Definition:Metric System/Mass/Kilogram
Definition
The kilogram is the SI base unit of mass.
It is defined as follows:
- $1$ kilogram is the quantity of mass that would make the fixed numerical value of the Planck constant $h$ to be $6 \cdotp 62607015 \times 10^{-34}$ when expressed in the unit Joule seconds.
The Joule second is equal to $1 \, \mathrm {kg} \, \mathrm m^2 \, \mathrm s^{−1}$, where the metre and the second are defined in terms of:
- the speed of light $c$
- the time of transition between the two hyperfine levels of the ground state of the caesium $133$ atom at rest at $0 \, \mathrm K$.
Conversion Factors
\(\ds \) | \(\) | \(\ds 1\) | kilogram | |||||||||||
\(\ds \) | \(=\) | \(\ds 1000\) | grams | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 2 \cdotp 20462\) | pounds avoirdupois |
Symbol
- $\mathrm {kg}$
The symbol for the kilogram is $\mathrm {kg}$.
The $\LaTeX$ code for \(\mathrm {kg}\) is \mathrm {kg}
.
Also see
Historical Note
This itself was defined as the mass of one cubic centimetre of water at the melting point of ice.
- 1799: The actual reference kilogram was manufactured as a prototype.
It had a mass equal to the mass of $1 \, \mathrm {dm}^3$ of water at its maximum density, approximately $4 \cels$.
- 1875: The International Prototype Kilogram (IPK) was derived from this.
This has a mass which is almost exactly equal to the mass of one litre of water.
The weight of the IPK has been known to vary, and so a more stable alternative was sought, based on a fundamental constant.
- 2011: A decision was reached in principle that it should be redefined in terms of Planck's constant.
The actual decision was deferred to $2014$, and was once then deferred to the next meeting.
- 20 May 2019: The kilogram is no longer defined by a physical artefact, being the last of the fundamental units of physics which was so defined.
Linguistic Note
The original British English spelling of kilogram was kilogramme.
However, this is rarely used nowadays, as the American kilogram is now the international standard.
Linguistic Note on Kilo
The prefix kilo- derives from the Greek word χίλιοι (khilioi), which means thousand.
Sources
- 1966: Isaac Asimov: Understanding Physics ... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $3$: The Laws of Motion: Mass
- 1969: J.C. Anderson, D.M. Hum, B.G. Neal and J.H. Whitelaw: Data and Formulae for Engineering Students (2nd ed.) ... (previous) ... (next): $1.$ Units and Abbreviations: $1.2$ SI units $(1)$ Basic units
- 1976: Ralph J. Smith: Circuits, Devices and Systems (3rd ed.) ... (previous) ... (next): Chapter $1$: Electrical Quantities: Definitions and Laws: The International System of Units
- 1976: Ralph J. Smith: Circuits, Devices and Systems (3rd ed.) ... (previous) ... (next): Chapter $1$: Electrical Quantities: Definitions and Laws: The International System of Units: Table $1$-$1$ Basic Quantities
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): kilogram
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): kilogram
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): kilogram
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): kilogram