Density

In a well-known but probably apocryphal tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to the gods and replacing it with another, cheaper alloy.[3] Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass; but the king did not approve of this. Baffled, Archimedes is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the displacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!" (Εύρηκα! Greek "I have found it"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.

The story first appeared in written form in Vitruvius' books of architecture, two centuries after it supposedly took place.[4] Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time.[5][6]

From the equation for density (ρ = m/V), mass density has units of mass divided by volume. As there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per cubic metre (kg/m³) and the cgs unit of gram per cubic centimetre (g/cm³) are probably the most commonly used units for density. One g/cm³ is equal to 1000 kg/m³. One cubic centimetre (abbreviation cc) is equal to one millilitre. In industry, other larger or smaller units of mass and or volume are often more practical and US customary units may be used. See below for a list of some of the most common units of density.

A number of techniques as well as standards exist for the measurement of density of materials. Such techniques include the use of a hydrometer (a buoyancy method for liquids), Hydrostatic balance (a buoyancy method for liquids and solids), immersed body method (a buoyancy method for liquids), pycnometer (liquids and solids), air comparison pycnometer (solids), oscillating densitometer (liquids), as well as pour and tap (solids).[7] However, each individual method or technique measures different types of density (e.g. bulk density, skeletal density, etc.), and therefore it is necessary to have an understanding of the type of density being measured as well as the type of material in question.

In general, density can be changed by changing either the pressure or the temperature. Increasing the pressure always increases the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behavior is observed in silicon at low temperatures.

The effect of pressure and temperature on the densities of liquids and solids is small. The compressibility for a typical liquid or solid is 10⁻⁶ bar⁻¹ (1 bar = 0.1 MPa) and a typical thermal expansivity is 10⁻⁵ K⁻¹. This roughly translates into needing around ten thousand times atmospheric pressure to reduce the volume of a substance by one percent. (Although the pressures needed may be around a thousand times smaller for sandy soil and some clays.) A one percent expansion of volume typically requires a temperature increase on the order of thousands of degrees Celsius.

In contrast, the density of gases is strongly affected by pressure. The density of an ideal gas is

${\displaystyle \rho ={\frac {MP}{RT}},}$

where M is the molar mass, P is the pressure, R is the universal gas constant, and T is the absolute temperature. This means that the density of an ideal gas can be doubled by doubling the pressure, or by halving the absolute temperature.

In the case of volumic thermal expansion at constant pressure and small intervals of temperature the temperature dependence of density is :

${\displaystyle \rho ={\frac {\rho _{T_{0}}}{1+\alpha \cdot \Delta T}}}$

where ${\displaystyle \rho _{T_{0}}}$ is the density at a reference temperature, ${\displaystyle \alpha }$ is the thermal expansion coefficient of the material at temperatures close to ${\displaystyle T_{0}}$.

The density of a solution is the sum of mass (massic) concentrations of the components of that solution.

Mass (massic) concentration of each given component ρ_i in a solution sums to density of the solution.

${\displaystyle \rho =\sum _{i}\varrho _{i}\,}$

Expressed as a function of the densities of pure components of the mixture and their volume participation, it allows the determination of excess molar volumes:

${\displaystyle \rho =\sum _{i}\rho _{i}{\frac {V_{i}}{V}}\,=\sum _{i}\rho _{i}\varphi _{i}=\sum _{i}\rho _{i}{\frac {V_{i}}{\sum _{i}V_{i}+\sum _{i}{V^{E}}_{i}}}}$

provided that there is no interaction between the components.

Knowing the relation between excess volumes and activity coefficients of the components, one can determine the activity coefficients.

${\displaystyle {\overline {V^{E}}}_{i}=RT{\frac {\partial \ln \gamma _{i}}{\partial P}}}$

The SI unit for density is:

• kilogram per cubic metre (kg/m³)

The litre and metric tons are not part of the SI, but are acceptable for use with it, leading to the following units:

• kilogram per litre (kg/L)
• gram per millilitre (g/mL)
• metric ton per cubic metre (t/m³)

Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m³). Liquid water has a density of about 1 kg/dm³, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm³.

• kilogram per cubic decimetre (kg/dm³)
• gram per cubic centimetre (g/cm³)
  • 1 g/cm³ = 1000 kg/m³
• megagram (metric ton) per cubic metre (Mg/m³)

In US customary units density can be stated in:

• Avoirdupois ounce per cubic inch (1 g/cm³ ≈ 0.578036672 oz/cu in)
• Avoirdupois ounce per fluid ounce (1 g/cm³ ≈ 1.04317556 oz/US fl oz = 1.04317556 lb/US fl pint)
• Avoirdupois pound per cubic inch (1 g/cm³ ≈ 0.036127292 lb/cu in)
• pound per cubic foot (1 g/cm³ ≈ 62.427961 lb/cu ft)
• pound per cubic yard (1 g/cm³ ≈ 1685.5549 lb/cu yd)
• pound per US liquid gallon (1 g/cm³ ≈ 8.34540445 lb/US gal)
• pound per US bushel (1 g/cm³ ≈ 77.6888513 lb/bu)
• slug per cubic foot

Imperial units differing from the above (as the Imperial gallon and bushel differ from the US units) in practice are rarely used, though found in older documents. The Imperial gallon was based on the concept that an Imperial fluid ounce of water would have a mass of one Avoirdupois ounce, and indeed 1 g/cm³ ≈ 1.00224129 ounces per Imperial fluid ounce = 10.0224129 pounds per Imperial gallon. The density of precious metals could conceivably be based on Troy ounces and pounds, a possible cause of confusion.

• "Density" . Encyclopædia Britannica. 8 (11th ed.). 1911.
•  "Density" . The New Students Reference Work . 1914.
• Video: Density Experiment with Oil and Alcohol
• Video: Density Experiment with Whiskey and Water
• Glass Density Calculation – Calculation of the density of glass at room temperature and of glass melts at 1000 – 1400°C
• List of Elements of the Periodic Table – Sorted by Density
• Calculation of saturated liquid densities for some components
• Field density test
• On-line calculator for densities and partial molar volumes of aqueous solutions of some common electrolytes and their mixtures, at temperatures up to 323.15 K.
• Water – Density and specific weight
• Temperature dependence of the density of water – Conversions of density units
• A delicious density experiment
• Water density calculator Water density for a given salinity and temperature.
• Liquid density calculator Select a liquid from the list and calculate density as a function of temperature.
• Gas density calculator Calculate density of a gas for as a function of temperature and pressure.
• Densities of various materials.
• Determination of Density of Solid, instructions for performing classroom experiment.
• density prediction
• density prediction