One litre of water is
1kg; but not other substances
The Sunday Nation
Nairobi,
30 May 2010
Peter Ndirangu sent in eight questions and I will try to answer some of
them. First off, he says that he has noted that a tin of shoe polish
indicates the amount as 40ml or 32g and is wondering if this is correct.
“I thought 40ml = 40g”; he adds.
This is a common misconception and it needs to be cleared: water is the
only substance whose mass in grams is numerically equal to its volume in
millilitres. Now 1,000ml makes one litre and 1,000g are one kilogram.
Thus one litre of water weighs one kg.
This is a curious coincidence since the litre is defined in terms of the
dimensions (lengths) of a container while the kilogram is a mass.
Indeed, long ago, one litre used to be defined as the volume of one
kilogram of water.
That definition proved cumbersome because it was mixing up volume and
mass. Strictly speaking, the volume of one kg of water varies with
environmental conditions (temperature and pressure) and the presence of
dissolved impurities. Thus the statement that one litre of water is one
kg is an approximation.
The important point to note, however, is that for other substances, this
approximation is not valid. Generally, you will find that one litre of a
solid will weigh more than the same volume of a liquid, which, in turn
will outweigh a gas. For example; one litre of air at sea-level and 20
degrees Celsius weighs only 0.0012g; one litre of water is 998g and one
litre of iron is 7,874g (7.875kg).
***
Ndirangu is also wondering how long it would take to count to one
billion. This problem was discussed here on 25th March 2007. It turned
out that it would take about 500 years. I don’t wish to repeat the
details but one important point must be highlighted: Many people
attempting this problem make the assumption that you can count one
number per second and therefore it would take one billion seconds or
about 32 years.
Unfortunately, it is not humanly possible to say a number like
48,532,165 in one second. Try it and see how long it takes to say “forty
eight million, five hundred and thirty two thousand, one hundred and
sixty five”.
***
Ndirangu’s third question is about the heights of mountains: why are
they given in relation to sea level and not from the base as the case
with other objects? Well, the reason is that it is not possible to
pin-point the base of a mountain. Where would you say is the foot of
mount Kenya, for example?
Man-made structures on the other hand, have a clearly visible base.
After all, they must stand on a flat surface: otherwise they will
topple. Thus it is easy to give their height from the (flattened)
ground.
In the case of mountains, the level of sea water provides a good
reference point because it is fairly constant. In addition, the seas
cover over two thirds of the Earth’s surface so they can be used as the
base for all land masses. Of course we have to take into consideration
the rising and falling of tides, therefore, the measurements are done
with reference to the Mean Sea Level (MSL).
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