Density

Density
Density
Dimension	L −3 M
Units
SI	kg / m³
GHS	g / cm³
Notes
	scalar quantity

Density is a scalar physical quantity , defined as the ratio of body mass to the volume occupied by this body ^[1] .

To denote density, the Greek letter ρ [ro] is usually used (the origin of the notation is to be specified), sometimes the Latin letters D and d are also used (from the Latin densitas “density”).

A more accurate determination of the density requires clarification of the wording:

Average body density is the ratio of body weight to its volume. For a homogeneous body, it is also called simply body density .
The density of a substance is the density of a homogeneous or uniformly inhomogeneous body consisting of this substance.
The density of a body at a point is the limit of the mass ratio of a small part of the body ( $\Delta m$ ${\ displaystyle \ Delta m}$ $\ Delta m$ ) containing this point to the volume of this small part ( $\Delta V$ ${\ displaystyle \ Delta V}$ ${\ displaystyle \ Delta V}$ ), when this volume tends to zero ^[2] , or, writing down briefly, $\lim _{\Delta V\to 0}{\Delta m/\Delta V}$ ${\ displaystyle \ lim _ {\ Delta V \ to 0} {\ Delta m / \ Delta V}}$ ${\ displaystyle \ lim _ {\ Delta V \ to 0} {\ Delta m / \ Delta V}}$ . With such a passage to the limit, it must be remembered that at the atomic level any body is inhomogeneous, therefore it is necessary to dwell on the volume corresponding to the physical model used .

Since the mass in the body can be distributed unevenly, a more adequate model determines the density at each point in the body as a derivative of the mass by volume. If we take into account the point masses, then the density can be defined as a measure , or as a Radon-Nicodemus derivative with respect to some reference measure.

Content

1 Types of density and units
2 Density Formula
3 Density versus temperature
4 Range of densities in nature
5 Densities of astronomical objects
6 Densities of some gases
7 Density of some liquids
8 Density of some wood species
9 Density of some metals
10 Density Measurement
11 See also
12 Notes
13 Literature
14 References

Density Types and Units

Based on the definition of density, its dimension is kg / m³ in SI and g / cm³ in the GHS system.

For bulk and porous bodies distinguish:

true density, determined without taking into account voids;
specific (apparent) density , calculated as the ratio of the mass of a substance to the entire volume occupied by it. The true density is obtained from the apparent density using the value of the porosity coefficient - a fraction of the volume of voids in the occupied volume. For bulk solids, specific gravity is called bulk density .

Density Formula

Density (density of a homogeneous body or average density of a heterogeneous) is found by the formula:

\rho ={\frac {m}{V}},

{\ displaystyle \ rho = {\ frac {m} {V}},}

where m is body weight, V is its volume; the formula is simply a mathematical record of the definition of the term “density” given above.

When calculating the density of gases under normal conditions, this formula can be written in the form:

\rho ={\frac {M}{V_{m}}},

{\ displaystyle \ rho = {\ frac {M} {V_ {m}}},}

where M is the molar mass of gas,

V_{m}

{\ displaystyle V_ {m}}

- molar volume (under normal conditions, approximately equal to 22.4 l / mol).

The density of a body at a point is written as

\rho ={\frac {dm}{dV}},

{\ displaystyle \ rho = {\ frac {dm} {dV}},}

then the mass of the inhomogeneous body (body with a density depending on the coordinates) is calculated as

m=\int \rho (\mathbf {r} )d^{3}\mathbf {r} =\int \rho (\mathbf {r} )dV=\int dm.

{\ displaystyle m = \ int \ rho (\ mathbf {r}) d ^ {3} \ mathbf {r} = \ int \ rho (\ mathbf {r}) dV = \ int dm.}

Density versus temperature

As a rule, with decreasing temperature, the density increases, although there are substances whose density in a certain temperature range behaves differently, for example, water , bronze and cast iron . Thus, the density of water has a maximum value at 4 ° C and decreases both with increasing and decreasing temperature relative to this value.

When the state of aggregation changes, the density of the substance changes stepwise: the density increases during the transition from the gaseous state to the liquid state and upon solidification of the liquid. Water , silicon , bismuth, and some other substances are exceptions to this rule, since their density during solidification decreases.

Density Range in Nature

For various natural objects, the density varies in a very wide range.

The intergalactic medium has the lowest density (2 · 10 ⁻³¹ –5 · 10 ⁻³¹ kg / m³, excluding dark matter ) ^[3] .
The density of the interstellar medium is approximately 10 ⁻²³ –10 ⁻²¹ kg / m³.
The average density of red giants within their photospheres is much lower than that of the Sun - due to the fact that their radius is hundreds of times larger with a comparable mass.
The density of gaseous hydrogen (the lightest gas) under normal conditions is 0.0899 kg / m³.
The density of dry air under normal conditions is 1.293 kg / m³.
One of the heaviest gases, tungsten hexafluoride , is about 10 times heavier than air (12.9 kg / m³ at +20 ° C)
At atmospheric pressure and a temperature of −253 ° C, liquid hydrogen has a density of 70 kg / m³.
The density of liquid helium at atmospheric pressure is 130 kg / m³.
The average density of the human body is from 940–990 kg / m³ with a full breath, up to 1010–1070 kg / m³ with a full exhalation.
The density of fresh water at 4 ° C is 1000 kg / m³.
The average density of the Sun within the photosphere is about 1410 kg / m³, about 1.4 times higher than the density of water.
Granite has a density of 2600 kg / m³.
The average density of the Earth is 5520 kg / m³.
The density of iron is 7874 kg / m³.
The density of uranium metal is 19100 kg / m³.
The density of gold is 19320 kg / m³.
The density of heavy platinum metals is 21,400–22,700 kg / m³.
The density of atomic nuclei is approximately 2 · 10 ¹⁷ kg / m³.
Theoretically, the upper limit of density according to modern physical concepts is the Planck density of 5.1⋅10 ⁹⁶ kg / m³.

Densities of astronomical objects

The average density of solar celestial bodies
systems (in g / cm³) ^[4] ^[5] ^[6]

The average density of the celestial bodies of the solar system, see the sidebar.
The interplanetary medium in the Solar system is quite heterogeneous and can change in time, its density in the vicinity of the Earth is ~ 10 ⁻²¹ ÷ 10 ⁻²⁰ kg / m³.
The density of the interstellar medium is ~ 10 ⁻²³ ÷ 10 ⁻²¹ kg / m³.
The density of the intergalactic medium is 2 × 10 ⁻³⁴ ÷ 5 × 10 ⁻³⁴ kg / m³.
The average density of red giants is many orders of magnitude lower due to the fact that their radius is hundreds of times larger than that of the Sun.
White dwarf density 10 ⁸ ÷ 10 ¹² kg / m³
The density of neutron stars is of the order of 10 ¹⁷ ÷ 10 ¹⁸ kg / m³.
The average (in volume under the event horizon ) density of a black hole depends on its mass and is expressed by the formula:

\rho ={\frac {3\,c^{6}}{32\pi M^{2}G^{3}}}.

{\ displaystyle \ rho = {\ frac {3 \, c ^ {6}} {32 \ pi M ^ {2} G ^ {3}}}.}

The average density decreases inversely with the square of the black hole mass (ρ ~ M ⁻² ). So, if a black hole with a mass of the order of the sun has a density of about 10 ¹⁹ kg / m³ exceeding the nuclear density (2 × 10 ¹⁷ kg / m³), then a supermassive black hole with a mass of 10 ⁹ solar masses (the existence of such black holes is assumed in quasars ) has an average density of about 20 kg / m³, which is significantly less than the density of water (1000 kg / m³).

Density of some gases

The density of gases , kg / m³ at NU .
Nitrogen	1,250	Oxygen	1,429
Ammonia	0.771	Krypton	3,743
Argon	1,784	Xenon	5,851
Hydrogen	0,090	Methane	0.717
Water vapor (100 ° C)	0.598	Neon	0,900
Air	1,293	Radon	9.81
Tungsten Hexafluoride	12.9	Carbon dioxide	1,977
Helium	0.178	Chlorine	3,164
Dizian	2,38	Ethylene	1,260

To calculate the density of an arbitrary ideal gas under arbitrary conditions, you can use the formula derived from the equation of state of an ideal gas : ^[7]

\rho ={\frac {pM}{RT}}

{\ displaystyle \ rho = {\ frac {pM} {RT}}}

,

Where:

$p$ ${\ displaystyle p}$ - pressure
$M$ ${\ displaystyle M}$ - molar mass ,
$R$ ${\ displaystyle R}$ - universal gas constant equal to approximately 8.314 J / (mol · K)
$T$ ${\ displaystyle T}$ - thermodynamic temperature .

Densities of some liquids

The density of liquids , kg / m³
Petrol	710	Milk	1040
Water (4 ° C)	1000	Mercury (0 ° C)	13600
Kerosene	820	Diethyl ether	714
Glycerol	1260	Ethanol	789
Sea water	1030	Turpentine	860
Olive oil	920	Acetone	792
Motor oil	910	Sulphuric acid	1835
Oil	550-1050	Liquid hydrogen (−253 ° C)	70

Density of some wood species

The density of wood , g / cm³
Balsa	0.15	Siberian fir	0.39
Sequoia is evergreen	0.41	Spruce	0.45
Willow	0.46	Alder	0.49
Aspen	0.51	Pine	0.52
Linden	0.53	Horse chestnut	0.56
Edible chestnut	0.59	Cypress	0.60
Bird cherry	0.61	Hazel	0.63
Walnut	0.64	Birch	0.65
Cherry	0.66	Elm smooth	0.66
Larch	0.66	Field maple	0.67
Teak	0.67	Beech	0.68
Pear	0.69	Oak	0.69
Enlightenment ( Mahogany )	0.70	Sycamore	0.70
Joster ( buckthorn )	0.71	Yew	0.75
Ash	0.75	Plum	0.80
Lilac	0.80	Hawthorn	0.80
Pecan (hazel)	0.83	Sandalwood	0.90
Boxwood	0.96	Ebony	1,08
Quebracho	1.21	Lignum vitae	1.28
Bung	0.20

Density of some metals

The density of metals can vary within a very wide range: from the lowest value for lithium , which is lighter than water, to the highest value for osmium , which is heavier than gold and platinum.

The density of metals , g / cm³
Osmium	22.61 ^[8]	Rhodium	12.41 ^[9]	Chromium	7.19 ^[10]
Iridium	22.56 ^[11]	Palladium	12.02 ^[12]	Germanium	5.32 ^[13]
Plutonium	19.84 ^[14]	Lead	11.35 ^[15]	Aluminum	2.70 ^[16]
Platinum	19.59 ^[17]	Silver	10.50 ^[18]	Beryllium	1.85 ^[19]
Gold	19.30 ^[15]	Nickel	8.91 ^[20]	Rubidium	1.53 ^[21]
Uranus	19.05 ^[22]	Cobalt	8.86 ^[23]	Sodium	0.97 ^[24]
Tantalum	16.65 ^[25]	Copper	8.94 ^[26]	Cesium	1.84 ^[27]
Mercury	13.53 ^[28]	Iron	7.87 ^[29]	Potassium	0.86 ^[30]
Ruthenium	12.45 ^[31]	Manganese	7.44 ^[32]	Lithium	0.53 ^[33]

Density Measurement

For density measurements are used:

Pycnometer - a device for measuring true density
Different types of hydrometers are liquid density meters.
Kachinsky drill and Zeidelman drill - instruments for measuring soil density.
Vibration densitometer - a device for measuring the density of liquid and gas under pressure.

Notes

↑ There are also surface densities (mass-to- area ratios) and linear densities (mass-to-length ratios) applied respectively to flat (two-dimensional) and elongated (one-dimensional) objects.
↑ It is also understood that the region is contracted to a point, that is, not only its volume tends to zero (which could be not only when the region is contracted to a point, but, for example, to a segment), but also its diameter tends to zero ( maximum linear size).
↑ Agekyan T.A. Expansion of the Universe. Model of the Universe // Stars, galaxies, Metagalaxy. 3rd ed. / Ed. A. B. Vasiliev. - M .: Nauka , 1982 .-- 416 p. - S. 249.
↑ Planetary Fact Sheet
↑ Sun Fact Sheet
↑ Stern, SA, et al. The Pluto system: Initial results from its exploration by New Horizons (Eng.) // Science: journal. - 2015. - Vol. 350 , no. 6258 . - P. 249-352 . - DOI : 10.1126 / science.aad1815 .
↑ MECHANICS. MOLECULAR PHYSICS. Teaching aid for laboratory work No. 1-51, 1-61, 1-71, 1-72 (neopr.) . St. Petersburg State Technological University of Plant Polymers (2014). Date of treatment January 4, 2019.
↑ Krebs, 2006 , p. 158.
↑ Krebs, 2006 , p. 136.
↑ Krebs, 2006 , p. 96.
↑ Krebs, 2006 , p. 160.
↑ Krebs, 2006 , p. 138.
↑ Krebs, 2006 , p. 198.
↑ Krebs, 2006 , p. 319.
↑ ¹ ² Krebs, 2006 , p. 165.
↑ Krebs, 2006 , p. 179.
↑ Krebs, 2006 , p. 163.
↑ Krebs, 2006 , p. 141.
↑ Krebs, 2006 , p. 67.
↑ Krebs, 2006 , p. 108.
↑ Krebs, 2006 , p. 57.
↑ Krebs, 2006 , p. 313.
↑ Krebs, 2006 , p. 105.
↑ Krebs, 2006 , p. fifty.
↑ Krebs, 2006 , p. 151.
↑ Krebs, 2006 , p. 111.
↑ Krebs, 2006 , p. 60.
↑ Krebs, 2006 , p. 168.
↑ Krebs, 2006 , p. 101.
↑ Krebs, 2006 , p. 54.
↑ Krebs, 2006 , p. 134.
↑ Krebs, 2006 , p. 98.
↑ Krebs, 2006 , p. 47.

Literature

Density - an article from the Great Soviet Encyclopedia . - M .: "Soviet Encyclopedia", 1975. - T. 20. - P. 49.
Density - an article from the Physical Encyclopedia . T. 3, S. 637.
Krebs R. E. The History and Use of Our Earth's Chemical Elements: A Reference Guide. 2nd edition . - Westport : Greenwood Publishing Group , 2006 .-- xxv + 422 p. - ISBN 0-313-33438-2 .

Links

[1] There are also surface densities (mass-to- area ratios) and linear densities (mass-to-length ratios) applied respectively to flat (two-dimensional) and elongated (one-dimensional) objects.

[2] It is also understood that the region is contracted to a point, that is, not only its volume tends to zero (which could be not only when the region is contracted to a point, but, for example, to a segment), but also its diameter tends to zero ( maximum linear size).

[Агекян-3] Agekyan T.A. Expansion of the Universe. Model of the Universe // Stars, galaxies, Metagalaxy. 3rd ed. / Ed. A. B. Vasiliev. - M .: Nauka , 1982 .-- 416 p. - S. 249.

[4] Planetary Fact Sheet

[5] Sun Fact Sheet

[Stern2015-6] Stern, SA, et al. The Pluto system: Initial results from its exploration by New Horizons (Eng.) // Science: journal. - 2015. - Vol. 350 , no. 6258 . - P. 249-352 . - DOI : 10.1126 / science.aad1815 .

[7] MECHANICS. MOLECULAR PHYSICS. Teaching aid for laboratory work No. 1-51, 1-61, 1-71, 1-72 (neopr.) . St. Petersburg State Technological University of Plant Polymers (2014). Date of treatment January 4, 2019.

[_087a23abab575da2-8] Krebs, 2006 , p. 158.

[_087a1dabab57535e-9] Krebs, 2006 , p. 136.

[_16b6547b64708d05-10] Krebs, 2006 , p. 96.

[_087a22abab575bd7-11] Krebs, 2006 , p. 160.

[_087a1dabab575350-12] Krebs, 2006 , p. 138.

[_087a17abab57490e-13] Krebs, 2006 , p. 198.

[_08808babab5c7a39-14] Krebs, 2006 , p. 319.

[_087a22abab575bd2-15] ¹ ² Krebs, 2006 , p. 165.

[_087a21abab575a0d-16] Krebs, 2006 , p. 179.

[_087a22abab575bd4-17] Krebs, 2006 , p. 163.

[_087a24abab575f7c-18] Krebs, 2006 , p. 141.

[_16b6617b6470a37d-19] Krebs, 2006 , p. 67.

[_087a20abab5758b9-20] Krebs, 2006 , p. 108.

[_16b6607b6470a1a0-21] Krebs, 2006 , p. 57.

[_08808babab5c7a33-22] Krebs, 2006 , p. 313.

[_087a20abab5758b4-23] Krebs, 2006 , p. 105.

[_16b6607b6470a1a7-24] Krebs, 2006 , p. fifty.

[_087a23abab575dab-25] Krebs, 2006 , p. 151.

[_087a1fabab5756ff-26] Krebs, 2006 , p. 111.

[_16b6617b6470a37a-27] Krebs, 2006 , p. 60.

[_087a22abab575bdf-28] Krebs, 2006 , p. 168.

[_087a20abab5758b0-29] Krebs, 2006 , p. 101.

[_16b6607b6470a1a3-30] Krebs, 2006 , p. 54.

[_087a1dabab57535c-31] Krebs, 2006 , p. 134.

[_16b6547b64708d0b-32] Krebs, 2006 , p. 98.

[_16b65f7b64709fd3-33] Krebs, 2006 , p. 47.

Density
$\rho ={\frac {m}{V}}$ ${\ displaystyle \ rho = {\ frac {m} {V}}}$ $\ rho = {\ frac {m} {V}}$
Dimension	L ⁻³ M
Units
SI	kg / m³
GHS	g / cm³
Notes
scalar quantity