UCSB Science Line
Sponge Spicules Nerve Cells Galaxy Abalone Shell Nickel Succinate X-ray Lens Lupine
UCSB Science Line
How it Works
Ask a Question
Search Topics
Our Scientists
Science Links
Contact Information
I heard that there are 60 billion droplets in a cup of water, enough to cover a small town in a fog. Is there a formula to determine how much space (in cubic feet) it takes to accomodate the evaporation or steam in, say, a pint of water? (I'm curious how the vaporized water (from earth?) in the "Big Bang" didn't extinguish the hot gases....) Thanks.
Question Date: 2006-01-25
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,


(R is just a number that is equal to 0.0821). We can rearrange this equation to say that


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 two-hundred 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.

Click Here to return to the search form.

University of California, Santa Barbara Materials Research Laboratory National Science Foundation
This program is co-sponsored by the National Science Foundation and UCSB School-University Partnerships
Copyright © 2017 The Regents of the University of California,
All Rights Reserved.
UCSB Terms of Use