 14 hydrometers is generally used in laboratories to measure densities between 0.630 and 2000 g / cm3 to be measured (measuring span per spindle 0.1 g / cm3). The density is measured using a cylinder into which the liquid is poured. When reading, the hydrometer must float freely and motionless and the temperature must correspond to the reference temperature of the hydrometer. The measurement uncertainty is typically 1 · 10, depending on the spindle-3 g / cm³ to at best 1 x 10-4 g / cm³ for very special designs.
In addition to the special forms, which are adjusted to the high, medium or low surface tension of the material to be measured and which take transparency or opacity into account, there are also special hydrometers such as alcoholometers, milk hydrometers and saccharimeters, which, by means of a specific calibration, e.g. direct reading of the percentage on the scale enable. In addition to the division of the scale according to density values, other scales are also in use. There is a subdivision into degrees Baumé, Cartier, Beck, Brix, Balling, Gay-Lussac and Twaddle.
DIN 12790, ISO 387 hydrometers; general provisions
5.2. Pycnometer (volume weighing, density bottle)
It is a mostly pear-shaped weighing bottle with a ground-joint stopper, which is provided with a capillary bore (= pycnometer according to Gay-Lussac; other shapes partly due to viscosity or volatility according to Sprengel, Bingham, Reischauer, Lipkin). The precisely defined volume, often around 10, 25 or 50 cm3 e.g. precisely calibrated with water, the liquid to be tested must be filled up to the end of the capillary at the specified temperature and then weighed. While hydrometers are mainly used for overview measurements, higher accuracies are achieved with pycnometers. Depending on the version, a measurement uncertainty of 1 · 10-5 g / cm³ can be achieved. However, the quality of the measurement is very dependent on the skill and experience of the tester.
ISO 3507 pycnometers
Pycnometers can also be used to determine the density of solids. A solid sample is placed in a pycnometer, the rest of the volume is filled with a liquid of precisely known density and the whole is weighed.
Gas pycnometer: Another method of pycnometric measurement is based on gas displacement in a defined space. It is particularly used for solid-state density measurements. The reproducibility for commercial gas pycnometers is reported to be up to 0.01%. A ►GasPyknoIMETER was developed among the IMETER ►Ad-Hoc methods. It turned out, however, that samples with a large surface area were affected by adsorbed substancesSubstances with vapor pressure) e.g. due to the humidity, the accuracy of the measurement can be significantly disrupted by the pressure contributions.
5.3. Hydrostatic weighing (buoyancy method, immersion body method, Mohr-Westphal balance)
The essence of the hydrostatic method is the phenomenon that a body submerged in a liquid appears as much lighter as the amount of liquid corresponding to its volume weighs. According to this principle, where there is gravity and solid and fluid matter meet, pretty much works - ships float, airships float and stones sink. The hydrostatic weighing can be used for the density measurement of liquids as well as for the solid matter density measurement. Either you have to know the density of the immersion body or that of the liquid.
Although hydrometers also work according to the buoyancy method, one understands under Measurement using the hydrostatic method a special procedure. In contrast to Archimedes’s historical method, which will be discussed below, the "overflowing amount of liquid" is not measured, but a direct weighing is carried out. A special weighing device for this is the Mohr's scales. With hydrostatic weighing, a measuring body (= body with precisely known volume and mass, also as a density standard) is weighed first in air and then in the liquid to be examined. The Mohr balance is an apparatus refinement of the method: on a balance beam that carries a glass body on a Pt wire and on the same side of the balance beam a set of (five) decadic different tare weights ("tabs") is used to zero the A counterweight is attached to the glass body. If the glass body is immersed in the liquid to be examined, its density is determined by moving the tabs on the graduated scale, at whose position the density can be read off directly with buoyancy compensation (the position of the tabs gives the units, tenths, hundredths, ... . Place the density). This instrument is tricky and actually no longer usable with highly viscous liquids, since an equilibrium position can hardly be set due to the correspondingly slowed settling. The one widely used today hydrostatic density measurement - also mostly with a glass body - uses an electronic balance and thereby facilitates the measurement. The Displacement method is a variation on the Archimedes' principle, whereby not the buoyancy on the measuring body, but the Weight gain a liquid container is weighed, which stands on a weighing device (pan), while a volume standard is immersed (also known as a gamma sphere). By weighing over the liquid container, the amount of liquid displaced by the volume is determined directly. The weighing shows how much more the immersed volume weighs as the amount of sample.
ISO 901 ISO 758
A more special arrangement that uses the volume buoyancy principle is the magnetic levitation balance (►Uni Bochum), also called "magnetic flotation" or levitation, which is characterized by the fact that no holding wire carries the measuring body. In principle, this would be the most precise and universally adjustable device. Because the force that otherwise acts unpredictably on the suspensions, i.e. the liquid meniscus above the phase boundary, is the main precision destruction. But there is now another, simple and robust solution, namely ►meniscus elimination. Weighing methods are fundamentally advantageous because balances can generally be adjusted / calibrated easily, quickly and without complications. The plausibility is easy to represent. Monitoring of test equipment, calibration and traceability are therefore not the subject of complicated derivations.
IMETER processes also use the hydrostatic method with some refinements: for liquids (►Method N ° 8), solids (►Method N ° 9) and in viscometry (►Method N ° 5). By paying attention to many details, they form the practically most precise and undoubtedly most correct instrument available. As a simpler, everyday procedure, was added the fastest density measurement (►IMETER-AIM) developed through some simplifications; the measurement only takes a few seconds.
The following chapters deal with this measurement method from different points of view. The formulaic relationship for hydrostatic measurements is summarized at the end of this page.
5.4. Vibration measuring device (flexural vibrator)
The method is based on the natural frequency of an oscillating system. A certain volume of the liquid to be examined is part of a resonator, whereby the oscillation frequency (f) is fixed by the oscillating mass and with the fixed volume there is a calibratable proportionality to the density (ρ). The relationship obeys the form ρ = A · f -2 + B.
Illustration: a hollow tuning fork that is filled with liquid vibrates in different pitches depending on the density of the filling.
DIN 51757 Testing of mineral oils and related substances; Determination of density, method D., PTB requirements
Flexural transducers are quite practical devices, especially because of their ease of use and the small sample volume. However, accuracy (correctness) and application possibilities are limited. Emulsions, suspensions, outgassing or unstable liquids can often not be measured correctly. The accuracy in the sense of correctness with up to 5 · 10-6 Specifying g / cm³ seems risky. In this resolution, the temperature (of organic liquids) must also be determined more precisely than 0.01 temperature degrees. Vibration-related flow, compression, internal friction in the liquid (temperature increase) and also possibly co-determining environmental densities (air density) mean non-linear dependencies and links with other unknown and sample properties. A more detailed discussion can be found in the overview article by Prof. Hradetzky (Hochschule Merseburg).
5.5. Coriolis force - density measurement
A technique that sometimes appears somewhat similar in the technical implementation of the oscillating vibration method is based on the Coriolis force and is used particularly in process measurement technology:
With regard to correctness, similar restrictions apply as for the vibration measuring device.
(Roland Steffen offers a nice elaboration, especially with regard to flow measurement, in a project at http://www.rolandsteffen.de/Corioliskraft.pdf)
5.6. Other methods
Coarse methods (search or overview methods or "π times thumb"):
Schlieren method: Whether there is a difference in density in questionably identical, equally dense, transparent liquids can be checked by gently mixing or stirring. Due to differences in the refractive indices, streaks form, which also indicate differences in density. Such an effect is known, for example, from water that is heated, whereby the rippling streaks indicate the density-related convection.
Hollow body weighing: The volume of the liquid is weighed in a standing cylinder (error 1-5%) or, more precisely, in a volumetric flask filled to the calibration mark (roughly pycnometric).
Weighing regular bodies: To estimate the density of solids, you create a regular body, such as a cuboid, a cube, a cylinder or a sphere, weigh it and determine the volume geometrically, e.g. with a ruler. ASTM C 559-90 provides guidance for bodies made from carbon or graphite.
Overflow method (classic Archimedes): You weigh the body, then you put it in a vessel full to the brim. The overflowing amount of water is collected and weighed. The amount in grams corresponds to the body volume in milliliters (https://de.wikipedia.org/wiki/Archimedisches_Prinzip).
Hydrostatic pressure: In sufficiently high cylinders (also e.g. in storage silos) or with appropriate pressure sensors (p) or a scale (W.) and the face (A.) the density can be derived from the hydrostatic pressure (ρ · g · h) can be determined (h is the filling level in the silo; ρ = p / (g h) or by scales ρ = W / (A g h).
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