Answer 1:
Here is how I would calculate the volume that one
liter of water would fill if it were
steam:
1. Since the density of liquid water
is 1gram/1mL, then 1 Liter (which is 1000 mL)
contains 1000 grams of water. We can convert this
mass into "moles" by dividing by 18 (the mass of
an oxygen atom plus two hydrogen atoms). So in 1
liter of water, there are 55.55 moles of
water. 2. We can assume that our pressure is
atmospheric pressure, or 1atm. We can also assume
the temperature is 25 degrees Celsius (room
temperature) which is 298 Kelvin (to go from
Celsius to Kelvin just add 273). 3. The
ideal gas law says that, for a gas,
pressure*volume=moles*temperature*R
(R is just a number that is equal to
0.0821). We can rearrange this equation to say
that
volume=moles*temperature*R/pressure
Now we plug in our numbers and we get the
volume (in liters) equals
55.55moles*298Kelvin*0.0821/1atm or the volume
is 1358 liters.

Answer 2:
There are two measures of the amount of water;
these are mass and volume. A cup is approximately
one quarter of a liter, which would fill a cube 10
cm on aside (ten cubed is a thousand  we are
talking in three dimensions, so we cube changes in
length to get volume) There are a thousand cubic
centimeters in a liter. Water droplets in a fog
would be on the order of 0.01 mm on a side, so
there would be about a million of them in a cubic
millimeter, and a billion of them in a cubic
centimeter, and a trillion of them in a liter. If
you spread out a trillion water droplets over a
small town, say a kilometer on a side,then that's
about one million of them per square meter(square
of the length difference, now that it's area).
With a million water droplets in a square meter,
or even only twohundred and fifty thousand (one
cup, not one liter), you have a lot of water
droplets.
A pint is about two liters, so
would be two trillion water droplets. How much
would that evaporate into?Well, two liters is two
kilograms (definition of a kilogram), or about
four and a half pounds. I do not know what the
density of air is, unfortunately (you could easily
look it up), but if you divide two kilograms by
the density of air you will get the volume that
that amount of steam would occupy.
As for
the Big Bang, first off, steam can be very hot, up
to thousands of degrees. Water is only cool
because there is a temperature at which it boils,
and it takes a lot of energy to take water from
the boiling temperature and turn it into steam at
the boiling temperature (this is about 5.5 times
the amount of energy needed to take water from
freezing to boiling). However, the material in the
Big Bang wasn't even gas; it was plasma. In
plasma, there are no molecules, since all of the
atoms have had all of their electrons stripped
off. There was no water until the universe became
cool enough (by expanding) that the electrons
could attach to their atoms  and, for that
matter, there wasn't even any water then. Water
contains two atoms of hydrogen and one of oxygen,
and oxygen didn't come into existence until the
first stars.
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