09 April 2004

Tales of a Home Lab: Measuring the Unmeasurable

by James Firmiss, MAST

One of the common problems encountered in the lab is how to obtain a measurement of something when you don't have the ability to measure it directly.

Thickness

One example of a difficult measurement is the thickness of a piece of paper.  How would you go about measuring that?  You could use a micrometer, or certain microscope setups; but what if you don't have these available.  Can you do it with an ordinary ruler?  The answer is yes.

The key to this and other similar problems is to infer the desired measurement based on something you can measure.  In the case of a sheet of paper, You can scale up your unknown to a more convenient thickness simply by measuring more sheets.  I just so happen to have 400 sheets of paper (and yes, I counted them to make sure) on my soon-to-be lab bench weighted down with an old monitor to make sure that any air gap between pages is minimal.  A careful measurement of this stack with a simple ruler shows it is 43.5 mm.

If 400 sheets are 43.5 mm one can infer a single sheet is 1/400 of this value.

at least for the type of paper I use in my printer.

Volume

Dianna is writing a feature that discusses, among other things, standard measures of volume.  Here is a method, similar to that above, that is applicable to small volumes, below what you can measure with a small spoon.

How can you measure the volume of a 'drop' of water?  A small 25 ml burette or 10 ml graduated cylinder isn't even precise enough for this kind of measurement.  Nonetheless this value can be inferred even with a common set of kitchen measuring spoons by counting the number of drops it takes to fill one of these spoons.

On my soon-to-be lab bench (see George's feature on making a home lab)  I had set up a 1/2-teaspoon measuring spoon and secured it in place.  Using a household eyedropper I filled the spoon with distilled water until I could just barely see the water viewing the spoon from edge on. I didn't count that last drop because if I could see the water above the horizon of the spoon that meant the spoon was overfilled.

58 drops later I declared the 1/2-teaspoon measuring spoon 'filled'.  A handy kitchen metric conversion chart (see link below) indicates that 1 teaspoon is approximately 4.929 ml.  Half of this is 2.4645 ml.

Now, this is for my particular dropper and for distilled water.  Other eyedroppers and other liquids may produce larger or smaller drops.  You will have to determine these for each case.

Mass

Think about ways you might be able to measure a very small mass if the only piece of equipment you had was a balance.  For example, what's the mass of a single grain of rice?  Here's a hint ... US coinage is minted to have specific masses.  Penny = 2.500 g, Nickel = 5.000 g, Dime = 2.268g (see US Mint link for more info on coinage).

Closing Remarks

That's all for this week.  Next week I'll continue these examples by looking into the accuracy and precision of measurements (and what the difference is) and hopefully I'll have a more complete lab bench by then.

References

Metric Conversions for the Kitchen
http://www.mcgees.com/kitchen/metric.htm   for metric conversion info
US Mint Fact Sheet for Currently Circulating Coins.
http://www.usmint.gov/faqs/circulating_coins/index.cfm?action=faq_circulating_coin

Created by Mathematica  (April 8, 2004)