on 3/26/2002 4:48 PM, Duncan Bath at [EMAIL PROTECTED] wrote:
> This ("joules") had to do with considerations such as dimensional analysis
> of a formula or, even dealing with an expression where there are litres in
> some places and m^3 in others. How 'coherrent' is it?
> D.
By "it", did you mean joules, litres or cubic metres? Perhaps I can answer
for all three with a single example.
The joule is THE unit of energy in SI. Therefore, it is totally coherent
with all other SI units. That is, after all, what SI is all about: it is a
system of completely coherent units.
The litre is NOT an SI unit, although it is officially "permitted for use
with SI". It is not an SI unit because it is NOT coherent, and all SI units
are REQUIRED to be coherent.
The cubic metre is the SI unit (the coherent unit) for volume.
The simplest example I can think of is the equation for the mechanical
energy provided (the "work done") by an expanding gas. The energy (E)
depends on the pressure of the gas (p) and the increase in its volume (�V).
(The symbol � should be the Greek capital delta.
It is possible that it will not be transmitted accurately
to your system. The symbol � is used to
indicate difference or change)
The equation is:
E = p.�v
The general principle is that, if values are substituted into equations
using only SI units (which are always coherent) then the result will ALWAY
come out in the SI unit for that kind of quantity. Thus, substituing values
into the equation, if p is in pascals (the SI unit of pressure) and �V is in
cubic metres (the SI unit of volume) then the result, E, will automatically
come out in joules (the SI unit of energy).
The same cannot be said if one substitutes the volume in litres, therefore,
the litre cannot be the SI unit. Of course, it is always possible to find
other combinations of units that will give the correct result*. But one
would have to figure out which combinations do and which combinations do not
work. The beauty of SI is that, if you put SI into a calculation then SI
comes out, without having to "figure out" anything.
Regards, Bill Hooper
college physics teacher (retired), USA (Florida)
*Example:
If you use litres for the volume change in the equation E = p.�V and you
also use kilopascals for the pressure, the energy will also come out in
joules. That's because the volume unit is 1000 times smaller than the
coherent SI unit and the pressure unit is 1000 times larger than the
coherent SI volume unit. Thus the two "errors" cancel ech other out and you
get the right answer in joules, the SI unit. If youn use this equation
frequently enough, and if your data comes to you in litres and kilopascals,
there's nothing really wrong with using this short cut for yourself. In
explaining your work to others, however, you need to be ready to demonstrate
why your incorrect method gives the correct answer.
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Do It Easy, Do It Metric!
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