Units of Measurement
1. 1. PHYSICAL QUANTITIES AND UNITS
Physical quantities: In everyday life, we come across measurement length in meters, volume of liquids in litres and mass of substances in kilograms. In addition to this, we also measure temperature, pressure, force, density etc. during scientific studies.
All such quantities which we come across during our scientific studies are called physical quantities.
Clearly, the measurement of a physical quantity consist of two parts (i)the number and (ii)the unit. For example, if a piece of cloth measures 3.8 meters, it involves two parts ; 3.8 is the number and meter is the unit.
A unit is defined as the standard of reference chosen to measure any physical quantity.
Three commonly used systems are :
CGS (Centimeter-Gram- Second) System
FPS (Foot-Pound- Second) System
MKS (Meter-Kilogram- Second) System
Metric system of mass and measures is adopted by most of the nations. In the metric system, the units are expressed in the multiples of ten.
Advantages of Metric System
- Its small and large units are multiples of ten and hence can be inter converted easily.
- It is universal and forms a good mode of communication.
- There is a relationship between different kinds of measurements. For example, mass of the substance is expressed in gms ans volume in ml. By relating the two, density is expressed in gms per mil.
*1 ml (millimeter) = 1.000021 cc (cubic centimeters).
Some less common units are
Temperature of a body is measured with an instrument called Thermometer. There are 3 Scales which are used for temperature measurement, such as
Celsius (known until 1948 as centigrade) is a temperature scale that is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale two years before his death. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale as well as a unit to indicate a temperature interval (a difference between two temperatures or an uncertainty).
From 1744 until 1954, 0 °C was defined as the freezing point of water and 100 °C was defined as the boiling point of water, both at a pressure of one standard atmosphere. Although these defining correlations are commonly taught in schools today, by international agreement the unit “degree Celsius” and the Celsius scale are currently defined by two different points: absolute zero, and the triple point of VSMOW (specially prepared water). This definition also precisely relates the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature (symbol: K). Absolute zero, the hypothetical but unattainable temperature at which matter exhibits zero entropy, is defined as being precisely 0 K and −273.15 °C. The temperature value of the triple point of water is defined as being precisely 273.16 K and 0.01 °C.
This definition fixes the magnitude of both the degree Celsius and the kelvin as precisely 1 part in 273.16 parts, the difference between absolute zero and the triple point of water. Thus, it sets the magnitude of one degree Celsius and that of one kelvin as exactly the same. Additionally, it establishes the difference between the two scales’ null points as being precisely 273.15 degrees Celsius (−273.15 °C = 0 K and 0 °C = 273.15 K).
On the Fahrenheit scale, the freezing point of water is 32 degrees Fahrenheit (°F) and the boiling point is 212 °F (at standard atmospheric pressure). This puts the boiling and freezing points of water exactly 180 degrees apart. Therefore, a degree on the Fahrenheit scale is 1⁄180 of the interval between the freezing point and the boiling point. On the Celsius scale, the freezing and boiling points of water are 100 degrees apart. A temperature interval of 1 °F is equal to an interval of 5⁄9 degrees Celsius. The Fahrenheit and Celsius scales intersect at −40° (i.e., −40 °F = −40 °C).
Absolute zero is −273.15 °C or −459.67 °F. The Rankine temperature scale uses degree intervals of the same size as those of the Fahrenheit scale, except that absolute zero is 0 R—the same way that the Kelvin temperature scale matches the Celsius scale, except that absolute zero is 0 K.
The Fahrenheit scale uses the symbol ° to denote a point on the temperature scale (as does Celsius) and the letter F to indicate the use of the Fahrenheit scale (e.g. “Gallium melts at 85.5763 °F”), as well as to denote a difference between temperatures or an uncertainty in temperature (e.g. “The output of the heat exchanger experiences an increase of 72 °F” and “Our standard uncertainty is ±5 °F”).
For an exact conversion, the following formulas can be applied. Here, f is the value in Fahrenheit and c the value in Celsius:
- f °Fahrenheit to c °Celsius : (f − 32) °F × 5°C/9°F = (f − 32)/1.8 °C = c °C
- c °Celsius to f °Fahrenheit : (c °C × 9°F/5°C) + 32 °F = (c × 1.8) °F + 32 °F = f °F
This is also an exact conversion making use of the identity -40°F = -40°C. Again, f is the value in Fahrenheit and c the value in Celsius:
- f °Fahrenheit to c °Celsius : ((f + 40) ÷ 1.8) − 40 = c.
- c °Celsius to f °Fahrenheit : ((c + 40) * 1.8) − 40 = f.
Absolute scale(Kelvin scale)
he kelvin is a unit of measure for temperature based upon an absolute scale. It is one of the seven base units in the International System of Units (SI) and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin is defined as the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F).In other words, it is defined such that the triple point of water is exactly 273.16 K.
The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Lord Kelvin (1824–1907), who wrote of the need for an “absolute thermometric scale”. Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or typeset as a degree. The kelvin is the primary unit of temperature measurement in the physical sciences, but is often used in conjunction with the Celsius degree, which has the same magnitude. The definition implies that absolute zero (0 K) is equivalent to −273.15 °C (−459.67 °F).
|from Celsius||to Celsius|
|Fahrenheit||[°F] = [°C] × 9⁄5 + 32||[°C] = ([°F] − 32) × 5⁄9|
|Kelvin||[K] = [°C] + 273.15||[°C] = [K] − 273.15|
|Rankine||[°R] = ([°C] + 273.15) × 9⁄5||[°C] = ([°R] − 491.67) × 5⁄9|
|Delisle||[°De] = (100 − [°C]) × 3⁄2||[°C] = 100 − [°De] × 2⁄3|
|Newton||[°N] = [°C] × 33⁄100||[°C] = [°N] × 100⁄33|
|Réaumur||[°Ré] = [°C] × 4⁄5||[°C] = [°Ré] × 5⁄4|
|Rømer||[°Rø] = [°C] × 21⁄40 + 7.5||[°C] = ([°Rø] − 7.5) × 40⁄21|
|from Fahrenheit||to Fahrenheit|
|Celsius||[°C] = ([°F] − 32) × 5⁄9||[°F] = [°C] × 9⁄5 + 32|
|Kelvin||[K] = ([°F] + 459.67) × 5⁄9||[°F] = [K] × 9⁄5 − 459.67|
|Rankine||[°R] = [°F] + 459.67||[°F] = [°R] − 459.67|
|Delisle||[°De] = (212 − [°F]) × 5⁄6||[°F] = 212 − [°De] × 6⁄5|
|Newton||[°N] = ([°F] − 32) × 11⁄60||[°F] = [°N] × 60⁄11 + 32|
|Réaumur||[°Ré] = ([°F] − 32) × 4⁄9||[°F] = [°Ré] × 9⁄4 + 32|
|Rømer||[°Rø] = ([°F] − 32) × 7⁄24 + 7.5||[°F] = ([°Rø] − 7.5) × 24⁄7 + 32|
|from Kelvin||to Kelvin|
|Celsius||[°C] = [K] − 273.15||[K] = [°C] + 273.15|
|Fahrenheit||[°F] = [K] × 9⁄5 − 459.67||[K] = ([°F] + 459.67) × 5⁄9|
|Rankine||[°R] = [K] × 9⁄5||[K] = [°R] × 5⁄9|
|Delisle||[°De] = (373.15 − [K]) × 3⁄2||[K] = 373.15 − [°De] × 2⁄3|
|Newton||[°N] = ([K] − 273.15) × 33⁄100||[K] = [°N] × 100⁄33 + 273.15|
|Réaumur||[°Ré] = ([K] − 273.15) × 4⁄5||[K] = [°Ré] × 5⁄4 + 273.15|
|Rømer||[°Rø] = ([K] − 273.15) × 21⁄40 + 7.5||[K] = ([°Rø] − 7.5) × 40⁄21 + 273.15|
International System of Units
The International System of Units (French: Système international d’unités pronounced: [sistɛm ɛ̃tɛʁnasjɔnal dynite]; abbreviated as SI) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units. The system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units.
The system was published in 1960 as the result of an initiative that began in 1948. It is based on the metre-kilogram-second system of units (MKS) rather than any variant of the centimetre-gram-second system (CGS). SI is intended to be an evolving system, so prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves. The 24th and 25th General Conferences on Weights and Measures (CGPM) in 2011 and 2014, for example, discussed a proposal to change the definition of the kilogram, linking it to an invariant of nature rather than to the mass of a material artefact, thereby ensuring long-term stability.
The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems and the lack of coordination between the various disciplines that used them. The CGPM, which was established by the Metre Convention of 1875, brought together many international organisations to not only agree on the definitions and standards of the new system but also agree on the rules for writing and presenting measurements in a standardised manner around the world.
Units and prefixes
The International System of Units consists of a set of base units, a set of derived units with special names, and a set of decimal-based multipliers that are used as prefixes. The term SI Units covers all three categories, but the term coherent SI units includes only base units and coherent derived units.:103–106
The SI base units are the building blocks of the system and all other units are derived from them. When Maxwell first introduced the concept of a coherent system, he identified three quantities that could be used as base units: mass, length and time. Giorgi later identified the need for an electrical base unit. Theoretically any one of electric current, potential difference, electrical resistance, electrical charge or a number of other quantities could have provided the base unit, with the remaining units then being defined by the laws of physics. In the event, the unit of electric current was chosen for SI. Another three base units (for temperature, substance and luminous intensity) were added later.
|Definition (incomplete)[n 1]||Dimension
|mole||mol||amount of substance||N|
The derived units in the SI are formed by powers, products or quotients of the base units and are unlimited in number.:103:3 Derived units are associated with derived quantities, for example velocity is a quantity that is derived from the base quantities of time and length, so in SI the derived unit is metres per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units.
Coherent units are derived units that contain no numerical factor other than 1—quantities such as standard gravity and density of water are absent from their definitions. In the example above, one newton is the force required to accelerate a mass of one kilogram by one metre per second squared. Since the SI units of mass and acceleration are kg and m·s−2 respectively and F ∝ m × a, the units of force (and hence of newtons) is formed by multiplication to give kg·m·s−2. Since the newton is part of a coherent set of units, the constant of proportionality is 1.
For the sake of convenience, some derived units have special names and symbols. Such units may themselves be used in combination with the names and symbols for base units and for other derived units to express the units of other derived quantities. For example, the SI unit of force is the newton (N), the SI unit of pressure is the pascal (Pa)—and the pascal can be defined as “newtons per square metre” (N/m2).
other SI units
SI base units
|joule||J||energy, work, heat||N·m||kg·m2·s−2|
|watt||W||power, radiant flux||J/s||kg·m2·s−3|
|coulomb||C||electric charge or quantity of electricity||s·A|
|volt||V||voltage (electrical potential difference), electromotive force||W/A||kg·m2·s−3·A−1|
|ohm||Ω||electric resistance, impedance, reactance||V/A||kg·m2·s−3·A−2|
|tesla||T||magnetic flux density||Wb/m2||kg·s−2·A−1|
|degree Celsius||°C||temperature relative to 273.15 K||K|
|becquerel||Bq||radioactivity (decays per unit time)||s−1|
|gray||Gy||absorbed dose (of ionizing radiation)||J/kg||m2·s−2|
|sievert||Sv||equivalent dose (of ionizing radiation)||J/kg||m2·s−2|
1. The radian and steradian, once given special status, are now considered dimensionless derived units.:3
2. The ordering of this table is such that any derived unit is based only on base units or derived units that precede it in the table.
Prefixes are added to unit names to produce multiple and sub-multiples of the original unit. All multiples are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth, so there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, so for example a millionth of a metre is a micrometre, not a millimillimetre. Multiples of the kilogram are named as if the gram were the base unit, so a millionth of a kilogram is a milligram, not a microkilogram.:122:14