Density
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In physics, density is mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as:
- <math>\rho = \frac {m}{V}</math>
where, in SI units:
- ρ (rho) is the density of the substance, measured in kg·m-3
- m is the mass of the substance, measured in kg
- V is the volume of the substance, measured in m3
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[edit] Measurement of density
For a homogeneous object, the formula Mass/Volume may be used. The mass is normally measured with an appropriate scale; the volume may be measured directly (from the geometry of the object) or by the displacement of a liquid. A very common instrument for the direct measurement of the density of a liquid is the hydrometer. A less common device for measuring fluid density is a pycnometer, a similar device for measuring the absolute density of a solid is a gas pycnometer.
The density of a solid material can be ambiguous, depending on exactly how it is defined, and this may cause confusion in measurement. A common example is sand: if gently filled into a container, the density will be small; when the same sand is compacted into the same container, it will occupy less volume and consequently carry a greater density. This is because "sand" contains a lot of air space in between individual grains, this overall density is called the bulk density, which differs significantly from the density of an individual grain of sand.
[edit] Common units
In U.S. customary units or Imperial units, the units of density include;
- ounces per cubic inch (oz/in³)
- pounds per cubic inch (lb/in³)
- pounds per cubic foot (lb/ft³)
- pounds per cubic yard (lb/yd³)
- pounds per gallon (for U.S. or imperial gallons) (lb/gal)
- pounds per U.S. bushel (lb/bu)
- slugs per cubic foot.
[edit] Changes of density
In general density can be changed by changing either the pressure or the temperature. Increasing the pressure will always increase the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalisation. For example, the density of water increases between its melting point at 0 °C and 4 °C and similar behaviour is observed in silicon at low temperatures.
The effect of pressure and temperature on the densities of liquids and solids is small so that a typical compressibility for a liquid or solid is 10-6 bar-1 (1 bar=0.1 MPa) and a typical thermal expansivity is 10-5 K-1.
In contrast, the density of gases is strongly affect by pressure. Boyle's law says that the density of a perfect gas is given by
- <math>\rho = \frac {mP}{RT}</math>
where <math>R</math> is the universal gas constant, <math>P</math> is the pressure, <math>m</math> the molar mass, and <math>T</math> the absolute temperature.
This means that a gas at 300 K and 1 bar will have its density doubled by increasing the pressure to 2 bar or by reducing the temperature to 150 K.
[edit] Density of water
| Temperature | Density[1] (at 1 atm) | |
|---|---|---|
| °C | °F | kg/m³ |
| 0.0 | 32.0 | 999.8425 |
| 4.0 | 39.2 | 999.9750 |
| 15.0 | 59.0 | 999.1026 |
| 20.0 | 68.0 | 998.2071 |
| 25.0 | 77.0 | 998.0479 |
| 37.0 | 98.6 | 993.3316 |
| 100 | 212.0 | 958.3665 |
[edit] Density of air at 1 atm
| T in °C | ρ in kg/m³ |
|---|---|
| −10 | 1.341 |
| −5 | 1.316 |
| 0 | 1.293 |
| 5 | 1.269 |
| 10 | 1.247 |
| 15 | 1.225 |
| 20 | 1.204 |
| 25 | 1.184 |
| 30 | 1.164 |
[edit] References
- ^ Density of water, as reported by Daniel Harris in Quantitative Chemical Analysis, 4th ed., p. 36, W. H. Freeman and Company, New York, 1995.
[edit] Books
- Fundamentals of Aerodynamics Second Edition, McGraw-Hill, John D. Anderson, Jr.
- Fundamentals of Fluid Mechanics Wiley, B.R. Munson, D.F. Young & T.H. Okishi
- Introduction to Fluid Mechanics Fourth Edition, Wiley, SI Version, R.W. Fox & A.T. McDonald
- Thermodynamics: An Engineering Approach Second Edition, McGraw-Hill, International Edition, Y.A. Cengel & M.A. Boles
[edit] See also
- Charge density
- Dord
- Energy density
- Number density
- Population density
- Specific weight
- Standard temperature and pressureaf:Digtheid
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