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Makeshift Mercury Measurement: CR4 Challenge (06/23/09)

Posted June 21, 2009 5:01 PM

This week's Challenge Question:

John is making a homemade mercury thermometer. He has figured out that he needs 10 mL of Mercury but is reluctant to use his only measuring cup and too cheap to buy one for the one time he'll be handling mercury. Instead he plans on measuring out 10 mL of water, pour it into a thin glass test tube, and draw a line to mark the height of the water. Then he'll remove the water, let the test tube dry, and then fill the test tube with mercury to that line. When John ran this idea by his friend Tom, assuring him he was taking all kinds of precautions with regards to temperature and atmospheric pressure, Tom warned that he'll be under the desired 10 mL even with those precautions. Why did Tom believe he'd measured out less than 10 mL of Mercury?

And the answer is...

The problem with the makeshift mercury measurement using the glass test tube is the meniscus. Water has a concave meniscus whereas mercury has a convex meniscus. As you can see in the image below, a concave meniscus is bowed in the middle whereas a convex meniscus is curved upward. The 10 mL water line will be lower than the 10 mL mercury line, meaning John is measuring less than 10 mL


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#101
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Re: Makeshift Mercury Measurement: CR4 Challenge (06/23/09)

06/29/2009 3:38 PM

The volume specific heat of mercury is about 45% that of water. In addition, its thermal conductivity is about 10x greater. Either of these factors alone would cause the mercury to be more affected by the temperature of your hand (or the tube) than the water. That would totally overwhelm the small difference in expansion coefficient. (Just as well John is being careful about temperature??)

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Join Date: Mar 2009
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#102

Re: Makeshift Mercury Measurement: CR4 Challenge (06/23/09)

08/06/2009 2:07 AM

The other (in this case better way to measure the exact volume is to measure the weigth of the equivalent mass of mercury, mercury's density is 13579,04kg/m³ at the normal temperature and air pressure; 10ml is 10 times a millionth of a m³ - this volume is equivalent to a mass of 135,7904g of mercury with or without a meniscus!

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