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Relative density

Relative density, also known as specific gravity, is a dimensionless physical property defined as the ratio of the density of a substance to the density of a reference material, typically water at 4 °C for liquids and solids, or air for gases.^[1] This ratio provides a unitless measure that facilitates direct comparisons of how compact or sparse the mass distribution is in different materials relative to the standard. Since density itself depends on units like kg/m³, relative density eliminates such variability, making it particularly useful in scientific and engineering contexts where consistency across measurements is essential. In physics, relative density plays a crucial role in understanding buoyancy and fluid mechanics, as outlined by Archimedes' principle, where an object's tendency to float or sink in a fluid depends on whether its relative density is less than or greater than 1.^[2] For instance, materials with a relative density below 1, such as wood or ice, will float in water, while those above 1, like iron or mercury, will sink.^[3] In chemistry, it is employed to assess the concentration of solutions, purity of substances, and composition of mixtures; for example, hydrometers measure the relative density of liquids like battery acid or urine to evaluate their properties.^[4] The concept extends to engineering and industry, where relative density informs material selection, quality control, and process optimization—such as determining the alcohol content in beverages or the grade of petroleum products via scales like API gravity, which is inversely related to specific gravity. Historically rooted in early volumetric comparisons, relative density remains a fundamental metric, with modern instrumentation like digital density meters enabling precise determinations for applications in pharmaceuticals, environmental monitoring, and materials science.

Definition and Fundamentals

Definition

Relative density, also known as specific gravity, is a dimensionless quantity defined as the ratio of the density of a substance to the density of a reference substance measured under specified conditions of temperature and pressure.^[1] For liquids and solids, the reference is typically water at its maximum density of 4°C, while for gases, it is usually dry air at standard temperature (15°C) and pressure (101.325 kPa).^[1] This ratio allows for a standardized comparison of material properties without regard to absolute units, making it particularly useful in scientific and engineering contexts where direct density values may vary with measurement systems.^[4] The concept traces its origins to the principles of buoyancy discovered by Archimedes in the 3rd century BCE, when he determined the purity of a gold crown by comparing the weights of equal volumes of gold and the displaced water, effectively calculating an early form of relative density.^[5] The term "specific gravity" emerged in the 17th century, evolving from gravitational considerations to a purely densitometric ratio.^[6] In modern usage, particularly within the International System of Units (SI), "relative density" is the preferred term to emphasize its dimensionless nature, distinguishing it from the older "specific gravity" which implied units of gravity.^[1] One key advantage of relative density is its unitless format, which eliminates the need for unit conversions and facilitates direct comparisons across substances and international standards.^[4] It standardizes reporting in fields like geotechnical engineering, as seen in ISO 17892-3, where soil particle density is expressed relative to water to assess material composition and behavior.^[7] Additionally, it simplifies identification and quality assessment, as each pure substance has a unique value that highlights deviations from expected densities without absolute measurements.^[4] Common reference substances include water at 4°C with a density of 1000 kg/m³ (precisely approximately 999.97 kg/m³ under standard conditions).^[8] For gases, dry air at 15°C and 101.325 kPa has a density of approximately 1.225 kg/m³, enabling relative comparisons in atmospheric and industrial applications. In specialized cases, such as high-density liquids, mercury (density 13,534 kg/m³ at 0°C) may be used as the reference to avoid impractical dilutions with water.^[9]

Basic Calculation

The relative density (RD) of a substance is computed as the ratio of its mass density to the mass density of a reference material, expressed as

\text{RD} = \frac{\rho_\text{substance}}{\rho_\text{reference}},

where \rho denotes mass density in units such as kg/m³.^[1] The reference density is typically that of water at 4°C, which has a standard value of 1000 kg/m³ under atmospheric pressure.^[8] This formula assumes the densities are measured under identical conditions for both the substance and the reference.^[1] For mixtures assuming ideal behavior and additive volumes, the relative density can be estimated as a weighted average using mass fractions of the components:

\text{RD}_\text{mix} = \sum_i (w_i \times \text{RD}_i),

where w_i is the mass fraction of component i and \text{RD}_i is its individual relative density.^[10] This approach provides a practical approximation when component densities are similar, facilitating quick assessments in applications like alloy design or solution preparation.^[11] Valid calculations require isothermal (constant temperature) and isobaric (constant pressure) conditions to minimize variations in density during measurement.^[12] For non-homogeneous samples, such as heterogeneous materials or emulsions, relative density is obtained by averaging densities from multiple representative subsamples to account for compositional variability.^[13] Error in relative density arises primarily from inaccuracies in the reference density value. Standards for water at 4°C provide high precision, ensuring the overall computation achieves uncertainties below 0.1% in typical laboratory settings.^[8]

Influencing Factors

Temperature Dependence

The relative density of a substance varies with temperature primarily due to differences in thermal expansion between the substance and the reference material, typically water for liquids. As temperature increases, most substances expand volumetrically, leading to a decrease in density. The relative density at temperature T, denoted RD(T), can be approximated from its value at a reference temperature T_0 using the formula:

RD(T) \approx RD(T_0) \times \frac{1 + \beta_\text{substance} (T - T_0)}{1 + \beta_\text{reference} (T - T_0)},

where \beta is the volumetric thermal expansion coefficient. This approximation assumes small temperature changes where \beta is constant; for water as the reference at 20°C, \beta_\text{water} \approx 2.1 \times 10^{-4} /^\circ\text{C}.^[14]^[15] The net effect on relative density depends on the difference \beta_\text{substance} - \beta_\text{reference}; substances with higher \beta than water exhibit a more pronounced decrease in relative density with rising temperature. In industries like petroleum, standardized correction methods account for this dependence to ensure accurate measurements. The American Petroleum Institute (API) and ASTM International provide tables in ASTM D1250 for volume correction factors (VCF) that adjust relative density or API gravity for temperature deviations from 15°C (60°F). For example, gasoline, with a volumetric expansion coefficient of approximately $9.5 \times 10^{-4} /^\circ\text{C}, shows a relative density decrease of about 0.00065 per °C temperature rise, reflecting the combined expansion of gasoline relative to water.^[16]^[17] These corrections are essential for custody transfer and quality control, where even small errors in density can impact economic transactions. Experimental data for common substances illustrate these trends. For ethanol, the density is 793.7 kg/m³ at 15°C and 789.0 kg/m³ at 20°C, yielding relative densities of approximately 0.794 (relative to water at 15°C, density 999.1 kg/m³) and 0.790 (relative to water at 20°C, density 998.2 kg/m³), respectively, demonstrating an increase in relative density as temperature decreases.^[18] Similar patterns hold for other liquids, such as mercury (relative density rising from 13.55 at 20°C to 13.58 at 15°C) or olive oil, where thermal expansion coefficients around $6.8 \times 10^{-4} /^\circ\text{C} lead to measurable shifts over typical laboratory ranges.^[17] At high temperatures above 100°C, the linear approximation often fails due to non-linear variations in the expansion coefficient, influenced by molecular interactions, phase changes, or increased compressibility. For instance, water's \beta rises nonlinearly beyond 100°C, approaching 7.5 × 10^{-4} /°C near boiling, complicating relative density calculations in applications like steam systems or high-temperature processing without advanced models or empirical data.^[19]^[8]

Pressure and Composition Effects

The relative density of gases is significantly influenced by pressure, particularly when deviations from ideal behavior are considered. Under ideal gas assumptions, the relative density remains constant when the gas and reference (typically air) are evaluated at the same temperature and pressure, as it is proportional to the ratio of molar masses. However, if the substance is at a different pressure from the reference, an approximate correction is RD ≈ (P_substance / P_reference) × (T_reference / T_substance), derived from the ideal gas law where density ρ ∝ P / T.^[20] For real gases, the compressibility factor Z accounts for non-ideal effects, modifying the density to ρ = P M / (Z R T), so the relative density becomes RD = (M_substance / M_air) × (Z_air / Z_substance), with Z depending on pressure and temperature; at higher pressures, Z < 1 for many gases near their critical points, increasing density and thus RD relative to ideal predictions.^[21] A representative example is natural gas, which has a relative density of approximately 0.6 relative to air at 1 atm and standard temperature, varying with composition but typically in the range of 0.55 to 0.65 due to its methane-rich makeup.^[22] Pressure effects are more pronounced in gases than liquids; for instance, carbon dioxide's relative density increases by about 5% at 10 atm compared to 1 atm at room temperature, owing to its compressibility factor dropping below 1, which elevates density beyond ideal expectations.^[23] In contrast, liquids exhibit minimal compressibility, with density changes under 0.5% per 100 atm for water (bulk modulus ≈ 2.2 GPa, yielding ΔV/V ≈ -4.5 × 10^{-5} per atm).^[24] Material composition profoundly affects relative density in mixtures, as it alters the average molar mass for gases or the weighted densities for solids and liquids. For gas mixtures like natural gas, relative density is calculated from mole fractions using standards such as ISO 6976, which employs component properties and compressibility corrections for pressures above 0.9 Z; for a binary methane-ethane blend (e.g., 90% CH₄, 10% C₂H₆), RD ≈ 0.58, computed as the molar mass ratio adjusted for real gas behavior at base conditions.^[25] In alloys and solutions, additivity rules apply, where relative density is RD = [∑ (volume fraction_i × ρ_i)] / ρ_reference for volume-based mixing, assuming no volume change on mixing; for a binary copper-nickel alloy (50 vol% each), with ρ_Cu = 8.96 g/cm³ and ρ_Ni = 8.91 g/cm³ relative to water (ρ_reference = 1 g/cm³), RD ≈ 8.94, reflecting near-identical component densities.^[11] These compositional effects are essential for predicting properties in engineering mixtures, complementing pressure influences without thermal overlaps.^[26]

Applications

In Chemistry and Materials Science

In chemistry and materials science, relative density serves as a critical parameter for assessing the purity of substances, where deviations from expected values often signal the presence of impurities. For instance, absolute ethanol has a relative density of approximately 0.789 at 20°C; contamination with water, which has a higher density, results in an increased relative density (e.g., above 0.789), allowing for straightforward detection through density measurements during quality control processes.^[27]^[28] This method is routinely employed in pharmaceutical and industrial chemical analysis to ensure compliance with purity standards, as supported by guidelines from the American Chemical Society (ACS) for reagent characterization.^[29] Relative density also plays a key role in phase identification, particularly for polymorphs of the same chemical composition, which exhibit distinct densities due to differences in atomic packing. A classic example is carbon: diamond, with its tetrahedral structure, has a relative density of 3.51–3.53, while graphite, featuring layered hexagonal sheets, has a lower relative density of 2.09–2.23.^[30] These differences enable differentiation between phases using gravimetric techniques, aiding in material characterization for applications like semiconductor synthesis or advanced ceramics, where phase purity directly impacts properties such as hardness and conductivity. In polymer and composite analysis, relative density facilitates density-based sorting, essential for recycling and quality assurance in materials science. High-density polyethylene (HDPE), with a relative density of about 0.95, floats in aqueous media during sink-float separation processes, allowing efficient isolation from denser contaminants like PVC (relative density ~1.4).^[31] This technique supports sustainable polymer recovery by enabling the segregation of resins based on their inherent densities, reducing contamination in recycled streams and preserving material performance in composites. Laboratory standards further integrate relative density with other analytical methods, such as titrations and spectroscopy, to correlate concentration and composition. Per ACS guidelines, density measurements provide baseline data for preparing standard solutions in acid-base or redox titrations, ensuring accurate volume-to-mass conversions, while in spectroscopy, relative density helps validate sample concentrations by linking refractive index or absorbance to known density-composition relationships in binary mixtures.^[29]^[32] This multifaceted use underscores its foundational role in precise chemical and materials characterization.

In Engineering and Geology

In engineering applications, particularly in fluid dynamics and naval architecture, relative density plays a critical role in buoyancy calculations for ships and floating structures. The buoyancy of a vessel depends on the density of the surrounding water, with saltwater typically exhibiting a relative density of 1.025 compared to pure water, which influences the maximum allowable draft to ensure reserve buoyancy and stability.^[33] This value is standardized in the International Convention on Load Lines (1966), administered by the International Maritime Organization (IMO), where load line marks on hulls are adjusted based on water density zones—such as tropical fresh water (relative density 1.000), brackish water (transition zones), and saltwater (1.025)—to prevent overloading and maintain freeboard. For instance, in saltwater ports, ships can load deeper due to the higher supporting density, directly affecting cargo capacity and safety compliance under IMO regulations.^[34] In the petroleum industry, relative density is essential for grading and classifying crude oils, often through the API gravity scale, which inversely relates to density. The API gravity is calculated using the formula:

^\circ \text{API} = \frac{141.5}{\text{RD}} - 131.5

where RD is the relative density (specific gravity) of the oil at 15.6°C (60°F) relative to water at the same temperature.^[35] This scale, developed by the American Petroleum Institute, categorizes crude oils: light crudes have relative densities around 0.80–0.85 (API >35°), medium crudes 0.85–0.90 (API 22–35°), and heavy crudes 0.90–0.95 (API <22°), influencing refining processes, transportation, and pricing due to variations in viscosity and yield. For example, West Texas Intermediate crude typically has a relative density of about 0.83, enabling efficient pipeline flow, while heavier Venezuelan crudes near 0.95 require specialized handling to mitigate settling and pumping challenges.^[36] In geotechnical engineering, particularly soil mechanics, relative density (often denoted as D_r) quantifies the compaction state of granular soils like sands, aiding in foundation design and stability assessments. It is defined as:

D_r = \frac{e_{\max} - e}{e_{\max} - e_{\min}} \times 100\%

where e is the in-situ void ratio, e_{\max} is the maximum void ratio (loosest state), and e_{\min} is the minimum void ratio (densest state), determined per ASTM D4254 standard test methods.^[37] Soils with D_r < 30\% are classified as loose, exhibiting lower shear strength and higher settlement potential, while those with D_r > 70\% are dense, providing greater bearing capacity and resistance to liquefaction during seismic events.^[38] This parameter guides compaction specifications in construction, such as achieving D_r > 70\% for highway embankments to ensure long-term durability.^[39] In geological prospecting, relative density contrasts between ore bodies and host rocks enable detection via gravimetric surveys, exploiting density differences for subsurface mapping. High-density minerals like galena (lead sulfide, relative density approximately 7.5) create measurable gravitational anomalies when embedded in lower-density rocks such as granite (relative density ~2.75), facilitating the identification of lead deposits without invasive drilling.^[40] For instance, in epithermal or sedimentary-hosted systems, these anomalies—often on the order of 1–5 mGal for meter-thick veins—guide targeted exploration, as demonstrated in surveys for Mississippi Valley-type lead-zinc ores where galena's density signature outperforms other geophysical methods in resistive terrains. This approach has been instrumental in high-impact discoveries, prioritizing regions with pronounced density gradients for efficient resource delineation.^[41]

Measurement Techniques

Volumetric Methods

Volumetric methods for measuring relative density rely on the displacement of volume by a liquid sample, typically using devices like hydrometers or pycnometers that compare the sample's volume to that of water under controlled conditions. These techniques are particularly suited for liquids, as they exploit principles of buoyancy and precise volume calibration to determine the ratio of the sample's density to that of water. Measurements are standardized at a temperature of 20°C to minimize variations due to thermal expansion, ensuring consistency across applications.^[4] The hydrometer is a buoyant instrument consisting of a weighted bulb and a graduated stem, operating on Archimedes' principle of flotation equilibrium. When immersed in a liquid sample contained in a tall cylinder, the hydrometer floats such that the displaced liquid's weight equals the instrument's weight, with the equilibrium position indicated on the scale corresponding directly to the relative density (RD), calibrated against water as 1.000. For example, in the Baumé scale commonly used for industrial liquids denser than water, the reading °Bé relates to RD via the formula

^\circ\text{Bé} = 145 - \frac{145}{\text{RD}}

allowing conversion for substances like acids or brines.^[42]^[43] To perform a hydrometer measurement, first equilibrate the liquid sample to 20°C in a clean glass cylinder, ensuring the volume is sufficient to allow free floating without wall effects. Gently lower the calibrated hydrometer into the sample, allowing it to settle without touching the sides, and read the scale at the bottom of the meniscus for accuracy. If the observation temperature differs from 20°C, apply correction tables to adjust the reading, accounting for the liquid's thermal expansion coefficient. This method achieves a typical accuracy of ±0.001 in relative density, making it efficient for routine assessments in fields like petroleum testing.^[42]^[44] The pycnometer, a flask of known volume with a ground-glass stopper and capillary side arm, provides higher precision for small liquid samples by directly comparing masses at fixed volume. The relative density is calculated as

\text{RD} = \frac{m_\text{liquid} - m_\text{empty}}{m_\text{water} - m_\text{empty}}

where m_\text{liquid} is the mass of the pycnometer filled with the sample, m_\text{water} is the mass when filled with water, and m_\text{empty} is the unfilled mass, all at 20°C; the volume terms cancel since the same pycnometer is used. This approach yields precision up to 0.0001 for volumes around 10–25 mL, ideal for volatile or viscous liquids.^[45] For pycnometer use, begin by cleaning and drying the flask, then weigh it empty to four decimal places. Fill it completely with distilled water at 20°C, ensuring no air bubbles via the capillary, insert the stopper, dry the exterior, and reweigh. Empty and rinse the pycnometer thoroughly, then repeat the filling and weighing process with the liquid sample at the same temperature, using a water bath for equilibration if necessary. Subtract the empty mass from each filled mass and compute RD as shown; for enhanced accuracy (±0.0002 or better), calibrate the pycnometer volume periodically against standard weights. These steps ensure reliable results for laboratory analysis of pure liquids or solutions.^[45]^[46]

Gravimetric Methods

Gravimetric methods for determining relative density rely on measuring the mass of a sample in air and when immersed in a fluid, typically water, to infer density through principles of buoyancy. These techniques are particularly suited for solid objects and powders where direct volume measurement is challenging due to irregular shapes. The core approach stems from Archimedes' principle, which states that the buoyant force on an immersed object equals the weight of the displaced fluid.^[47] In hydrostatic weighing, the relative density (RD) of a solid is calculated using the formula:

\text{RD} = \frac{W_{\text{air}}}{W_{\text{air}} - W_{\text{immersed}}}

where W_{\text{air}} is the weight of the sample in air and W_{\text{immersed}} is its apparent weight when fully submerged in water at a standard temperature (usually 4°C, where water density is 1 g/cm³). This equation derives directly from Archimedes' principle by equating the volume of the sample to the volume of displaced water and normalizing by water's density, yielding a dimensionless ratio.^[47]^[48] A small correction is applied for air buoyancy, as the sample experiences an upward force in air equivalent to approximately 0.0012 times its relative density (using standard air density of 1.2 kg/m³). The corrected weight in air is thus W_{\text{air, corr}} = W_{\text{air}} - 0.0012 \cdot \text{RD} \cdot \rho_{\text{water}}, though for most practical purposes with densities above 1, this adjustment is minor (less than 0.1% error if neglected). This correction ensures higher precision in vacuum-referenced measurements.^[49] The procedure involves suspending the sample from a balance using a thin wire or cradle to avoid contact with container walls, weighing it in air, then immersing it in degassed water while minimizing oscillations. Error sources include surface tension effects at the sample-water interface, which can add spurious forces up to 0.1-0.5% for small or porous samples; these are mitigated by adding wetting agents like a few drops of surfactant (e.g., Triton X-100) to reduce interfacial tension or by heating the water slightly to 20-25°C for better flow. Additionally, incomplete immersion or air bubbles are avoided through pre-wetting and vacuum degassing.^[50]^[48] These methods excel for solids and powders, including irregular shapes like rock fragments or metal alloys, where volumetric techniques falter. For powders, the sample is formed into a cohesive pellet or measured in a sealed container to prevent water ingress. Achievable accuracy is typically ±0.005 in relative density units, limited by balance precision (0.1 mg) and immersion stability, making it suitable for metallurgical quality control and material characterization.^[47]^[48]

Instrumental Methods

Digital density meters represent a cornerstone of modern instrumental methods for determining relative density, primarily through automated oscillation-based techniques that offer high precision and speed for liquid samples. These devices operate on the oscillating U-tube principle, where a U-shaped tube filled with the sample is vibrated electronically at its resonant frequency. The resonant frequency f is inversely proportional to the square root of the sample's density \rho, such that f \propto 1 / \sqrt{\rho}.^[51] Consequently, the density is proportional to the inverse square of the frequency, \rho \propto 1 / f^2, allowing relative density (RD) to be calculated as \mathrm{RD} = f_{\mathrm{reference}}^2 / f_{\mathrm{sample}}^2, where the reference is typically water at a standard temperature.^[52] This method achieves accuracies of ±0.0001 g/cm³, making it suitable for applications requiring precise compositional analysis.^[51] Many advanced digital density meters integrate viscometers to simultaneously measure viscosity, as the damping of the U-tube oscillation provides data on viscous effects that can influence density readings in non-Newtonian fluids. However, these instruments are primarily designed for liquids and face limitations with gases or highly viscous samples. For gases, relative density is typically measured using specialized gas densitometers or calculated from the molecular weight relative to air.^[53] Post-2000 models have incorporated full automation, including sample injection and temperature control, in compliance with standards like ISO 12185 for petroleum products, enabling rapid measurements in seconds compared to minutes for traditional volumetric or gravimetric approaches, though they necessitate periodic calibration with certified reference fluids to maintain accuracy.^[54] Emerging technologies address challenges with opaque or complex samples that are incompatible with optical or transparent-tube methods. Time-domain nuclear magnetic resonance (TD-NMR) instruments, for instance, enable non-invasive density determination by analyzing relaxation times of hydrogen nuclei in the sample, providing relative density insights for opaque liquids and solids without requiring transparency or dilution.^[55] These NMR-based systems, such as benchtop analyzers, offer portability and minimal sample preparation, extending instrumental capabilities to materials like polymers where conventional U-tube methods falter.^[56]

Illustrative Examples

Everyday Substances

Relative density, also known as specific gravity, provides a dimensionless measure of how the density of everyday substances compares to a standard reference—typically water at 4°C for liquids and solids (density of 1000 kg/m³), and dry air at standard conditions for gases. This property influences practical phenomena such as buoyancy and material selection in daily life. For common liquids encountered in households and food preparation, water serves as the baseline with a relative density of 1.000 (at 4 °C) by definition. Milk, a staple beverage, has a relative density of approximately 1.03 at 20°C, varying slightly with fat content and seasonal factors due to its composition of water, fats, proteins, and lactose.^[57] Olive oil, used in cooking, exhibits a relative density of 0.91 at 20°C, making it less dense than water and thus able to float on aqueous mixtures.^[58] Among everyday solids, ice—formed from frozen water—has a relative density of 0.917 at 0°C, which explains why it floats in liquid water despite both being composed of H₂O molecules arranged differently in solid and liquid phases.^[59] Aluminum, a lightweight metal in cans and foil, possesses a relative density of 2.70, indicating it is 2.7 times denser than water and sinks readily.^[60] Wood, used in furniture and construction, shows a variable relative density ranging from 0.4 to 0.8 depending on species (e.g., pine around 0.4–0.5, oak around 0.6–0.8), influenced by cellular structure and moisture content; this range allows many woods to float while providing structural strength. For gases in daily environments, such as those in balloons or breathing air, helium has a relative density of 0.138 compared to air, enabling it to rise and fill party balloons due to its low molecular weight.^[20] Oxygen, comprising about 21% of air and essential for respiration, has a relative density of 1.105 relative to air, making it slightly denser and contributing to its tendency to settle in confined spaces if pure.^[61] These relative densities manifest in everyday contexts like buoyancy during swimming, where the average human body has a relative density of approximately 0.98—close enough to water's 1.000 that people float with minimal effort, aided by lung air volume.^[62] In automotive use, gasoline's relative density of 0.74 at 20°C affects fuel efficiency, as its lower density relative to water influences storage volume, engine performance, and energy yield per unit mass in vehicles.^[63]

Specialized Cases

Among the densest naturally occurring elements, osmium exhibits a relative density of 22.59, making it exceptionally heavy for its volume and historically alloyed with iridium for applications requiring extreme durability, such as the tipping of fountain pen nibs to resist wear during prolonged use.^[64]^[65] At the opposite extreme, aerogels represent some of the least dense solid materials known, with silica-based variants achieving relative densities as low as 0.001, owing to their nanoporous structure that traps over 99% air by volume, enabling uses in thermal insulation and cosmic dust capture. A seminal historical application of relative density measurement dates to around 287 BC, when Archimedes of Syracuse was tasked by King Hieron II to verify the purity of a golden crown suspected of being adulterated with silver by a fraudulent goldsmith; by comparing the crown's mass to the volume of water it displaced in a bath—revealing a relative density lower than pure gold's 19.3—the method confirmed the alloy's impurity through the principle that equal masses of pure gold and the alloy would displace unequal volumes due to the latter's reduced density.^[66] This anecdote, first recorded by the Roman architect Vitruvius in the first century BC, illustrates an early quantitative verification: for a 700-gram crown of pure gold (volume ≈36.3 cm³ at density 19.3 g/cm³) versus a gold-silver alloy (e.g., 70% gold, density ≈15.6 g/cm³, volume ≈44.9 cm³), the greater displacement by the alloy exposes the fraud without damaging the artifact.^[66] In industrial contexts, supercritical fluids exemplify anomalous relative densities under extreme conditions; for instance, carbon dioxide at its critical point (31°C and 73 atm) achieves a relative density of approximately 0.47, behaving as a hybrid of liquid and gas with tunable solvating properties for extraction processes in pharmaceuticals and decaffeination.^[67] Similarly, food emulsions like mayonnaise demonstrate relative densities ranging from 0.9 to 1.0, arising from the stabilized oil-in-water mixture of lipids, vinegar, and emulsifiers, which influences product stability and pourability in manufacturing.^[68] Outdated practices highlight safety-driven shifts away from high-density liquids; mercury, with a relative density of 13.6, was once ubiquitous in barometers for its uniform expansion and visibility in measuring atmospheric pressure, but its use has been largely phased out since the early 2000s due to neurotoxic vapor emissions and environmental persistence, replaced by safer digital or aneroid alternatives under regulations like the Minamata Convention.^[69]^[70]

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Carbon dioxide - Density and Specific Weight vs. Temperature and ...
This page provides online calculators, figures, and tables showing carbon dioxide density and specific weight at temperatures from -50 to 775 °C and various ...
[25]
Compressibility of Liquids - HyperPhysics
For each atmosphere increase in pressure, the volume of water would decrease 46.4 parts per million. The compressibility k is the reciprocal of the Bulk modulus ...
[26]
ISO 6976:2016 - Natural gas — Calculation of calorific values ...
CHF 199.00 In stockISO 6976:2016 specifies methods for the calculation of gross calorific value, net calorific value, density, relative density, gross Wobbe index and net Wobbe ...
[27]
How to Calculate Alloy Density?
Method 1: Rule of Mixtures (Theoretical Density Calculation). The most commonly used approach to estimate the density of an alloy is the Rule of Mixtures.
[28]
Gauging Manual | TTB - Alcohol and Tobacco Tax and Trade Bureau
That liquid which contains one-half its volume of ethyl alcohol of a specific gravity of seven thousand nine hundred and thirty-nine ten-thousandths (0.7939) in ...
[29]
Measurement of Physical Properties | ACS Reagent Chemicals
Feb 28, 2017 · The ACS Committee on Analytical Reagents defines procedures for measuring the physical properties of substances including: Boiling Range, Color (APHA), ...<|control11|><|separator|>
[30]
Graphite Mineral Data - Mineralogy Database
note: Specific Gravity of Graphite =2.25 gm/cc. U=PEGraphite x rElectron Density= 0.36 barns/cc.
[31]
Sorting Recyclable Plastics by Density - Chemistry LibreTexts
Mar 10, 2023 · Plastics are sorted by density using floatation in brine solutions. Heavy plastics sink, while lighter ones float, based on mass per unit ...
[32]
[PDF] Test No. 109: Density of Liquids and Solids (EN) - OECD
Oct 2, 2012 · The density measurement of an aerosol product is performed on the liquid remaining after the aerosol product has been depressurized.
[33]
[PDF] resolution msc.143(77) - International Maritime Organization
Jun 5, 2003 · Resolution MSC.143(77) adopts amendments to the 1988 Load Lines Protocol, specifically to Annex B, which relates to the International ...
[34]
[PDF] MERCHANT SHIPPING (LOAD LINES) REGULATIONS 2019
tonne per cubic meter) is less dense than salt seawater (density 1.025 tonnes per cubic meter), ... Figure 1 - Load line mark and lines to be used with this mark.<|control11|><|separator|>
[35]
API Gravity: Definition, Calculation, and Converter
API gravity express the gravity or density of crude oil and liquid petroleum products. API is devised jointly by the American Petroleum Institute and the NIST.
[36]
API Gravity | FSC 432: Petroleum Refining
... the API gravity (°API) as a measure of the crude oil density. The API gravity is calculated from the following equation: °API=141.5SG15.6°C/15.6°C ...
[37]
D4254 Standard Test Methods for Minimum Index Density and Unit ...
Jul 10, 2025 · 5.2 Relative density/unit weight expresses the degree of compactness of a cohesionless soil with respect to the loosest and densest condition as ...Missing: mechanics formula
[38]
2.4: Soil Mechanical Parameters - Engineering LibreTexts
Mar 5, 2021 · Table 2-6: Designation of Granular Soil Based on Relative Density. Dr (%). Description. 0 - 20. Very loose. 20 - 40. Loose. 40 - 70. Medium ...<|control11|><|separator|>
[39]
Relative density of soil and its significance and limits - eigenplus
Limit for granular soil ; Relative density %, Classification ; <15, Very loose ; 15-35, Loose ; 35-65, Medium ; 65-85, Dense.Missing: thresholds | Show results with:thresholds
[40]
Geophysical Prospecting Using ERT and IP Techniques to Locate ...
Galena (PbS) has a much larger density (7600 kg/m3) than the hosting rock (granite, 2750 kg/m3). However, the gravimetric anomaly [9] of a one-meter-thick ...Missing: relative | Show results with:relative
[41]
Test method for minimum and maximum densities of small quantities ...
The objective of this study is to develop an alternative test method for evaluating the minimum and maximum densities of soil.Missing: mechanics formula
[42]
D1298 Standard Test Method for Density, Relative Density, or API ...
Mar 14, 2023 · ASTM D1298 is a standard test method for determining the density, relative density, or API gravity of petroleum products using a hydrometer in ...
[43]
Baume's Hydrometer - The Engineering ToolBox
Baume's Hydrometer measures liquid density in degree Baumé, with two scales: one for liquids heavier than water and one for lighter.Missing: relative | Show results with:relative
[44]
How to Use and Read a Hydrometer - Grainger KnowHow
Dec 16, 2022 · A hydrometer is an instrument used to determine specific gravity. It operates based on the Archimedes principle that a solid body displaces its own weight ...
[45]
Determination of Weight Per Millilitre and Relative Density
Jul 17, 2011 · Subtract the tare weight of the pycnometer from the filled weight of the pycnometer. Determine the weight per milliliter by dividing the weight ...
[46]
[PDF] 3 Ways to Measure Density Know-How, Hints, and More
In simple terms, a hydrometer tells the user if a liquid is more or less dense than water.
[47]
[PDF] Density of Solids and Liquids | 911 Metallurgist
The hydrostatic weighing method may be used preferable to a silk thread since large errors may for determiming the density of solids and liquids be introduced ...
[48]
[PDF] Procedure for high precision density determinations by hydrostatic ...
The procedure involves simplifications, balance modifications, a heating technique to minimize surface tension, and a boiling procedure for degassing samples.Missing: specific agents
[49]
[PDF] SOP 2 Applying Air Buoyancy Corrections
Calculate the average density of air at the balance during the weighing. Then determine the mass of the unknown, Mx, as follows: If a two-pan balance is ...Missing: hydrostatic specific solids
[50]
Study on influence of liquid surface tension on solid density ...
Aug 6, 2025 · Hydrostatic weighing is widely used in solid density measurement, and it is also a method with high accuracy. The influence of liquid ...
[51]
[PDF] IS 2720-28 (1974): Methods of test for soils, Part 28
The steel core cutter shall be pressed evenly and carefully into the soil until its top edge is flush with the levelled surface. Soil to a depth of. leO mm (sre ...
[52]
[PDF] IS 2720-29 (1975): Methods of Test for Soils, Part 29
This part [ IS:2720 (Part XXIX )-1975] deals with the determina- tion of dry density of soil in-place by using a core-cutter. The in-place density of soil is ...<|control11|><|separator|>
[53]
Density Measurement: All You Need to Know | METTLER TOLEDO
Determination of density using digital meters is based on two factors: The oscillation, or vibration, of a U-shaped glass tube (U-tube).Density Explained · Factors That Affect Density... · Examples of Specific Gravity...
[54]
U-tube technology in digital laboratory density meters
Common laboratory density meters make use of a Y-oscillator (“U-tube”). Its bend moves up and down. This setup is compact and allows for precise temperature ...Missing: relative | Show results with:relative
[55]
Gas pycnometers - Micromeritics
Gas pycnometry is a fast, precise, and cost-effective technique for measuring the volume of powders, solid, and liquid materials, enabling reproducible and ...
[56]
ISO 12185:2024 - Determination of density
In stock 2–5 day deliveryThis document specifies a method for the determination, using an oscillating U-tube density meter, of the density of crude petroleum and related products.
[57]
MQC-R - Oxford Instruments Magnetic Resonance
Oxford Instruments MQC-R is a highly flexible benchtop time domain (TD-NMR) instrument designed to be the perfect benchtop materials analysis solution.
[58]
Oxford Instruments launches the MQC+ benchtop NMR analyser for ...
Jun 15, 2017 · It can also measure physical properties including crystallinity and density of polymers. MQC+ available as three models. MQC+23 has been ...
[59]
Density of Milk - The Physics Factbook - hypertextbook
Weight Density and Specific Gravity of Various Liquids. ... "With all of this in mind, the density of milk varies within the range of 1027 to 1033 kg m(-3) at 20° ...
[60]
Liquids - Specific Gravities - The Engineering ToolBox
Olive oil, 15.6, 0.91 - 0.92. Palm oil, 15.6, 0.924. Peanut oil, 15.6, 0.92. Pentane ... Viscosity at 20°C/68°F and 50°C/122°F for more than 120 crudes is shown ...
[61]
Density of Ice - The Physics Factbook - hypertextbook
At 0° C it has specific gravity 0.9168 as compared to specific gravity 0.9998 of water at the same temperature. As a result, ice floats in water."
[62]
Metals and Alloys - Densities - The Engineering ToolBox
Densities of some common metals, metallic elements and alloys - aluminum, bronze, copper, iron and more. ; Aluminum, 2712 ; Aluminum - melted, 2560 - 2640.<|separator|>
[63]
Gases - Specific Gravities - The Engineering ToolBox
Specific gravities of air, ammonia, butadiene, carbon dioxide, carbon monoxide and some other common gases. ; Oxygen - O · 1.1044 ; Ozone, 1.660 ; n - Pentane ...
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The Basics of Buoyancy | AQUA Magazine
Jun 14, 2016 · On average, the human body has a buoyancy of . 98 in water; meaning most of us are just barely lighter than water and therefore able to float.
[65]
Specific Gravity Table: Liquids, Gases, and Solids - Alfa Chemistry
Alfa Chemistry provides the following table of the specific gravity of liquids, gases, and solids for you to look over.Missing: contamination | Show results with:contamination
[66]
Density | Periodic Table of Elements - PubChem
Density [g/cm³]. 1, H, Hydrogen · 0.00008988. 2, He, Helium · 0.0001785. 3, Li, Lithium ... Osmium · 22.57. 77, Ir, Iridium · 22.42. 78, Pt, Platinum · 21.46. 79
[67]
Osmium Used in Fountain Pen Tips - TANAKA Precious Metals
Alloy of osmium and iridium improves durability of fountain pens. Osmium alloy is used for fountain pen points, with the alloy called osmiridium when osmium is ...
[68]
The Golden Crown (Introduction)
Silver has a density of 10.5 grams/cubic-centimeter and so the gold-silver crown would have a volume of 700/19.3 + 300/10.5 = 64.8 cubic-centimeters. Such a ...
[69]
Carbon Dioxide | CO2 | CID 280 - PubChem
... K and 101.3 kPa; gas density = 1.976 g/L at 273 K and 101.3 kPa. Pierantozzi R; Carbon Dioxide. Kirk-Othmer Encyclopedia of Chemical Technology. (1999-2015) ...
[70]
Specific gravities - Food Standards Australia New Zealand
Sep 30, 2025 · Mayonnaise, low fat, 1.08. Mayonnaise, reduced fat, 1.05. Mayonnaise, regular fat, 0.99. Milk, canned, evaporated, regular or reduced fat ...Missing: relative | Show results with:relative
[71]
https://www.physics.nist.gov/cgi-bin/Star/compos.pl?mode=text&matno=080
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Phasing Out Mercury Thermometers Used in Industrial and ...
Mercury spilled from broken thermometers also poses an environmental and safety risk. Alternatives exist for almost all uses of mercury-filled glass ...Questions and Answers · Selecting Alternatives