Definition:Kilogram
Definition
The kilogram is the SI base unit of mass.
It is defined as being equal to:
- 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 $0 \ \mathrm K$.
\(\ds \) | \(\) | \(\ds 1\) | kilogram | |||||||||||
\(\ds \) | \(=\) | \(\ds 1000\) | grams |
Symbol
The symbol for the kilogram is $\mathrm {kg}$.
Also see
Historical Note
The kilogram was defined in $1795$ as $1000$ times one gram.
This itself was defined as the mass of one cubic centimetre of water at the melting point of ice.
Subsequently, the actual reference kilogram was manufactured as a prototype in $1799$.
It had a mass equal to the mass of $1 \, \mathrm {dm}^3$ of water at its maximum density, approximately $4^\circ C$.
The International Prototype Kilogram (IPK) was derived from this in $1875$.
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 is being sought, based on a fundamental constant.
In $2011$, 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.
As from $20$ 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.
Sources
- 1966: Isaac Asimov: Understanding Physics ... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $3$: The Laws of Motion: Mass
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Entry: kilogram
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: kilogram
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: kilogram