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 RUM BAROMETER RIDDLE

METEOROLOGIST JEFF HABY

A liquid in-glass barometer can be used to measure air pressure. How this works is that liquid completely fills the glass tube and then the tube is inverted into a dish of the liquid. The height of the liquid in the glass tube varies as pressure rises and falls. The space left in the tube is a vacuum. There is a balance between the liquid wanting to fill the vacuum above it and gravity trying the push the liquid back into the dish. This balance changes as air pressure changes. The balance at any one time is the current air pressure. When the air pressure is higher there is more force pushing on the liquid in the dish and this pushes the liquid higher into the tube. Mercury is the liquid of choice due to its density. Mercury has a density of 13,580 kg/m^3. Have you been able to see an actual Mercury barometer? They are more rare to see since barometers have advanced to using other technologies. The average sea level pressure is 29.92". On average the Mercury will rise to a level of 29.92 inches (2 feet 5.92 inches) in the tube.

Mercury is not the only liquid that can be used. Any liquid will do but another liquid will have a disadvantage to Mercury. Do you know why that is?

Riddle: You construct a glass tube barometer that uses Rum instead of Mercury. The Rum is 80 proof (40% ethanol alcohol and 60% water, ignoring mass of other minor ingredient). Once you construct this Rum barometer, what will be the height of the liquid (give in feet and inches) on a day with average atmospheric pressure? The density of water is 1,000 kg/m^3 and the density of ethanol alcohol is 789 kg/m^3

Answer to Riddle: Rum has a much lower density than mercury. Because Mercury is very dense the height of the glass tube only needs to be about 3 feet tall. Mercury is about 14 times denser than water thus the water level will be about 14 times as high. We need to compute the density of the Rum. The density is 0.4*(789 kg/m^3) + 0.6*(1000 kg/m^3) = 915.6 kg/m^3. Dividing density of Mercury by density of Rum determines how many times more the Mercury is denser than the Rum. 13,580 kg/m^3 / 915.6 kg/m^3 = 14.83180428. The average barometric pressure using mercury is 29.92 inches. The height of the Rum under average barometric pressure = 29.92 * 14.83180428 = 443.77 inches = 36 feet 11.77 inches. The height of the column of Rum would need to extend to about 37 feet.