Weighing The Atmosphere

If we are at the bottom of the layer of atmosphere, how much pressure do we feel? We can find out with this simple experiment.

(under construction - 08/04/07)

*Please see the notes at the end of the instructions before you start.


1.  A good quality polyethylene syringe with a rubber or vinyl-sealed piston (West Systems #318311, available at West Marine stores or  www.westmarine.com for roughly $2 each, used for squirting epoxy glue into tiny spaces), modified by drilling a 1/8" (3 mm) hole sideways through the very end of the handle portion of the piston so that a hook can be attached to the piston.

Here's where to drill the hole.

2.  A platform made from small piece of ¼” plywood, roughly 2” x 4”; this piece will be used to hold the syringe off of the edge of a worktable.  A small hole is drilled toward one end, loosely matching the diameter of the piston of the syringe.  For the West Marine syringe, the hole should be 5/8”.  Make sure that the piston end of the syringe can move freely through the hole.  The hole should be small enough to keep the body of the syringe from falling through the hole.

3.  A 1 ½” or 2”  “C”-clamp for fastening the wood platform to a worktable.

4.  A 1 gallon plastic water bottle with a handle.

5.  A hook formed from a metal coat hanger.  In the picture below, the right side goes into the hole in the syringe and the left side will hold the water bottle.  The hook is bent so that when the water bottle is hung from one end, the weight of the water bottle will be approximately centered on the axis of the syringe.

6.  A small funnel to permit the easy filling of the water bottle.

7.  Lubricant for the syringe piston.  WD-40 is really ideal for this, consisting of a volatile solvent and mineral oil.  When the WD-40 is sprayed onto the piston, the solvent will evaporate, leaving a thin film of mineral oil lubricant.  However, it is often much better to use something less “mysterious” than something in a spray can, so simple cooking oil or dish detergent will make a good lubricant.

8.  Something for measuring the area of the syringe piston.  A college lab may include a vernier caliper for making a precise measurement of diameter, thereafter calculating the piston area.  However, a more instructive tool may be to use grid paper, onto which the outline of the piston may be drawn and thereby measured by counting up little squares of a fraction of a square inch or fraction of a square centimeter. If making measurements in the “English” system, the grid paper should be 0.1” grid, while for our Metric colleagues, 1 mm grid paper is recommended.

9.  A postal scale or fish scale for measuring the weight of the plastic water bottle and water.  The weight to be measured will be on the order of 5 pounds or 20 Newtons or 2 kilograms-weight.


1.  Slide the Piston.

First examine the syringe and push the piston in and out.  The pointed end of the syringe has a tiny hole that can be covered with a finger.  First, leave the pointed end open and push the piston back and forth,  The piston should move back and forth relatively easily, because the air in front of the piston flows back and forth through the hole in the pointed end.  The piston will move more smoothly if you put a tiny amount of liquid dish soap on the rubber seal part of the piston to reduce friction.

Something to think about:

What can you say about how much air pressure exists on either side of the piston when the piston is not moving and the pointed end is open? ____________________________________________________________________


2.  Stop the Piston

Close the pointed end with your thumb and try to move the piston (if the pointed end of the syringe is too sharp, use a utility knife to cut off a short length of the end so that the hole is a little bigger, but still easily covered and sealed by your thumb.).
Some things to think about:

What happens when you try to move the piston with the syringe end closed? 


Do you have an explanation (if you don't, that's OK because that's what we'll try to discover)?



When you pull on the piston, is there now something different about the air on the side of the piston closest to the pointed end? 


If you can manage to hold your finger onto the end of the syringe, and pull on the piston at the same time, the piston will snap back into the syringe when you let go of the piston.  Can you guess why this happens?  _____________________________________________________________


When your finger covers the end of the syringe and you pull on the piston, it seems like there is something pulling the piston.  But can you think of a way that this could actually be caused by something pushing instead of pulling?  ____________________________


3.  Add A Hook and Bottle.

You’ll need a partner for these steps.
a.  Clamp the wood platform to a table so that the hole in the platform is suspended past the edge of the table and above the floor.
b.  Set up the syringe onto the wood platform so that the piston goes up through the hole in the platform.  The body of the syringe rests on the top of the platform with the pointed end up.  Make sure that the piston slides freely without getting stuck on the platform.
c.  Attach the metal hook and a plastic water bottle to hang from the piston.
d. Push the piston all the way up into the syringe. 
e.  Put your finger over the open, pointed end of the syringe.
f.  Slowly add water to the plastic bottle by using the funnel.  As you do this, the water bottle gets heavier and heavier and the piston moves farther down.  Remember that the water bottle will crash onto the floor if you take your finger off of the end of the syringe, so make sure that you and your partner are both paying attention to what you’re doing!!

As you add water, and the piston slowly falls in the syringe, what is happening to the air in the space above the piston?



Check out this picture above!  How is it possible that putting your finger over the tiny, tiny hole in the end of the syringe could possibly hold up that big bottle of water?



g.  As you add more and more water, the piston moves lower and lower.  The space above the piston still has the same number of air molecules that it started with, but now those molecules are spread out over a larger and larger space.  Because of this, they don’t push as hard onto the piston because they are spread out pushing over the whole insides of the larger container at the top of the syringe.  Air still pushes up on the piston from the outside just as much as before.  The push of air from the outside upwards minus the weight of the water downwards equals the remaining small push from air inside the syringe.

h.  Add more and more water until the piston reaches the end of the syringe.  If you had a very long syringe, you could make the air pressure inside the syringe very small and nearly zero. At this point, the weight of the water downwards is equal to the force of the air from the outside upwards onto the end of the piston.

i.  Carefully take off the water bottle and weigh it.  The weight is __________________

4. Weigh the Atmosphere.

Now we know the weight of the water that can be supported by the outside air when the inside of the syringe has very little pressure.  But the size of the piston is important!  If the piston were very large, we would be able to pour a lot more water into the bottle because the outside air could push against a larger piston.

We need to know the area of the piston.  One way to measure the area of the piston is to draw a picture of the end of it onto paper that is divided up into small squares, each one of which has an area of only 1/100 square inch.  So there are one hundred of these 1/100 square inch pieces in a full square inch, just like 100 pennies in a dollar.

Remove the piston and draw the circle of the end of the piston onto a piece of the 1/100 square inch graph paper.

When you are done, then your job is to try to count how many full squares (each of which is 1/100 square inch) will cover up the end of the piston.  You will have lots of little squares that are a fraction of a full square.  You will have to estimate how many of the small broken pieces equal one full square.  See the picture below to find out how to count the squares.

( Here is the outline that I drew.  You should count a total of about 28 full squares, so the area of the piston is 0.28 square inches.  Sometimes coloring in the squares as you proceed is useful to keep track of full squares and pieces of squares.  For students in higher grades, the concept of area should be clearer, so it is probably better to just measure the diameter of the piston, and use A = pi x R2 to calculate the area.)

I measure the area to be ______________________ little squares that are each 1/100 of a square inch.  So the area of the piston is _____________ square inches (think about converting pennies to dollars).

5.  Finally, the Air Pressure

To calculate atmospheric pressure, the weight of the water and bottle supported by the force of the atmosphere on the piston is divided by the area of the piston. 

The weight of the water in the bottle is  ________________.

The area of the piston is  _________________ square inches.

So, atmospheric pressure in pounds per square inch is just the weight of the water divided by the piston area in square inches.

I've calculated the pressure of the atmosphere to be _________________ pounds per each square inch.  Can you do a Google search to find out the value for the atmospheric pressure at sea level?

(For English units:   Because the area of the piston is very nearly 1/3 square inch, then three of these pistons will fit into a full square inch.  So you only need to multiply the number for the weight of the water in the bottle by 3 to get the number for the atmospheric pressure in pounds per square inch.  We’ve already noted that you should expect to need about 5 pounds of water to extend the piston fully, corresponding to a pressure measurement of about 15 pounds per square inch, roughly in agreement with the nominal value for sea-level atmospheric pressure of 14.7 psi)


A note to the instructor:
     There are many ways that this experiment may be adapted to a wide range of skill levels, ranging from elementary school students to college students.  We’ll suggest some changes as we work through the experiment.  We’ve written this experiment for the fourth or fifth grade:  the most difficult concept will be the concept of area and the concept of pressure as a weight per unit of area. In earlier experiments that we do with this age group, we’ve talked about pressure as a force distributed over the area of an opening and how a child’s finger can resist the pressure within a vessel if the opening is small, but not so easily resisted if the opening is larger.
     This experiment does not match our criteria for a “Noon Science” experiment for material cost under $2 per student, and it is also a little impractical for the students to take results of the experiment with them, but it is great for smaller classes (two students per each set of components), and all of the materials may be used repeatedly year after year (unlike most of our Noon Science experiments).  You'll need access to basic tools to assemble some of the parts.

A note about units:
Our colleagues outside of the United States will most likely measure weight in units such as “kilogram-weight” or Newtons, while in the US, we’ll measure weight in pounds.  A Google search tells us that postal scales in Europe are calibrated in “kilograms”, which is actually “kilograms-weight”:  1 kilogram-weight is 9.8 Newtons.  So making measurements of the weight of the water suspended by the syringe in “kilograms” will need multiplication by 9.8 to get to Newtons.  Then a measurement of piston area in square millimeters will need division by one million to convert to square meters, the eventual goal being to get to air pressure measured in Pascals (Newtons per square meter).  How a fourth grader is to perform all of these manipulations in a way that does not overwhelm the point of the experiment is not clear to me.

A possible simplification is to measure air pressure in units of “kilograms per square meter” (really kilograms-weight per square meter).  The instructor is still faced with the task of converting the piston area in square millimeters to square meters in a manner appropriate for the fourth grade.

A note about the experimental procedure:
We’ve included some suggested questions that one may include in a worksheet or demonstration.

A note about sources of error:
While very simple, this experiment is certainly practical for the basic physics lab at the college level.  However, for these students, it is also appropriate to include some examination of the sources of error in the experiment, and thereby determine the uncertainty in the final calculation for atmospheric pressure.  Here are some possible error sources:

1.  Friction

Certainly, a large source of experimental error is the additional force needed to overcome the friction of the piston within the syringe body.  This is easily measured by determining how much weight is needed to make the piston start to slide within the syringe.

2.  Incomplete Vacuum in the Syringe.

Another large source of error is the fact that the experimental procedure assumes that, when the piston is fully extended, the space above the piston is a vacuum.  This approximation depends on the volume above the piston being essentially zero when the piston is fully inserted at the start of the experiment.  Of course, the finite volume of the tapered syringe point prevents this.  Boyle’s law can be used to estimate how much of a fraction of one atmosphere is retained in the volume of the extended piston.  It is easy to measure the volume of the syringe when the piston is fully inserted and fully extended (use water and a graduated cylinder) and cutting of the end of the syringe tip to reduce the tip volume.  The instructor can also fabricate a display apparatus that includes a vacuum gauge connected to the syringe which can be used to verify what the calculations might imply about the quality of the vacuum in the extended syringe.

3.  Leakage.

This is difficult to determine.  Certainly there may be some leakage around the sides of the piston seal and around the edge of your finger used to close the pointed end of the syringe.  Some experiment might be performed to determine how much leakage is expected by adding enough water to extend the piston halfway, and then monitoring the creep of the piston over several minutes.  Of course, this depends on the endurance of the finger used to plug the end of the syringe.

4.  Determining the Piston Area.

If a caliper is used to measure the piston diameter (or better yet, the cylinder diameter), the error in measuring the piston area is rather small.  But it should be calculated so that it can be included into the overall error analysis and thereby convince oneself that this error can be made negligible.

5.  Measuring the Weight Hanging From the Piston.

The typical spring balance is usually accurate to no better than 10%.  This can be improved somewhat by a comparison with standard masses.  Of course, a better way to measure the weight suspended from the piston is to use a laboratory beam balance.  In principle, one should include the weight of the piston and hook in the measurement.