Time :

Historical detail : There was a trial to "metricate" the time and the calendar during the French revolution. Months were to be made of three weeks, each ten days long. Each day had 10 hours. The system lasted only a few years. The clockmakers opposed violently the millihours ( = 8.64 sec), while the clergy resented the cancellation of the Sabbath. This last opposition is probably at the root of the long time dislike towards the metric system in the US (The Great Fear of the Godless Society !) It must be acknowledged that there was no real need for such a change provided the old system was already quite universal, but one had to try to be sure. New proposals keep popping up from time to time. Anyway, the unit being now a fully metric second (at least in the scientific world), the main problem was avoided : see the nanosecond, etc.

Temperature :

In 1730, in France, Rene Antoine Ferchault de Reaumur built the first alcohol thermometer. He allocated 0 to freezing water and 80 to boiling water.

In 1742, in Sweden, the astronomer Anders Celsius used a scale allocating 100 to freezing water and 0 (!) to boiling water. His scale was later inverted (0 to freezing water and 100 for boiling) and long known as "centigrade".
Comparing the scales, 9 deg. Fahrenheit = 4 deg. Reaumur = 5 deg. Celsius.
(There was also a de Lisle scale, with 0 and 150 for freezing and boiling water)

• C = (F - 32) * 5/9
• F = 32 + C * 9/5

Absolute temperature : starting from the absolute zero (at -273.15 C or -459.67 F), it was tempting to follow the old idea of Fahrenheit and have only a positive scale. This was done by Sir William Thomson, lord Kelvin, from the Celsius scale and by William Rankine from the Fahrenheit scale. ( K = C + 273.15 and rankine = F + 459.67 ) (with 1 rankine = 5 / 9 kelvin)
So water is freezing at 273.15 K or 491.67 rankine, and boiling at 373.15 K or 671.67 rankine.

The SI uses the kelvin scale, defined by the triple point of water (at 273.16 K or 0.01°C) and the absolute zero.

Area :

The "are" - old metric unit - is still in use, although not officially :

• centiare : 1 m2
• are : 100 centiares ( = 10 m * 10 m = 100 m2 = 1 square decameter)
• hectare : 100 ares ( = 100 m * 100 m = 10 000 m2 = 1 square hectometer)

Volume :

The litre is a bit special : metric but not really SI. It is a cubic decimeter.
Example : 10 hectolitres (or hectoliters) = 1 cubic meter.
Or 1000 milliliters (or cubic centimeters) = 1 litre.

The original unit of volume in the metric system was the stere equal to 1 cubic meter (and still in use when buying firewood in France.)

Old Anglo-Saxon units : rather complicated.

The other basic units :

• Intensity of electric current : 1 ampere is the intensity which, when flowing through two infinite parallel wires separated by 1 meter, generates a force of 2 * 10 ^ newton between the wires. (See the newton under "Force".)
• Quantity of matter : 1 mole is the quantity of matter containing as many elementary entities as 12 gram of C12. (This is Avogadro : 6.022045 * 10 ^23 entities/mol.)
• candela : luminous intensity in a given direction of a source which emits monochromatic radiation of frequency 640 terahertz and of which the radiant intensity in that direction is 1/683 watt per steradian.

Force :

Pressure :

• The pascal (in the SI system) is 1 newton per square meter.
• The pieze (in the MTS system) is 1 sthene per square meter (therefore = 1000 Pascal)
• The barye (in the CGS system) is 1 dyne per square centimeter ( = 0.1 Pascal)
• The PSI is 1 pound-force per square inch ( = 6894.76 pascal with the standard "g")
• The kg/cm2 is 1 kilogram-force per square centimeter ( = 98066.5 Pa - long used because very close to 1 atmosphere)

• Bar = 1 hectopieze = 100 000 pascal (still often used by meteorologists.)
• OSI = 1 ounce per square inch = 1/16 PSI (used by burner manufacturers in the US)

To set the scale, we'll compare all these different units to a standard atmosphere :

• 101 325 pascal - or 101.325 kPa - or 0.101325 MPa - or 1.01325 Bar - or 1013.25 mbar
• 760 mm mercury - or 760 torr - or 29.921 inches mercury
• 14.696 PSI - or 235.1375 OSI - or 2116.2382 lb/sq.ft.
• 10332 mm water - or 1.0332 kg/cm2 (a column of water 10.3323 m high on 1 square meter at 4°C weighs 10332.3 kg - multiplied by 9.80665 gives 101 325 Pa)
• the equivalent will be, of course, 406.78 inches of water
• I have never heard of poundal per square inch but, adapting the units, it should be 472.828

Work & energy :

• The joule in the SI or MKSA systems is the work done by a force of 1 newton moving 1 meter.
• erg is the CGS unit : a force of 1 dyne moving 1 cm. (1 erg = 10^-7 newton)
• The MTS system didn't have a specific name (the kilojoule was readily used.)
• The kilogram-meter : 1 kilogram(force) over 1 meter. ( 1 kg.m = 9.80665 joule)
• The foot-poundal : 1 poundal over 1 foot. ( = 0.138255 * 0.3048 = 0.04214 joule)
• The foot-pound : 1 pound(force) over 1 foot. ( = 4.4481765 * 0.3048 = 1.355804 J)
• We may mention also the electron-Volt ( = 1.602189 10^-19 J)

• calorie : was the quantity of heat needed to increase by 1°C the temperature of 1 gram of water (around 15°C). Also called "small calorie". Several different equivalencies have been proposed over the years, with the third decimal changing for excellent reasons. Let's just remember today : 1 (thermochemical) calorie = 4.184 Joule. This was an excellent unit, quite adapted to all problems involving water. As with all old units, several names appeared over the years :
  • "Large calorie" or "Calorie" or kcal : equal to 1000 cal (the heat needed to increase 1 kg of water by 1°C)
  • "Frigorie" : 1 Large calorie with a minus sign (standard unit for the calculation of fridges, etc.)
  • "Thermie" : equal to 1000 kcal or 1 Megacalorie
• The BTU or British Thermal Unit, was the equivalent in the Anglo-Saxon system : the energy needed to heat up 1 pound of water by 1°F. Therefore we have : 1 BTU = 453.5924 * 5 / 9 = 251.9958 cal and, times 4.184, we find : 1 BTU = 1054.35 Joule.
• There has also been a hybrid unit, the CHU (for Centigrade Heat Unit) - required to increase by 1°C the temp. of 1 pound of water. (It's of course equal to 453.59 cal or 1.8 BTU or 1897.83 J)
• An old unit is the therm, equiv. to 1 erg.
• not to be confused with the other therm equal to 100 000 BTU !

Power :

• The SI unit is the Watt, equal to 1 joule per second.
• The erg/sec in the CGS system (no special name) and the kilowatt in the MTS system
• The foot-pound per second ( = 1.3558 W, of course)
• and, surprisingly, the foot-pound per minute ( = 1/60 foot-pound per sec.)
• The Horse-Power (H.P.) is worth an explanation. In the old mines, a horse would pull a load of 150 lb. up the shaft and through a pulley at a steady speed of 2.5 miles/hr (or 220 ft per minute) all day long. Its power was therefore : 150 * 220 = 33 000 ft.lb/min or 550 ft.lb/sec. (Equiv. to 745.69 Watt)
• An old metric unit was the C.V. (for "Cheval-Vapeur" in French - or Steam-Horse) equal to 75 kilogram-meter per second. Times 9.80665 = 735.5 Watt. One may wonder, why 75 kg.m/s in a decimal universe ? Surely to get a metric equivalent to the British H.P. (Shame !)
• An even older unit was the poncelet equal to 100 kg.m/s (or 980.665 W)

• kilowatt-hour (kWh) : 1 kW is 1000 joule per second - during one hour, a kWh delivers 3 600 000 joule. (It's therefore equiv. to 860 kcal or 2 655 251 foot-pound)
• horse-power-hour : same principle. (= 2 684 500 Joule or 2.6845 MJ or 1 980 000 foot-pound)

Jacques Proot 276, Grosvenor
Beaconsfield (Quebec) H9W 1S5
Canada

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