Physical quantities and their units. Units of measurement of physical quantities
In 1875, the International Bureau of Weights and Measures was founded by the Metric Conference; its goal was to create a unified measurement system that would be used throughout the world. It was decided to take as a basis the metric system, which appeared back in the days French Revolution and was based on the meter and kilogram. Later, the standards of the meter and kilogram were approved. Over time, the system of units of measurement has evolved, now it has seven basic units of measurement. In 1960, this system of units received modern name The international system of units (SI system) (Systeme Internatinal d "Unites (SI)). The SI system is not static, it develops in accordance with the requirements that are currently required for measurements in science and technology.
Basic units of measurement of the International System of Units
The definition of all auxiliary units in the SI system is based on seven basic units of measurement. The main physical quantities in the International System of Units (SI) are: length ($l$); mass ($m$); time($t$); strength electric current($I$); Kelvin temperature (thermodynamic temperature) ($T$); amount of substance ($\nu $); light intensity ($I_v$).
The basic units in the SI system are the units of the above quantities:
\[\left=m;;\ \left=kg;;\ \left=c;\ \left=A;;\ \left=K;;\ \ \left[\nu \right]=mol;;\ \left=cd\ (candela).\]
Standards of the main units of measurement in SI
Here are the definitions of the standards of the main units of measurement as it is done in the SI system.
By meter (m) is called the length of the path that light travels in vacuum in a time equal to $\frac(1)(299792458)$ s.
Mass standard for SI is a weight having the shape of a straight cylinder, the height and diameter of which is 39 mm, consisting of an alloy of platinum and iridium weighing 1 kg.
One second (s) called the time interval, which is equal to 9192631779 periods of radiation, which corresponds to the transition between two hyperfine levels of the ground state of the cesium atom (133).
One ampere (A)- this is the strength of the current passing in two straight, infinitely thin and long conductors located at a distance of 1 meter, located in a vacuum generating Ampère force (the force of interaction of conductors) equal to $2\cdot (10)^(-7)H$ for each meter of the conductor .
One kelvin (K) is the thermodynamic temperature equal to $\frac(1)(273,16)$ of the triple point temperature of water.
One mol (mol)- this is the amount of a substance in which there are as many atoms as there are in 0.012 kg of carbon (12).
One candela (cd) is equal to the intensity of light emitted by a monochromatic source with a frequency of $540\cdot (10)^(12)$Hz with an energy force in the direction of radiation $\frac(1)(683)\frac(W)(sr).$
Science is developing, measuring equipment is being improved, the definitions of units of measurement are being revised. The higher the accuracy of measurements, the greater the requirements for the definition of units of measurement.
SI derivative quantities
All other quantities are considered in the SI system as derivatives of the main ones. The units of measurement of derived quantities are defined as the result of the product (taking into account the degree) of the main ones. Let us give examples of derived quantities and their units in the SI system.
There are also dimensionless quantities in the SI system, for example, the reflection coefficient or the relative permittivity. These quantities have the unit dimension.
The SI system includes derived units with special names. These names are compact forms for representing combinations of base quantities. Let us give examples of units of the SI system that have their own names (Table 2).
Each quantity in the SI system has only one unit of measure, but the same unit of measure can be used for different quantities. Joule is a unit of measure for the amount of heat and work.
SI system, units of measurement multiples and submultiples
The International System of Units has a set of prefixes to units of measurement that are used if the numerical values of the quantities in question are significantly greater or less than the unit of the system, which is used without a prefix. These prefixes are used with any unit of measure, in the SI system they are decimal.
We give examples of such prefixes (Table 3).
When writing, the prefix and the name of the unit are written together, so that the prefix and the unit of measure form a single character.
Note that the SI unit of mass (kilogram) historically already has a prefix. Decimal multiples and submultiples of the kilogram are obtained by adding the prefix to the gram.
Off-system units
The SI system is universal and is convenient in international communication. Almost all non-SI units can be defined using SI terms. The use of the SI system is preferred in science education. However, there are some quantities that are not included in the SI, but are widely used. Thus, units of time such as minutes, hours, days are part of the culture. Some units are used for historical reasons. When using units that do not belong to the SI system, it is necessary to indicate how they are converted to SI units. An example of units is shown in Table 4.
The method of setting temperature values is the temperature scale. Several temperature scales are known.
- Kelvin scale(by the name English physics W. Thomson, Lord Kelvin).
Unit designation: K(not "degree Kelvin" and not °K).
1 K \u003d 1/273.16 - part of the thermodynamic temperature of the triple point of water, corresponding to the thermodynamic equilibrium of a system consisting of ice, water and steam. - Celsius(named after the Swedish astronomer and physicist A. Celsius).
Unit designation: °C .
In this scale, the melting temperature of ice at normal pressure is taken equal to 0°C, the boiling point of water is 100°C.
The Kelvin and Celsius scales are related by the equation: t (°C) \u003d T (K) - 273.15. - Fahrenheit(D. G. Fahrenheit - German physicist).
Unit designation: °F. It is widely used, in particular in the USA.
The Fahrenheit scale and the Celsius scale are related: t (°F) = 1.8 t (°C) + 32°C. By absolute value 1 (°F) = 1 (°C). - Reaumur scale(named after the French physicist R.A. Reaumur).
Designation: °R and °r.
This scale has almost fallen into disuse.
Relationship with degrees Celsius: t (°R) = 0.8 t (°C). - Rankin scale (Rankine)- named after the Scottish engineer and physicist W. J. Rankin.
Designation: °R (sometimes: °Rank).
The scale is also used in the USA.
The temperature on the Rankin scale corresponds to the temperature on the Kelvin scale: t (°R) = 9/5 T (K).
The main temperature indicators in units of measurement of different scales:
The SI unit of measurement is the meter (m).
- Off-system unit: angstrom (Å). 1Å = 1 10-10 m.
- Inch(from Dutch duim - thumb); inch; in; ´´; 1´ = 25.4 mm.
- Hand(English hand - hand); 1 hand=101.6mm.
- Link(English link - link); 1 li = 201.168 mm.
- Span(English span - span, scope); 1 span = 228.6mm.
- Foot(English foot - foot, feet - feet); 1 ft = 304.8 mm.
- Yard(English yard - yard, paddock); 1 yd = 914.4 mm.
- Fatom, face(English fathom - a measure of length (= 6 ft), or a measure of the volume of wood (= 216 ft 3), or a mountain measure of area (= 36 ft 2), or a fathom (Ft)); fath or fth or Ft or ƒfm; 1 Ft = 1.8288 m.
- chain(English chain - chain); 1 ch = 66 ft = 22 yd = = 20.117 m.
- Furlong(English furlong) - 1 fur = 220 yd = 1/8 mile.
- Mile(English mile; international). 1 ml (mi, MI) = 5280 ft = 1760 yd = 1609.344 m.
The unit of measure in SI is m 2 .
- square foot; 1 ft 2 (also sq ft) = 929.03 cm 2.
- Square inch; 1 in 2 (sq in) = 645.16 mm 2.
- Square veil (face); 1 fath 2 (ft 2; Ft 2; sq Ft) \u003d 3.34451 m 2.
- square yard; 1 yd 2 (sq yd) \u003d 0.836127 m 2 .
Sq (square) - square.
The unit of measure in SI is m 3 .
- Cubic foot; 1 ft 3 (also cu ft) = 28.3169 dm 3.
- Cubic Fathom; 1 fath 3 (fth 3 ; Ft 3 ; cu Ft) = 6.11644 m 3.
- cubic yard; 1 yd 3 (cu yd) = 0.764555 m 3.
- cubic inch; 1 in 3 (cu in) \u003d 16.3871 cm 3.
- Bushel (UK); 1 bu (uk, also UK) = 36.3687 dm 3.
- Bushel (USA); 1 bu (us, also US) = 35.2391 dm 3.
- Gallon (UK); 1 gal (uk, also UK) = 4.54609 dm 3.
- Gallon liquid (US); 1 gal (us, also US) = 3.78541 dm 3.
- US gallon dry; 1 gal dry (us, also US) = 4.40488 dm3.
- Jill (gill); 1 gi = 0.12 L (US), 0.14 L (UK).
- Barrel (USA); 1bbl \u003d 0.16 m 3.
UK - United Kingdom - United Kingdom (Great Britain); US - United Stats (USA).
Specific volume
The unit of measurement in SI is m 3 / kg.
- ft 3 /lb; 1 ft3 / lb = 62.428 dm3 / kg .
The unit of measurement in SI is kg.
- Pound (trading) (English libra, pound - weighing, pound); 1 lb = 453.592 g; lbs - pounds. In the system of old Russian measures 1 lb = 409.512 g.
- Gran (English grain - grain, grain, pellet); 1 gr = 64.799 mg.
- Stone (English stone - stone); 1 st = 14 lb = 6.350 kg.
Density, incl. bulk
The unit of measurement in SI is kg / m 3.
- lb/ft 3 ; 1 lb / ft 3 \u003d 16.0185 kg / m 3.
Line Density
The unit of measure in SI is kg/m.
- lb/ft; 1 lb / ft = 1.48816 kg/m
- Pound/yard; 1 lb / yd = 0.496055 kg/m
Surface density
The unit of measurement in SI is kg / m 2.
- lb/ft 2 ; 1 lb / ft 2 (also lb / sq ft - pound per square foot) = 4.88249 kg / m 2.
Line speed
The SI unit is m/s.
- ft/h; 1 ft / h = 0.3048 m/h.
- ft/s; 1 ft/s = 0.3048 m/s.
The SI unit is m/s 2 .
- ft/s 2 ; 1 ft / s 2 \u003d 0.3048 m / s 2.
Mass flow
The SI unit is kg/s.
- Pound/h; 1 lb / h = 0.453592 kg/h.
- Pound/s; 1 lb/s = 0.453592 kg/s.
Volume flow
The SI unit is m 3 / s.
- ft 3 /min; 1 ft 3 / min = 28.3168 dm 3 / min.
- Yard 3 /min; 1 yd 3 / min = 0.764555 dm 3 / min.
- Gallon/min; 1 gal/ min (also GPM - gallon per min) = 3.78541 dm3/min.
Specific volume flow
- GPM/(sq ft) - gallon (G) per (P) minute (M)/(square (sq) foot (ft)) - gallon per minute per square foot;
1 GPM / (sq ft) \u003d 2445 l / (m 2 h) 1 l / (m 2 h) \u003d 10 -3 m / h. - gpd - gallons per day - gallons per day (days); 1 gpd \u003d 0.1577 dm 3 / h.
- gpm - gallons per minute - gallons per minute; 1 gpm \u003d 0.0026 dm 3 / min.
- gps - gallons per second - gallons per second; 1 gps \u003d 438 10 -6 dm 3 / s.
Sorbate consumption (for example, Cl 2) when filtering through a layer of sorbent (for example, active carbon)
- Gals/cu ft (gal/ft 3) - gallons/cubic foot (gallons per cubic foot); 1 Gals/cu ft = 0.13365 dm 3 per 1 dm 3 sorbent.
The unit of measure in SI is N.
- Pound-force; 1 lbf – 4.44822 N .44822 N 1N \u003d 1 kg m / s 2
- Poundal (English: poundal); 1 pdl \u003d 0.138255 N. (Poundal is the force that gives a mass of one pound an acceleration of 1 ft / s 2, lb ft / s 2.)
Specific gravity
The unit of measure in SI is N/m 3 .
- Pound-force/ft 3 ; 1 lbf/ft 3 = 157.087 N/m 3.
- Poundal/ft 3 ; 1 pdl / ft 3 \u003d 4.87985 N / m 3.
SI unit - Pa, multiple units: MPa, kPa.
Specialists in their work continue to use obsolete, canceled or previously optionally allowed pressure units: kgf / cm 2; bar; atm. (physical atmosphere); at(technical atmosphere); ata; ati; m of water. Art.; mmHg st; torr.
Concepts are used: "absolute pressure", "excessive pressure". There are errors when converting some units of pressure into Pa and into its multiple units. It should be taken into account that 1 kgf / cm 2 is equal to 98066.5 Pa (exactly), that is, for small (up to about 14 kgf / cm 2) pressures, with sufficient accuracy for work, we can take: 1 Pa \u003d 1 kg / (m s 2) \u003d 1 N / m 2. 1 kgf / cm 2 ≈ 105 Pa = 0.1 MPa. But already at medium and high pressures: 24 kgf / cm 2 ≈ 23.5 105 Pa = 2.35 MPa; 40 kgf / cm 2 ≈ 39 105 Pa = 3.9 MPa; 100 kgf / cm 2 ≈ 98 105 Pa = 9.8 MPa etc.
Ratios:
- 1 atm (physical) ≈ 101325 Pa ≈ 1.013 105 Pa ≈ ≈ 0.1 MPa.
- 1 at (technical) \u003d 1 kgf / cm 2 \u003d 980066.5 Pa ≈ 105 Pa ≈ 0.09806 MPa ≈ 0.1 MPa.
- 0.1 MPa ≈ 760 mmHg Art. ≈ 10 m w.c. Art. ≈ 1 bar.
- 1 Torr (torus, tor) \u003d 1 mm Hg. Art.
- Pound-force/inch 2 ; 1 lbf/in 2 = 6.89476 kPa (see below: PSI).
- Pound-force/ft 2 ; 1 lbf/ft 2 = 47.8803 Pa.
- Pound-force/yard 2 ; 1 lbf/yd 2 = 5.32003 Pa.
- Poundal/ft 2 ; 1 pdl/ft 2 = 1.48816 Pa.
- Foot of water column; 1 ft H 2 O = 2.98907 kPa.
- An inch of water column; 1 in H 2 O = 249.089 Pa.
- inch of mercury; 1 in Hg = 3.38639 kPa.
- PSI (also psi) - pounds (P) per square (S) inch (I) - pounds per square inch; 1 PSI = 1 lbƒ/in 2 = 6.89476 kPa.
Sometimes in the literature there is a designation of the pressure unit lb / in 2 - this unit does not take into account lbƒ (pound-force), but lb (pound-mass). Therefore, in numerical terms, 1 lb / in 2 is somewhat different from 1 lbf / in 2, since when determining 1 lbƒ, it is taken into account: g \u003d 9.80665 m / s 2 (at the latitude of London). 1 lb / in 2 \u003d 0.454592 kg / (2.54 cm) 2 \u003d 0.07046 kg / cm 2 \u003d 7.046 kPa. Calculation 1 lbƒ - see above. 1 lbf / in 2 \u003d 4.44822 N / (2.54 cm) 2 \u003d 4.44822 kg m / (2.54 0.01 m) 2 s 2 \u003d 6894.754 kg / (m s 2) = 6894.754 Pa ≈ 6.895 kPa.
For practical calculations, you can take: 1 lbf / in 2 ≈ 1 lb / in 2 ≈ 7 kPa. But, in fact, equality is illegal, as well as 1 lbƒ = 1 lb, 1 kgf = 1 kg. PSIg (psig) - same as PSI, but indicates overpressure; PSIa (psia) - the same as PSI, but emphasizes: absolute pressure; a - absolute, g - gauge (measure, size).
Water pressure
The unit of measure in SI is m.
- Head in feet (feet-head); 1 ft hd = 0.3048 m
Pressure loss during filtration
- PSI/ft - pounds (P) per square (S) inch (I)/foot (ft) - pounds per square inch/foot; 1 PSI/ft = 22.62 kPa per 1 m of filter bed.
SI unit - Joule(named after the English physicist J.P. Joule).
- 1 J is the mechanical work of a force of 1 N when a body moves a distance of 1 m.
- Newton (N) - SI unit of force and weight; 1 N is equal to the force imparting to a body with a mass of 1 kg an acceleration of 1 m 2 / s in the direction of the force. 1 J = 1 N m.
In heat engineering, the canceled unit of measurement of the amount of heat, the calorie (cal, cal), continues to be used.
- 1 J (J) = 0.23885 cal. 1 kJ = 0.2388 kcal.
- 1 lbf ft (lbf ft) = 1.35582 J.
- 1 pdl ft (poundal foot) = 42.1401 mJ.
- 1 Btu (British Heat Unit) = 1.05506 kJ (1 kJ = 0.2388 kcal).
- 1 Therm (therma - British big calorie) = 1 10 -5 Btu.
POWER, HEAT FLOW |
The SI unit is Watt (W)- named after the English inventor J. Watt - mechanical power at which 1 J work is done in 1 s, or a heat flux equivalent to 1 W mechanical power.
- 1 W (W) \u003d 1 J / s \u003d 0.859985 kcal / h (kcal / h).
- 1 lbf ft/s (lbf ft/s) = 1.33582 watts.
- 1 lbf ft / min (lbf ft/min) = 22.597 mW.
- 1 lbf ft / h (lbf ft/h) = 376.616 µW.
- 1 pdl ft/s (poundal feet/s) = 42.1401 mW.
- 1 hp (horsepower British / s) \u003d 745.7 watts.
- 1 Btu/s (British Heat Unit/s) = 1055.06 W.
- 1 Btu/h (Btu/h) = 0.293067 W.
Surface heat flux density
The unit of measure in SI is W / m 2.
- 1 W / m 2 (W / m 2) \u003d 0.859985 kcal / (m 2 h) (kcal / (m 2 h)).
- 1 Btu / (ft 2 h) \u003d 2.69 kcal / (m 2 h) \u003d 3.1546 kW / m 2.
Dynamic viscosity (viscosity factor), η.
SI unit - Pa s. 1 Pa s \u003d 1 N s / m 2;
off-system unit - poise (P). 1 P \u003d 1 dyne s / m 2 \u003d 0.1 Pa s.
- Dina (dyn) - (from the Greek dynamic - strength). 1 dyne \u003d 10 -5 N \u003d 1 g cm / s 2 \u003d 1.02 10 -6 kgf.
- 1 lbf h / ft 2 (lbf h/ft 2) = 172.369 kPa s.
- 1 lbf s / ft 2 (lbf s / ft 2) = 47.8803 Pa s.
- 1 pdl s / ft 2 (poundal s / ft 2) = 1.48816 Pa s.
- 1 slug /(ft s) (slug/(ft s)) = 47.8803 Pa s. Slug (slug) - a technical unit of mass in the English system of measures.
Kinematic viscosity, ν.
Unit of measurement in SI - m 2 / s; The unit cm 2 / s is called "Stokes" (after the English physicist and mathematician J. G. Stokes).
Kinematic and dynamic viscosities are related by the equation: ν = η / ρ, where ρ is the density, g/cm 3 .
- 1 m 2 / s = Stokes / 104.
- 1 ft 2 / h (ft 2 / h) \u003d 25.8064 mm 2 / s.
- 1 ft 2 /s (ft 2 /s) \u003d 929.030 cm 2 /s.
Tension unit magnetic field in SI - A/m(Ammeter). Ampère (A) is the surname of the French physicist A.M. Ampere.
Previously, the Oersted unit (E) was used - named after the Danish physicist H.K. Oersted.
1 A / m (A / m, At / m) \u003d 0.0125663 Oe (Oe)
The resistance to crushing and abrasion of mineral filter materials and, in general, of all minerals and rocks is indirectly determined on the Mohs scale (F. Moos is a German mineralogist).
In this scale, the numbers in ascending order denote minerals arranged in such a way that each subsequent one is able to leave a scratch on the previous one. Extreme substances in the Mohs scale: talc (hardness unit - 1, the softest) and diamond (10, the hardest).
- Hardness 1-2.5 (drawn with a fingernail): volskonkoite, vermiculite, halite, gypsum, glauconite, graphite, clay materials, pyrolusite, talc, etc.
- Hardness> 2.5-4.5 (not drawn with a fingernail, but drawn with glass): anhydrite, aragonite, barite, glauconite, dolomite, calcite, magnesite, muscovite, siderite, chalcopyrite, chabazite, etc.
- Hardness >4.5-5.5 (not drawn with glass, but drawn with a steel knife): apatite, vernadite, nepheline, pyrolusite, chabazite, etc.
- Hardness > 5.5-7.0 (not drawn with a steel knife, but drawn with quartz): vernadite, garnet, ilmenite, magnetite, pyrite, feldspars, etc.
- Hardness >7.0 (not drawn with quartz): diamond, garnet, corundum, etc.
The hardness of minerals and rocks can also be determined on the Knoop scale (A. Knup is a German mineralogist). In this scale, the values are determined by the size of the imprint left on the mineral when a diamond pyramid is pressed into its sample under a certain load.
Ratios of indicators on the Mohs (M) and Knoop (K) scales:
SI unit - Bq(Becquerel, named after the French physicist A.A. Becquerel).
Bq (Bq) is a unit of nuclide activity in a radioactive source (isotope activity). 1 Bq is equal to the activity of the nuclide, at which one decay event occurs in 1 s.
Radioactivity concentration: Bq/m 3 or Bq/l.
Activity is the number of radioactive decays per unit of time. Activity per unit mass is called specific activity.
- Curie (Ku, Ci, Cu) is a unit of nuclide activity in a radioactive source (isotope activity). 1 Ku is the activity of an isotope in which 3.7000 1010 decay events occur in 1 s. 1 Ku = 3.7000 1010 Bq.
- Rutherford (Rd, Rd) is an obsolete unit of activity of nuclides (isotopes) in radioactive sources, named after the English physicist E. Rutherford. 1 Rd \u003d 1 106 Bq \u003d 1/37000 Ci.
Radiation dose
Radiation dose - the energy of ionizing radiation absorbed by the irradiated substance and calculated per unit of its mass (absorbed dose). The dose accumulates over time of exposure. Dose rate ≡ Dose/time.
The unit of absorbed dose in SI is Gray (Gy, Gy). The off-system unit is Rad (rad), corresponding to a radiation energy of 100 erg absorbed by a substance weighing 1 g.
Erg (erg - from Greek: ergon - work) is a unit of work and energy in the non-recommended CGS system.
- 1 erg \u003d 10 -7 J \u003d 1.02 10 -8 kgf m \u003d 2.39 10 -8 cal \u003d 2.78 10 -14 kWh.
- 1 rad (rad) \u003d 10 -2 Gy.
- 1 rad (rad) \u003d 100 erg / g \u003d 0.01 Gy \u003d 2.388 10 -6 cal / g \u003d 10 -2 J / kg.
Kerma (abbreviated English: kinetic energy released in matter) - the kinetic energy released in matter, measured in grays.
The equivalent dose is determined by comparing the radiation of nuclides with X-rays. The radiation quality factor (K) shows how many times the radiation hazard in the case of chronic human exposure (in relatively small doses) for a given type of radiation is greater than in the case of X-rays with the same absorbed dose. For X-ray and γ-radiation K = 1. For all other types of radiation, K is established according to radiobiological data.
Deq = Dpogl K.
The absorbed dose unit in SI is 1 Sv(Sievert) = 1 J/kg = 102 rem.
- REM (rem, ri - until 1963 was defined as the biological equivalent of an roentgen) - a unit of equivalent dose of ionizing radiation.
- Roentgen (Р, R) - unit of measure, exposure dose of X-ray and γ-radiation. 1 P \u003d 2.58 10 -4 C / kg.
- Coulomb (C) - a unit in the SI system, the amount of electricity, electric charge. 1 rem = 0.01 J/kg.
Dose equivalent rate - Sv/s.
Permeability of porous media (including rocks and minerals)
Darcy (D) - named after the French engineer A. Darcy, darsy (D) 1 D \u003d 1.01972 μm 2.
1 D is the permeability of such a porous medium, when filtered through a sample of which with an area of 1 cm 2, a thickness of 1 cm and a pressure drop of 0.1 MPa, the flow rate of a liquid with a viscosity of 1 cP is 1 cm 3 / s.
Sizes of particles, grains (granules) of filter materials according to SI and standards of other countries
In the USA, Canada, Great Britain, Japan, France and Germany, grain sizes are estimated in meshes (English mesh - hole, cell, network), that is, by the number (number) of holes per inch of the finest sieve through which grains. And the effective grain diameter is considered to be the hole size in microns. AT last years US and UK mesh systems are more commonly used.
The ratio between the units of measurement of the grain (granule) size of filter materials according to SI and the standards of other countries:
Mass fraction
Mass fraction shows what mass amount of a substance is contained in 100 mass parts of a solution. Units of measurement: fractions of a unit; percentage (%); ppm (‰); parts per million (ppm).
Concentration of solutions and solubility
The concentration of the solution must be distinguished from the solubility - the concentration of a saturated solution, which is expressed by the mass amount of a substance in 100 mass parts of the solvent (for example, g / 100 g).
Volume concentration
Volume concentration is the mass amount of a solute in a certain amount solution (for example: mg / l, g / m 3).
Molar concentration
Molar concentration - the number of moles of a given substance dissolved in a certain volume of solution (mol / m 3, mmol / l, μmol / ml).
Molar concentration
Molar concentration - the number of moles of a substance contained in 1000 g of a solvent (mol / kg).
normal solution
A normal solution is a solution containing one equivalent of a substance per unit volume, expressed in mass units: 1H = 1 mg equiv / l = = 1 mmol / l (indicating the equivalent of a particular substance).
Equivalent
The equivalent is equal to the ratio of the part of the mass of the element (substance), which adds or replaces one atomic mass of hydrogen or half the atomic mass of oxygen in a chemical compound, to 1/12 of the mass of carbon 12. Thus, the equivalent of an acid is equal to its molecular weight, expressed in grams, divided by the basicity (the number of hydrogen ions); base equivalent - molecular mass, divided by acidity (the number of hydrogen ions, and for inorganic bases, divided by the number of hydroxyl groups); salt equivalent - molecular weight divided by the sum of charges (valency of cations or anions); the equivalent of a compound participating in redox reactions is the quotient of dividing the molecular weight of the compound by the number of electrons accepted (given away) by the atom of the reducing (oxidizing) element.
Relationships between units of measurement of the concentration of solutions
(Formulas for the transition from one expression of the concentration of solutions to another):
Accepted designations:
- ρ is the density of the solution, g/cm 3 ;
- m is the molecular weight of the solute, g/mol;
- E is the equivalent mass of a solute, that is, the amount of a substance in grams that interacts in a given reaction with one gram of hydrogen or corresponds to the transition of one electron.
According to GOST 8.417-2002 the unit of quantity of a substance is established: mole, multiples and submultiples ( kmol, mmol, µmol).
The unit of measure for hardness in SI is mmol/l; µmol/l.
In different countries, the canceled units of water hardness often continue to be used:
- Russia and CIS countries - mg-eq / l, mcg-eq / l, g-eq / m 3;
- Germany, Austria, Denmark and some other countries of the Germanic group of languages - 1 German degree - (H ° - Harte - hardness) ≡ 1 hour CaO / 100 thousand hours of water ≡ 10 mg CaO / l ≡ 7.14 mg MgO / l ≡ 17.9 mg CaCO 3 / l ≡ 28.9 mg Ca (HCO 3) 2 / l ≡ 15.1 mg MgCO 3 / l ≡ 0.357 mmol / l.
- 1 French degree ≡ 1 hour CaCO 3 / 100 thousand hours of water ≡ 10 mg CaCO 3 / l ≡ 5.2 mg CaO / l ≡ 0.2 mmol / l.
- 1 English degree ≡ 1 grain / 1 gallon of water ≡ 1 h CaCO 3 / 70 thousand hours of water ≡ 0.0648 g CaCO 3 / 4.546 l ≡ 100 mg CaCO 3 / 7 l ≡ 7.42 mg CaO / l ≡ 0.285 mmol / l. Sometimes the English degree of hardness is referred to as Clark.
- 1 American degree ≡ 1 hour CaCO 3 / 1 million hours of water ≡ 1 mg CaCO 3 / l ≡ 0.52 mg CaO / l ≡ 0.02 mmol / l.
Here: h - part; the conversion of degrees to their corresponding amounts of CaO, MgO, CaCO 3 , Ca(HCO 3) 2 , MgCO 3 is shown as examples mainly for German degrees; the dimensions of degrees are tied to calcium-containing compounds, since in the composition of hardness ions calcium, as a rule, is 75-95%, in rare cases - 40-60%. Numbers are rounded mostly to the second decimal place.
Relationship between water hardness units:
1 mmol/L = 1 mg equiv/L = 2.80°N (German degrees) = 5.00 French degrees = 3.51 English degrees = 50.04 US degrees.
The new unit for measuring water hardness is the Russian degree of hardness - °F, defined as the concentration of an alkaline earth element (mainly Ca 2+ and Mg 2+), numerically equal to ½ of its mole in mg / dm 3 (g / m 3).
Alkalinity units - mmol, µmol.
The unit of measure for electrical conductivity in SI is µS/cm.
The electrical conductivity of solutions and the reverse electrical resistance characterize the mineralization of solutions, but only the presence of ions. When measuring electrical conductivity, non-ionic organic matter, neutral suspended impurities, interferences that distort the results - gases, etc. It is impossible to calculate exactly the correspondence between the values of the electrical conductivity and the dry residue or even the sum of all separately determined substances of the solution, since different ions in natural water have different electrical conductivity, which simultaneously depends on the salinity of the solution and its temperature. To establish such a dependence, it is necessary to experimentally establish the ratio between these quantities for each specific object several times a year.
- 1 µS/cm = 1 MΩ cm; 1 S/m = 1 ohm m.
For pure solutions of sodium chloride (NaCl) in distillate, the approximate ratio is:
- 1 µS/cm ≈ 0.5 mg NaCl/l.
The same ratio (approximately), subject to the above reservations, can be taken for most natural waters with mineralization up to 500 mg/l (all salts are converted to NaCl).
With a mineralization of natural water of 0.8-1.5 g / l, you can take:
- 1 μS / cm ≈ 0.65 mg salts / l,
and with mineralization - 3-5 g / l:
- 1 µS/cm ≈ 0.8 mg salts/l.
The content of suspended impurities in water, transparency and turbidity of water
The turbidity of water is expressed in units:
- JTU (Jackson Turbidity Unit) - Jackson turbidity unit;
- FTU (Formasin Turbidity Unit, also referred to as EMF) - formazin turbidity unit;
- NTU (Nephelometric Turbidity Unit) - nephelometric turbidity unit.
It is impossible to give an exact ratio of the units of turbidity and the content of suspended solids. For each series of determinations, it is necessary to build a calibration graph that allows you to determine the turbidity of the analyzed water compared to the control sample.
Approximately you can imagine: 1 mg / l (suspended solids) ≡ 1-5 NTU.
If the cloudy mixture (diatomaceous earth) has a particle size of 325 mesh, then: 10 units. NTU ≡ 4 units JTU.
GOST 3351-74 and SanPiN 2.1.4.1074-01 equate 1.5 units. NTU (or 1.5 mg/l as silica or kaolin) 2.6 units FTU (EMF).
The relationship between font transparency and haze:
The ratio between the transparency of the "cross" (in cm) and turbidity (in mg / l):
The unit of measure in SI is mg / l, g / m 3, μg / l.
In the USA and in some other countries, mineralization is expressed in relative units (sometimes in grains per gallon, gr / gal):
- ppm (parts per million) - parts per million (1 10 -6) units; sometimes ppm (parts per mille) also denotes a thousandth (1 10 -3) of a unit;
- ppb - (parts per billion) billionth (billionth) share (1 10 -9) units;
- ppt - (parts per trillion) trillionth (1 10 -12) units;
- ‰ - ppm (also used in Russia) - a thousandth (1 10 -3) units.
The ratio between the units of measurement of mineralization: 1mg / l \u003d 1ppm \u003d 1 10 3 ppb \u003d 1 10 6 ppt \u003d 1 10 -3 ‰ = 1 10 -4%; 1 gr/gal = 17.1 ppm = 17.1 mg/l = 0.142 lb/1000 gal.
For measuring salinity of salt waters, brines and salinity of condensates The correct units to use are: mg/kg. In laboratories, water samples are measured by volume, not mass fractions, therefore, it is advisable in most cases to refer the amount of impurities to a liter. But for large or very small mineralization values, the error will be sensitive.
According to SI, volume is measured in dm 3, but the measurement is also allowed in liters, because 1 l \u003d 1.000028 dm 3. Since 1964 1 liter is equal to 1 dm 3 (exactly).
For salt water and brines sometimes salinity units are used in degrees Baumé(for mineralization >50 g/kg):
- 1°Be corresponds to a solution concentration of 1% in terms of NaCl.
- 1% NaCl = 10 g NaCl/kg.
Dry and calcined residue
Dry and calcined residue are measured in mg/l. The dry residue does not fully characterize the mineralization of the solution, since the conditions for its determination (boiling, drying the solid residue in an oven at a temperature of 102-110 ° C to constant weight) distort the result: in particular, part of the bicarbonates (conventionally accepted - half) decomposes and volatilizes in the form of CO 2 .
Decimal multiples and submultiples of quantities
Decimal multiples and submultiple units of measurement of quantities, as well as their names and designations, should be formed using multipliers and prefixes given in the table:
(based on materials from the site https://aqua-therm.ru/).
Consider a physical record m=4kg. In this formula "m"- designation of physical quantity (mass), "4" - numerical value or magnitude, "kg"- unit of measurement of a given physical quantity.
Values are different kind. Here are two examples:
1) The distance between points, the lengths of segments, broken lines - these are quantities of the same kind. They are expressed in centimeters, meters, kilometers, etc.
2) The durations of time intervals are also quantities of the same kind. They are expressed in seconds, minutes, hours, etc.
Quantities of the same kind can be compared and added:
BUT! It is pointless to ask which is greater: 1 meter or 1 hour, and you cannot add 1 meter to 30 seconds. The duration of time intervals and distance are quantities of various kinds. They cannot be compared or combined.
Values can be multiplied by positive numbers and zero.
Taking any value e per unit of measurement, it can be used to measure any other quantity a the same kind. As a result of the measurement, we get that a=x e, where x is a number. This number x is called numerical value quantities a with unit of measure e.
There are dimensionless physical quantities. They do not have units of measurement, that is, they are not measured in anything. For example, the coefficient of friction.
What is SI?
According to Professor Peter Kampson and Dr. Naoko Sano of Newcastle University, published in the journal Metrology (Metrology), the kilogram standard adds an average of about 50 micrograms per hundred years, which can ultimately affect very many physical quantities.
The kilogram is the only SI unit that is still defined using a standard. All other measures (meter, second, degree, ampere, etc.) can be determined with the required accuracy in a physical laboratory. The kilogram is included in the definition of other quantities, for example, the unit of force is the newton, which is defined as the force that changes the speed of a 1 kg body by 1 m/s in the direction of the force in 1 second. Other physical quantities depend on the Newton value, so that in the end the chain can lead to a change in the value of many physical units.
The most important kilogram is a cylinder with a diameter and height of 39 mm, consisting of an alloy of platinum and iridium (90% platinum and 10% iridium). It was cast in 1889 and is stored in a safe at the International Bureau of Weights and Measures in the city of Sèvres near Paris. The kilogram was originally defined as the mass of one cubic decimeter (liter). pure water at 4°C and standard atmospheric pressure at sea level.
Initially, 40 exact copies were made from the kilogram standard, which were sold all over the world. Two of them are located in Russia, at the All-Russian Research Institute of Metrology. Mendeleev. Later, another series of replicas was cast. Platinum was chosen as the base material for the reference because of its high oxidation resistance, high density, and low magnetic susceptibility. The standard and its replicas are used to standardize the mass in a wide variety of industries. Including where micrograms are essential.
Physicists believe that weight fluctuations are the result of atmospheric pollution and changes chemical composition on the surface of the cylinders. Despite the fact that the standard and its replicas are stored in special conditions, this does not save the metal from interacting with environment. The exact weight of a kilogram was determined using X-ray photoelectron spectroscopy. It turned out that the kilogram “recovered” by almost 100 mcg.
At the same time, copies of the standard from the very beginning differed from the original and their weight also changes in different ways. So, the main American kilogram initially weighed 39 micrograms less than the standard, and a check in 1948 showed that it had increased by 20 micrograms. Another American copy, on the contrary, is losing weight. In 1889, the kilogram number 4 (K4) weighed 75 micrograms less than the standard, and in 1989 already 106.
Since 1963, in the USSR (GOST 9867-61 "International System of Units"), in order to unify units of measurement in all areas of science and technology, the international (international) system of units (SI, SI) has been recommended for practical use - this is a system of units for measuring physical quantities , adopted by the XI General Conference on Weights and Measures in 1960. It is based on 6 basic units (length, mass, time, electric current, thermodynamic temperature and light intensity), as well as 2 additional units (flat angle, solid angle) ; all other units given in the table are their derivatives. The adoption of a single international system of units for all countries is intended to eliminate the difficulties associated with translating the numerical values of physical quantities, as well as various constants from any one currently operating system (CGS, MKGSS, ISS A, etc.), into another.
Value name | Units; SI values | Notation | |
---|---|---|---|
Russian | international | ||
I. Length, mass, volume, pressure, temperature | |||
Meter - measure of length, numerically equal to the length international standard meter; 1 m=100 cm (1 10 2 cm)=1000 mm (1 10 3 mm) |
m | m | |
Centimeter \u003d 0.01 m (1 10 -2 m) \u003d 10 mm | cm | cm | |
Millimeter \u003d 0.001 m (1 10 -3 m) \u003d 0.1 cm \u003d 1000 microns (1 10 3 microns) | mm | mm | |
Micron (micrometer) = 0.001 mm (1 10 -3 mm) = 0.0001 cm (1 10 -4 cm) = 10,000 |
mk | μ | |
Angstrom = one ten billionth of a meter (1 10 -10 m) or one hundred millionth of a centimeter (1 10 -8 cm) | Å | Å | |
Weight | Kilogram - the basic unit of mass in the metric system of measures and the SI system, numerically equal to the mass of the international standard of the kilogram; 1 kg=1000 g |
kg | kg |
Gram \u003d 0.001 kg (1 10 -3 kg) |
G | g | |
Ton = 1000 kg (1 10 3 kg) | t | t | |
Centner \u003d 100 kg (1 10 2 kg) |
c | ||
Carat - non-systemic unit of mass, numerically equal to 0.2 g | ct | ||
Gamma=one millionth of a gram (1 10 -6 g) | γ | ||
Volume | Liter \u003d 1.000028 dm 3 \u003d 1.000028 10 -3 m 3 | l | l |
Pressure | Physical, or normal, atmosphere - pressure balanced by a mercury column 760 mm high at a temperature of 0 ° = 1.033 at = = 1.01 10 -5 n / m 2 = 1.01325 bar = 760 torr = 1.033 kgf / cm 2 |
atm | atm |
Technical atmosphere - pressure equal to 1 kgf / cmg \u003d 9.81 10 4 n / m 2 \u003d 0.980655 bar \u003d 0.980655 10 6 dynes / cm 2 \u003d 0.968 atm \u003d 735 torr | at | at | |
Millimeter of mercury column \u003d 133.32 n / m 2 | mmHg Art. | mm Hg | |
Tor - the name of an off-system unit of pressure measurement, equal to 1 mm Hg. Art.; given in honor of the Italian scientist E. Torricelli | torus | ||
Bar - unit of atmospheric pressure \u003d 1 10 5 n / m 2 \u003d 1 10 6 dynes / cm 2 | bar | bar | |
Pressure (sound) | bar unit sound pressure(in acoustics): bar - 1 dyne / cm 2; at present, a unit with a value of 1 n / m 2 \u003d 10 dynes / cm 2 is recommended as a unit of sound pressure |
bar | bar |
The decibel is a logarithmic unit of measurement of the level of excess sound pressure, equal to 1/10 of the unit of measurement of excess pressure - white | dB | db | |
Temperature | Degree Celsius; temperature in °K (Kelvin scale), equal to temperature in °C (Celsius scale) + 273.15 °C | °C | °C |
II. Force, power, energy, work, amount of heat, viscosity | |||
Strength | Dyna - a unit of force in the CGS system (cm-g-sec.), At which an acceleration equal to 1 cm / sec 2 is reported to a body with a mass of 1 g; 1 din - 1 10 -5 n | din | dyn |
Kilogram-force is a force imparting to a body with a mass of 1 kg an acceleration equal to 9.81 m / s 2; 1kg \u003d 9.81 n \u003d 9.81 10 5 din | kg, kgf | ||
Power | Horsepower=735.5W | l. With. | HP |
Energy | Electron-volt - the energy that an electron acquires when moving in an electric field in vacuum between points with a potential difference of 1 V; 1 ev \u003d 1.6 10 -19 j. Multiple units are allowed: kiloelectron-volt (Kv) = 10 3 eV and megaelectron-volt (MeV) = 10 6 eV. In modern particles, the energy is measured in Bev - billions (billions) eV; 1 Bzv=10 9 ev |
ev | eV |
Erg=1 10 -7 J; erg is also used as a unit of work, numerically equal to the work done by a force of 1 dyne in a path of 1 cm | erg | erg | |
Work | Kilogram-force-meter (kilogrammeter) - a unit of work numerically equal to the work done by a constant force of 1 kg when the point of application of this force moves a distance of 1 m in its direction; 1kGm = 9.81 J (at the same time, kGm is a measure of energy) | kgm, kgf m | kgm |
Quantity of heat | Calorie - an off-system unit for measuring the amount of heat equal to the amount of heat required to heat 1 g of water from 19.5 ° C to 20.5 ° C. 1 cal = 4.187 j; common multiple unit kilocalorie (kcal, kcal), equal to 1000 cal | feces | cal |
Viscosity (dynamic) | Poise is a unit of viscosity in the CGS system of units; the viscosity at which a 1 dyne viscous force acts in a layered flow with a velocity gradient of 1 sec -1 per 1 cm 2 of the layer surface; 1 pz \u003d 0.1 n s / m 2 | pz | P |
Viscosity (kinematic) | Stokes is the unit of kinematic viscosity in the CGS system; equal to the viscosity of a liquid having a density of 1 g / cm 3, resisting a force of 1 dyne to the mutual movement of two layers of liquid with an area of \u200b\u200b1 cm 2 located at a distance of 1 cm from each other and moving relative to each other at a speed of 1 cm per second | st | St |
III. Magnetic flux, magnetic induction, magnetic field strength, inductance, capacitance | |||
magnetic flux | Maxwell - a unit of measurement of magnetic flux in the cgs system; 1 μs is equal to the magnetic flux passing through the area of 1 cm 2 located perpendicular to the lines of induction of the magnetic field, with an induction equal to 1 gauss; 1 μs = 10 -8 wb (Weber) - units of magnetic current in the SI system | ms | Mx |
Magnetic induction | Gauss is a unit of measure in the cgs system; 1 gauss is the induction of such a field in which a rectilinear conductor 1 cm long, located perpendicular to the field vector, experiences a force of 1 dyne if a current of 3 × 10 10 CGS units flows through this conductor; 1 gs \u003d 1 10 -4 t (tesla) | gs | Gs |
Magnetic field strength | Oersted - unit of magnetic field strength in the CGS system; for one oersted (1 e) the intensity at such a point of the field is taken, in which a force of 1 dyne (dyne) acts on 1 electromagnetic unit of the amount of magnetism; 1 e \u003d 1 / 4π 10 3 a / m |
uh | Oe |
Inductance | Centimeter - a unit of inductance in the CGS system; 1 cm = 1 10 -9 gn (henry) | cm | cm |
Electrical capacitance | Centimeter - unit of capacitance in the CGS system = 1 10 -12 f (farads) | cm | cm |
IV. Light intensity, luminous flux, brightness, illumination | |||
The power of light | A candle is a unit of luminous intensity, the value of which is taken so that the brightness of a full emitter at the solidification temperature of platinum is 60 sv per 1 cm 2 | St. | cd |
Light flow | Lumen - a unit of luminous flux; 1 lumen (lm) is radiated within a solid angle of 1 stere by a point source of light that has a luminous intensity of 1 St in all directions. | lm | lm |
Lumen-second - corresponds to the light energy generated by a luminous flux of 1 lm, emitted or perceived in 1 second | lm s | lm sec | |
Lumen hour equals 3600 lumen seconds | lm h | lm h | |
Brightness | Stilb is a unit of brightness in the cgs system; corresponds to the brightness of a flat surface, 1 cm 2 of which gives in the direction perpendicular to this surface, a luminous intensity equal to 1 ce; 1 sb \u003d 1 10 4 nt (nit) (unit of brightness in the SI system) | Sat | sb |
Lambert is an off-system unit of brightness, derived from the stilb; 1 lambert = 1/π st = 3193 nt | |||
Apostille = 1 / π St / m 2 | |||
illumination | Fot - unit of illumination in the SGSL system (cm-g-sec-lm); 1 ph corresponds to the surface illumination of 1 cm 2 with a uniformly distributed luminous flux of 1 lm; 1 f \u003d 1 10 4 lux (lux) | f | ph |
V. Radiation intensity and doses | |||
Intensity | Curie is the basic unit for measuring the intensity of radioactive radiation, curie corresponding to 3.7·10 10 decays in 1 sec. any radioactive isotope |
curie | C or Cu |
millicurie \u003d 10 -3 curie, or 3.7 10 7 acts radioactive decay in 1 sec. | mcurie | mc or mCu | |
microcurie = 10 -6 curie | microcurie | μC or μCu | |
Dose | X-ray - the amount (dose) of X-ray or γ-rays, which in 0.001293 g of air (i.e., in 1 cm 3 of dry air at t ° 0 ° and 760 mm Hg) causes the formation of ions that carry one electrostatic a unit of the amount of electricity of each sign; 1 p causes the formation of 2.08 10 9 pairs of ions in 1 cm 3 of air | R | r |
milliroentgen \u003d 10 -3 p | mr | mr | |
microroentgen = 10 -6 p | microdistrict | µr | |
Rad - the unit of the absorbed dose of any ionizing radiation is equal to rad 100 erg per 1 g of the irradiated medium; when air is ionized by x-rays or γ-rays, 1 p is equal to 0.88 rad, and when tissues are ionized, practically 1 p is equal to 1 rad | glad | rad | |
Rem (X-ray biological equivalent) - amount (dose) of any kind ionizing radiation, causing the same biological effect as 1 p (or 1 rad) of hard X-rays. Different biological effect with equal ionization different types radiation led to the need to introduce another concept: the relative biological effectiveness of radiation -RBE; the relationship between doses (D) and the dimensionless coefficient (RBE) is expressed as Drem =D rad RBE, where RBE=1 for x-rays, γ-rays and β-rays and RBE=10 for protons up to 10 MeV, fast neutrons and α - natural particles (on the recommendation of the International Congress of Radiologists in Copenhagen, 1953) | reb, reb | rem |
Note. Multiple and submultiple units of measurement, with the exception of units of time and angle, are formed by multiplying them by the corresponding power of 10, and their names are attached to the names of units of measurement. It is not allowed to use two prefixes to the name of the unit. For example, you cannot write millimicrowatts (mmkw) or micromicrofarads (mmf), but you must write nanowatts (nw) or picofarads (pf). You should not use prefixes to the names of such units that indicate a multiple or submultiple unit of measurement (for example, micron). Multiple units of time may be used to express the duration of processes and designate calendar dates of events.
The most important units of the International System of Units (SI)
Basic units
(length, mass, temperature, time, electric current, light intensity)
Value name | Notation | ||
---|---|---|---|
Russian | international | ||
Length | A meter is a length equal to 1650763.73 wavelengths of radiation in vacuum, corresponding to the transition between levels 2p 10 and 5d 5 krypton 86 * |
m | m |
Weight | Kilogram - mass corresponding to the mass of the international standard of the kilogram | kg | kg |
Time | Second - 1/31556925.9747 part of a tropical year (1900) ** | sec | S, s |
The strength of the electric current | Ampere - the strength of an unchanging current, which, passing through two parallel rectilinear conductors of infinite length and negligible circular cross section, located at a distance of 1 m from one another in a vacuum, would cause a force between these conductors equal to 2 10 -7 n for each meter length | a | A |
The power of light | Candle - a unit of luminous intensity, the value of which is taken so that the brightness of a full (absolutely black) emitter at the solidification temperature of platinum is 60 ce per 1 cm 2 *** | St. | cd |
Temperature (thermodynamic) | Degree Kelvin (Kelvin scale) - a unit of temperature measurement according to the thermodynamic temperature scale, in which the temperature of the triple point of water **** is set to 273.16 ° K | °K | °K |
** That is, a second is equal to the specified part of the time interval between two successive passages of the Earth in orbit around the Sun of the point corresponding to the vernal equinox. This gives greater accuracy in determining the second than defining it as part of a day, since the length of the day varies.
*** That is, the luminous intensity of a certain reference source emitting light at the melting temperature of platinum is taken as a unit. The old International Candlestick Standard is 1.005 of the new Candlestick Standard. Thus, within the limits of usual practical accuracy, their values can be considered as coinciding.
**** Triple point - melting temperature of ice in the presence of saturated water vapor above it.
Complementary and derived units
Value name | Units; their definition | Notation | |
---|---|---|---|
Russian | international | ||
I. Flat angle, solid angle, force, work, energy, amount of heat, power | |||
flat corner | Radian - the angle between two radii of a circle, cutting an arc on a circle rad, the length of which is equal to the radius | glad | rad |
Solid angle | A steradian is a solid angle whose vertex is located in the center of the ster sphere and which cuts out an area on the surface of the sphere, equal to the area a square with a side equal to the radius of a sphere | erased | sr |
Strength | Newton force, under the influence of which a body with a mass of 1 kg acquires an acceleration equal to 1 m / s 2 | n | N |
Work, energy, amount of heat | Joule - the work done by a constant force of 1 n acting on the body on a path of 1 m traveled by the body in the direction of the force | j | J |
Power | Watt - the power at which for 1 sec. work done in 1 j | Tue | W |
II. Quantity of electricity, electrical voltage, electrical resistance, electrical capacitance | |||
Quantity of electricity, electric charge | Pendant - the amount of electricity flowing through the cross section of the conductor for 1 second. at a direct current of 1 a | to | C |
Electric voltage, difference electrical potentials, electromotive force (EMF) | Volt - the voltage in the section of the electrical circuit, when passing through which the amount of electricity in 1 k, work is done in 1 j | in | V |
Electrical resistance | Ohm - the resistance of the conductor, through which, at a constant voltage at the ends of 1 V, a direct current of 1 A passes | ohm | Ω |
Electrical capacitance | Farad is the capacitance of a capacitor, the voltage between the plates of which changes by 1 V when it is charged with an amount of electricity of 1 kV. | f | F |
III. Magnetic induction, magnetic flux, inductance, frequency | |||
Magnetic induction | Tesla is the induction of a homogeneous magnetic field, which acts on a section of a rectilinear conductor 1 m long, placed perpendicular to the direction of the field, with a force of 1 n when a direct current of 1 a passes through the conductor | tl | T |
Flux of magnetic induction | Weber - magnetic flux, created by a uniform field with a magnetic induction of 1 t through an area of 1 m 2, perpendicular to the direction of the magnetic induction vector | wb | wb |
Inductance | Henry is the inductance of a conductor (coil) in which an EMF of 1 V is induced when the current in it changes by 1 A in 1 sec. | Mr | H |
Frequency | Hertz - the frequency of a periodic process, in which for 1 sec. one oscillation occurs (cycle, period) | Hz | Hz |
IV. Luminous flux, light energy, brightness, illumination | |||
Light flow | Lumen - the luminous flux that gives inside a solid angle of 1 ster a point source of light of 1 s, radiating equally in all directions | lm | lm |
light energy | Lumen second | lm s | lm s |
Brightness | Nit - the brightness of a luminous plane, each square meter of which gives in a direction perpendicular to the plane, a luminous intensity of 1 sv | nt | nt |
illumination | Lux - illumination created by a luminous flux of 1 lm with its uniform distribution over an area of 1 m 2 | OK | lx |
Light quantity | lux second | lx sec | lx s |
Basically, one can imagine any big number different systems of units, but only a few are widely used. All over the world, for scientific and technical measurements, and in most countries in industry and everyday life, the metric system is used.
Basic units.
In the system of units for each measured physical quantity, an appropriate unit of measurement must be provided. Thus, a separate unit of measure is needed for length, area, volume, speed, etc., and each such unit can be determined by choosing one or another standard. But the system of units turns out to be much more convenient if in it only a few units are chosen as the main ones, and the rest are determined through the main ones. So, if the unit of length is a meter, the standard of which is stored in the State Metrological Service, then the unit of area can be considered a square meter, the unit of volume is a cubic meter, the unit of speed is a meter per second, etc.
The convenience of such a system of units (especially for scientists and engineers, who are much more likely to deal with measurements than other people) is that the mathematical relationships between the basic and derived units of the system turn out to be simpler. At the same time, a unit of speed is a unit of distance (length) per unit of time, a unit of acceleration is a unit of change in speed per unit of time, a unit of force is a unit of acceleration per unit of mass, etc. In mathematical notation, it looks like this: v = l/t, a = v/t, F = ma = ml/t 2. The presented formulas show the "dimension" of the quantities under consideration, establishing relationships between units. (Similar formulas allow you to define units for quantities such as pressure or electric current.) Such relationships are general and hold regardless of the units in which length is measured (meter, foot, or arshin) and which units are chosen for other quantities.
In engineering, the basic unit of measurement of mechanical quantities is usually taken not as a unit of mass, but as a unit of force. Thus, if in the system most used in physical research, a metal cylinder is taken as a standard of mass, then in a technical system it is considered as a standard of force that balances the force of gravity acting on it. But since the force of gravity is not the same at different points on the surface of the Earth, for the exact implementation of the standard, it is necessary to indicate the location. Historically, the location was at sea level at geographical latitude 45° . At present, such a standard is defined as the force necessary to give the indicated cylinder a certain acceleration. It is true that measurements in technology are, as a rule, not carried out with such a high accuracy that it would be necessary to take care of variations in the force of gravity (if we are not talking about the calibration of measuring instruments).
A lot of confusion is associated with the concepts of mass, force and weight. The fact is that there are units of all these three quantities that have the same names. Mass is an inertial characteristic of a body, showing how difficult it is to be removed by an external force from a state of rest or uniform and rectilinear motion. A unit of force is a force that, acting on a unit of mass, changes its speed by a unit of speed per unit of time.
All bodies are attracted to each other. Thus, any body near the Earth is attracted to it. In other words, the Earth creates the force of gravity acting on the body. This force is called its weight. The force of weight, as mentioned above, is not the same at different points on the surface of the Earth and at different heights above sea level due to differences in gravitational attraction and in the manifestation of the rotation of the Earth. However, the total mass of a given amount of substance is unchanged; it is the same in interstellar space and at any point on Earth.
Precise experiments have shown that the force of gravity acting on different bodies(i.e. their weight) is proportional to their mass. Therefore, masses can be compared on a balance, and masses that are the same in one place will be the same in any other place (if the comparison is carried out in a vacuum to exclude the influence of the displaced air). If a certain body is weighed on a spring balance, balancing the force of gravity with the force of an extended spring, then the results of the weight measurement will depend on the place where the measurements are taken. Therefore, spring scales must be adjusted at each new location so that they correctly show the mass. The simplicity of the weighing procedure itself was the reason that the force of gravity acting on the reference mass was taken as an independent unit of measurement in technology. HEAT.
Metric system of units.
The metric system is the common name for the international decimal system of units, the basic units of which are the meter and the kilogram. With some differences in details, the elements of the system are the same all over the world.
Story.
The metric system grew out of the decrees adopted by the National Assembly of France in 1791 and 1795 to define the meter as one ten-millionth of a section of the earth's meridian from North Pole to the equator.
By a decree issued on July 4, 1837, the metric system was declared mandatory for use in all commercial transactions in France. It has gradually supplanted local and national systems elsewhere in Europe and has been legally accepted in the UK and the US. An agreement signed on May 20, 1875 by seventeen countries created an international organization designed to preserve and improve the metric system.
It is clear that by defining the meter as a ten millionth of a quarter of the earth's meridian, the creators of the metric system sought to achieve invariance and exact reproducibility of the system. They took a gram as a unit of mass, defining it as the mass of one millionth of a cubic meter of water at its maximum density. Since it would not be very convenient to make geodetic measurements of a quarter of the earth's meridian with each sale of a meter of cloth or to balance a basket of potatoes in the market with an appropriate amount of water, metal standards were created that reproduce these ideal definitions with the utmost accuracy.
It soon became clear that metal standards of length could be compared with each other, introducing a much smaller error than when comparing any such standard with a quarter of the earth's meridian. In addition, it became clear that the accuracy of comparing metal mass standards with each other is much higher than the accuracy of comparing any such standard with the mass of the corresponding volume of water.
In this regard, the International Commission on the Meter in 1872 decided to take the “archival” meter stored in Paris “as it is” as the standard of length. Similarly, the members of the Commission took the archival platinum-iridium kilogram as the standard of mass, “considering that the simple ratio established by the creators of the metric system between a unit of weight and a unit of volume represents the existing kilogram with an accuracy sufficient for ordinary applications in industry and commerce, and accurate science needs not a simple numerical ratio of this kind, but an extremely perfect definition of this ratio. In 1875, many countries of the world signed an agreement on the meter, and this agreement established the procedure for coordinating metrological standards for the world scientific community through the International Bureau of Weights and Measures and the General Conference on Weights and Measures.
The new international organization immediately took up the development of international standards of length and mass and the transfer of their copies to all participating countries.
Length and mass standards, international prototypes.
International prototypes of standards of length and mass - meters and kilograms - were deposited with the International Bureau of Weights and Measures, located in Sevres, a suburb of Paris. The standard meter was a ruler made of an alloy of platinum with 10% iridium, the cross section of which was given a special X-shape to increase flexural rigidity with a minimum volume of metal. There was a longitudinal flat surface in the groove of such a ruler, and the meter was defined as the distance between the centers of two strokes applied across the ruler at its ends, at a standard temperature of 0 ° C. The mass of a cylinder made from the same platinum was taken as the international prototype of the kilogram. iridium alloy, which is the standard of the meter, with a height and diameter of about 3.9 cm. The weight of this standard mass, equal to 1 kg at sea level at a geographical latitude of 45 °, is sometimes called a kilogram-force. Thus, it can be used either as a standard of mass for the absolute system of units, or as a standard of force for the technical system of units, in which one of the basic units is the unit of force.
The International Prototypes were selected from a significant batch of identical standards made at the same time. The other standards of this batch were transferred to all participating countries as national prototypes (state primary standards), which are periodically returned to the International Bureau for comparison with international standards. Comparisons made at various times since then show that they show no deviations (from international standards) beyond the limits of measurement accuracy.
International SI system.
The metric system was very favorably received by scientists of the 19th century. partly because it was proposed as an international system of units, partly because its units were theoretically supposed to be independently reproducible, and also because of its simplicity. Scientists began to derive new units for the various physical quantities they were dealing with, based on the elementary laws of physics and relating these units to the units of length and mass of the metric system. The latter increasingly won various European countries, in which many unrelated units for different quantities were previously in circulation.
Although in all countries that adopted the metric system of units, the standards of metric units were almost the same, there were various discrepancies in the derived units between different countries and different disciplines. In the field of electricity and magnetism, two separate systems of derived units have emerged: the electrostatic one, based on the force with which two electric charges act on each other, and the electromagnetic one, based on the force of the interaction of two hypothetical magnetic poles.
The situation became even more complicated with the advent of the so-called. practical electrical units, introduced in the middle of the 19th century. British Association for the Advancement of Science to meet the demands of rapidly developing wire telegraph technology. Such practical units do not coincide with the units of both systems named above, but from the units electromagnetic system differ only by factors equal to integer powers of ten.
Thus, for such common electrical quantities as voltage, current and resistance, there were several options for the accepted units of measurement, and each scientist, engineer, teacher had to decide for himself which of these options he should use. In connection with the development of electrical engineering in the second half of the 19th and first half of the 20th centuries. more and more practical units were used, which eventually came to dominate the field.
To eliminate such confusion in the early 20th century. a proposal was put forward to combine practical electrical units with the corresponding mechanical units based on metric units of length and mass, and to build some kind of consistent (coherent) system. In 1960, the XI General Conference on Weights and Measures adopted a unified International System of Units (SI), defined the basic units of this system and prescribed the use of some derived units, "without prejudice to the question of others that may be added in the future." Thus, for the first time in history, an international coherent system of units was adopted by international agreement. It is now accepted as the legal system of units of measurement by most countries in the world.
The International System of Units (SI) is a harmonized system in which for any physical quantity such as length, time or force, there is one and only one unit of measure. Some of the units are given specific names, such as the pascal for pressure, while others are named after the units from which they are derived, such as the unit of speed, the meter per second. The main units, together with two additional geometric ones, are presented in Table. 1. Derived units for which special names are adopted are given in Table. 2. Of all the derived mechanical units, the most important are the newton unit of force, the joule unit of energy, and the watt unit of power. Newton is defined as the force that gives a mass of one kilogram an acceleration equal to one meter per second squared. A joule is equal to the work done when the point of application of a force equal to one Newton moves one meter in the direction of the force. A watt is the power at which work of one joule is done in one second. Electrical and other derived units will be discussed below. The official definitions of primary and secondary units are as follows.
A meter is the distance traveled by light in a vacuum in 1/299,792,458 of a second. This definition was adopted in October 1983.
Kilogram equal to mass international prototype of the kilogram.
A second is the duration of 9,192,631,770 periods of radiation oscillations corresponding to transitions between two levels of the hyperfine structure of the ground state of the cesium-133 atom.
Kelvin is equal to 1/273.16 of the thermodynamic temperature of the triple point of water.
A mole is equal to the amount of a substance that contains the same amount structural elements, how many atoms are in the carbon-12 isotope with a mass of 0.012 kg.
A radian is a flat angle between two radii of a circle, the length of the arc between which is equal to the radius.
The steradian is equal to the solid angle with the vertex at the center of the sphere, which cuts out on its surface an area equal to the area of a square with a side equal to the radius of the sphere.
For the formation of decimal multiples and submultiples, a number of prefixes and multipliers are prescribed, indicated in Table. 3.
Table 3 INTERNATIONAL SI DECIMAL MULTIPLES AND MULTIPLE UNITS AND MULTIPLIERS |
|||||
exa | deci | ||||
peta | centi | ||||
tera | Milli | ||||
giga | micro |
mk |
|||
mega | nano | ||||
kilo | pico | ||||
hecto | femto | ||||
soundboard |
Yes |
atto |
Thus, a kilometer (km) is 1000 m, and a millimeter is 0.001 m. (These prefixes apply to all units, such as kilowatts, milliamps, etc.)
Initially, one of the basic units was supposed to be the gram, and this was reflected in the names of the units of mass, but now the basic unit is the kilogram. Instead of the name of megagrams, the word "ton" is used. In physical disciplines, for example, to measure the wavelength of visible or infrared light, a millionth of a meter (micrometer) is often used. In spectroscopy, wavelengths are often expressed in angstroms (Å); An angstrom is equal to one tenth of a nanometer, i.e. 10 - 10 m. For radiation with a shorter wavelength, such as X-ray, in scientific publications it is allowed to use a picometer and x-unit (1 x-unit = 10 -13 m). A volume equal to 1000 cubic centimeters (one cubic decimeter) is called a liter (l).
Mass, length and time.
All the basic units of the SI system, except for the kilogram, are currently defined in terms of physical constants or phenomena, which are considered to be invariable and reproducible with high accuracy. As for the kilogram, a method for its implementation with the degree of reproducibility that is achieved in the procedures for comparing various mass standards with the international prototype of the kilogram has not yet been found. Such a comparison can be carried out by weighing on a spring balance, the error of which does not exceed 1×10–8. The standards of multiples and submultiples for a kilogram are established by combined weighing on a balance.
Because the meter is defined in terms of the speed of light, it can be reproduced independently in any well-equipped laboratory. So, by the interference method, dashed and end gauges, which are used in workshops and laboratories, can be checked by comparing directly with the wavelength of light. The error with such methods under optimal conditions does not exceed one billionth (1×10–9). With the development of laser technology, such measurements have been greatly simplified and their range has been substantially extended.
Similarly, the second, in accordance with its modern definition, can be independently realized in a competent laboratory in an atomic beam facility. The beam atoms are excited by a high-frequency generator tuned to the atomic frequency, and the electronic circuit measures time by counting the oscillation periods in the generator circuit. Such measurements can be carried out with an accuracy of the order of 1×10 -12 - much better than was possible with previous definitions of the second, based on the rotation of the Earth and its revolution around the Sun. Time and its reciprocal, frequency, are unique in that their references can be transmitted by radio. Thanks to this, anyone with the appropriate radio receiving equipment can receive accurate time and reference frequency signals that are almost identical in accuracy to those transmitted on the air.
Mechanics.
temperature and warmth.
Mechanical units do not allow solving all scientific and technical problems without involving any other ratios. Although the work done when moving a mass against the action of a force and the kinetic energy of a certain mass are equivalent in nature to the thermal energy of a substance, it is more convenient to consider temperature and heat as separate quantities that do not depend on mechanical ones.
Thermodynamic temperature scale.
The thermodynamic temperature unit Kelvin (K), called the kelvin, is determined by the triple point of water, i.e. the temperature at which water is in equilibrium with ice and steam. This temperature is taken equal to 273.16 K, which determines the thermodynamic temperature scale. This scale, proposed by Kelvin, is based on the second law of thermodynamics. If there are two heat reservoirs with constant temperature and a reversible heat engine transferring heat from one of them to the other in accordance with the Carnot cycle, then the ratio of the thermodynamic temperatures of the two reservoirs is given by the equality T 2 /T 1 = –Q 2 Q 1 , where Q 2 and Q 1 - the amount of heat transferred to each of the reservoirs (the minus sign indicates that heat is taken from one of the reservoirs). Thus, if the temperature of the warmer reservoir is 273.16 K, and the heat taken from it is twice the heat transferred to another reservoir, then the temperature of the second reservoir is 136.58 K. If the temperature of the second reservoir is 0 K, then it no heat will be transferred at all, since all the energy of the gas has been converted into mechanical energy in the adiabatic expansion section of the cycle. This temperature is called absolute zero. The thermodynamic temperature commonly used in scientific research, coincides with the temperature included in the equation of state for an ideal gas PV = RT, where P- pressure, V- volume and R is the gas constant. The equation shows that for an ideal gas, the product of volume and pressure is proportional to temperature. For any of the real gases, this law is not exactly fulfilled. But if we make corrections for virial forces, then the expansion of gases allows us to reproduce the thermodynamic temperature scale.
International temperature scale.
In accordance with the above definition, the temperature can be measured with a very high accuracy (up to about 0.003 K near the triple point) by gas thermometry. A platinum resistance thermometer and a gas reservoir are placed in a heat-insulated chamber. When the chamber is heated, the electrical resistance of the thermometer increases and the gas pressure in the reservoir rises (in accordance with the equation of state), and when cooled, the reverse picture is observed. By simultaneously measuring resistance and pressure, it is possible to calibrate a thermometer according to gas pressure, which is proportional to temperature. Then the thermometer is placed in a thermostat in which liquid water can be maintained in equilibrium with its solid and vapor phases. By measuring its electrical resistance at this temperature, a thermodynamic scale is obtained, since the temperature of the triple point is assigned a value equal to 273.16 K.
There are two international temperature scales - Kelvin (K) and Celsius (C). The Celsius temperature is obtained from the Kelvin temperature by subtracting 273.15 K from the latter.
Accurate temperature measurements using gas thermometry require a lot of work and time. Therefore, in 1968 the International Practical Temperature Scale (IPTS) was introduced. Using this scale, thermometers of various types can be calibrated in the laboratory. This scale was established using a platinum resistance thermometer, a thermocouple and a radiation pyrometer used in the temperature intervals between some pairs of constant reference points (temperature benchmarks). The MTS was supposed to correspond with the greatest possible accuracy to the thermodynamic scale, but, as it turned out later, its deviations are very significant.
Fahrenheit temperature scale.
The Fahrenheit temperature scale, which is widely used in combination with the British technical system of units, as well as in non-scientific measurements in many countries, is usually determined by two constant reference points - the temperature of ice melting (32 ° F) and the boiling point of water (212 ° F) at normal (atmospheric) pressure. So to get the Celsius temperature from the Fahrenheit temperature, subtract 32 from the latter and multiply the result by 5/9.
Heat units.
Since heat is a form of energy, it can be measured in joules, and this metric unit has been adopted by international agreement. But since the amount of heat was once determined by changing the temperature of a certain amount of water, a unit called a calorie and equal to the amount of heat needed to raise the temperature of one gram of water by 1 ° C has become widespread. Due to the fact that the heat capacity of water depends on temperature , I had to specify the value of the calorie. At least two different calories appeared - "thermochemical" (4.1840 J) and "steam" (4.1868 J). The “calorie” used in dieting is actually a kilocalorie (1000 calories). The calorie is not an SI unit and has fallen into disuse in most areas of science and technology.
electricity and magnetism.
All common electrical and magnetic units of measurement are based on the metric system. In accordance with modern definitions of electrical and magnetic units, they are all derived units derived from certain physical formulas from metric units of length, mass and time. Since most electrical and magnetic quantities are not so easy to measure using the standards mentioned, it was considered that it was more convenient to establish, by appropriate experiments, derived standards for some of the indicated quantities, and measure others using such standards.
SI units.
Below is a list of electrical and magnetic units of the SI system.
The ampere, the unit of electric current, is one of the six basic units of the SI system. Ampere - the strength of an unchanging current, which, when passing through two parallel straight conductors of infinite length with a negligibly small circular cross-sectional area, located in vacuum at a distance of 1 m from one another, would cause an interaction force equal to 2 × 10 on each section of the conductor 1 m long - 7 N.
Volt, unit of potential difference and electromotive force. Volt - electric voltage in a section of an electrical circuit with a direct current of 1 A with a power consumption of 1 W.
Coulomb, a unit of quantity of electricity (electric charge). Coulomb - the amount of electricity passing through the cross section of the conductor at a constant current of 1 A in a time of 1 s.
Farad, unit of electrical capacitance. Farad is the capacitance of a capacitor, on the plates of which, with a charge of 1 C, an electric voltage of 1 V arises.
Henry, unit of inductance. Henry is equal to the inductance of the circuit in which an EMF of self-induction of 1 V occurs with a uniform change in the current strength in this circuit by 1 A in 1 s.
Weber, unit of magnetic flux. Weber - a magnetic flux, when it decreases to zero in a circuit coupled to it, which has a resistance of 1 Ohm, an electric charge equal to 1 C flows.
Tesla, unit of magnetic induction. Tesla - magnetic induction of a uniform magnetic field, in which the magnetic flux through a flat area of 1 m 2, perpendicular to the lines of induction, is 1 Wb.
Practical standards.
Light and illumination.
The units of luminous intensity and illuminance cannot be determined on the basis of mechanical units alone. One can express the energy flux in a light wave in W/m 2 and the intensity of a light wave in V/m, as in the case of radio waves. But the perception of illumination is a psychophysical phenomenon in which not only the intensity of the light source is essential, but also the sensitivity of the human eye to the spectral distribution of this intensity.
By international agreement, the candela (previously called a candle) is taken as a unit of luminous intensity, equal to the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540 × 10 12 Hz ( l\u003d 555 nm), the energy strength of the light radiation of which in this direction is 1/683 W / sr. This roughly corresponds to the light intensity of the spermaceti candle, which once served as a standard.
If the luminous intensity of the source is one candela in all directions, then the total luminous flux is 4 p lumens Thus, if this source is located in the center of a sphere with a radius of 1 m, then the illumination of the inner surface of the sphere is equal to one lumen per square meter, i.e. one suite.
X-ray and gamma radiation, radioactivity.
Roentgen (R) is an obsolete unit of exposure dose of X-ray, gamma and photon radiation, equal to the amount of radiation, which, taking into account secondary electron radiation, forms ions in 0.001 293 g of air, carrying a charge equal to one CGS charge unit of each sign. In the SI system, the unit of absorbed radiation dose is the gray, which is equal to 1 J/kg. The standard of the absorbed dose of radiation is the installation with ionization chambers, which measure the ionization produced by radiation.