I need an example of a problem in which you’d have to do some sort of unit conversion / dimensional analysis. For instance, in physics if I want force in newtons (kgm/s^2) but I have a person’s weight in pounds, I need to convert pounds to kg.
It’s for a paper about students’ understanding of area/volume units (data collected in a maths course) and I am trying to make the case that units are important and used all over the place 
Off the top of my head I would think that any temperature conversion would be applicable, and moles to grams would be good.
mililiters to liters
cubic inches to liters
grams to pounds
moles to grams
If I think about it, I’ll ask my wife when I get home from work.
Have them compare the volume of a pound of lead (in cm^3) versus a pound of Helium (in m^3).
I’m confused. A pound of helium as measured in cubic kilograms…?
Below is some conversion types. A mole conversion like stated above would be good to use, or any American to rest of the world, e.g, pound to kg… Many of the chemistry conversion are kind of like any science, and lots of crossover…or are you looking for some advanced high tech sounding conversion? Physical chemistry would have some of that…
Have we had this topic before? I’m having some deja vu.
Don’t even get me started on units. My recent two big pet peeves are tons and million. Some people abbreviate MT for million tons, some for metric tons. Some people say tons and mean metric, some mean short tons. Then MMBtu for million btu is standard. But then some people use MBtu, which should thousand btu, and some people use it and mean mega or million btu.
One of the most famous examples of units being important is NASA losing their Mars Climate Orbiter. Some recent college grad at Lockheed coded information in imperial units when NASA uses metric. Bam, years of work and $125 million crash landed on the surface of Mars.
Maybe a more practical basic-chemistry-like example is conversions between molarity and molality.
I’m confused. A pound of helium as measured in cubic kilograms…?
Totally. You gotta get METAphysical though.
Brain farted and typed kg instead of m as I was reading it in the first post. Edited for non-idiocy.
Dunno if this quite what you’re after, but check the Wiki for ‘Gimli Glider’ for an example of why units matter…
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Excerpt:
At the time of the incident, Canada was converting to the metric system. As part of this process, the new 767s being acquired by Air Canada were the first to be calibrated for metric units (litres andkilograms) instead of customary units (gallons and pounds). All other aircraft were still operating with Imperial units (gallons and pounds). For the trip to Edmonton, the pilot calculated a fuel requirement of 22,300 kilograms (49,000 lb). A dripstick check indicated that there were 7,682 litres (1,690 imp gal; 2,029 US gal) already in the tanks. To calculate how much more fuel had to be added, the crew needed to convert the quantity in the tanks to a weight, subtract that figure from 22,300 kg and convert the result back into a volume. In previous times, this task would have been completed by a flight engineer, but the 767 was the first of a new generation of airliners that flew only with a pilot and co-pilot, and without a flight engineer.
The volume of a kilogram of jet fuel varies with temperature. In this case the weight of a litre (known as “specific gravity”) was 0.803 kg, so the correct calculation was:
7682 L × 0.803 kg/L = 6169 kg22300 kg − 6169 kg = 16131 kg16131 kg ÷ (0.803 kg/L) = 20088 L of fuel to be transferred
Between the ground crew and pilots, they arrived at an incorrect conversion factor of 1.77, the weight of a litre of fuel in pounds. This was the conversion factor provided on the refueller’s paperwork and which had always been used for the airline’s imperial-calibrated fleet. Their calculation produced:
7682 L × 1.77 kg/L = 13597 kg22300 kg − 13597 kg = 8703 kg8703 kg ÷ (1.77 kg/L) = 4916 L of fuel to be transferred
Instead of 22,300 kg of fuel, they had 22,300 pounds on board — 10,100 kg, about half the amount required to reach their destination. Knowing the problems with the FQIS, Captain Pearson double-checked their calculations but was given the same incorrect conversion factor and inevitably came up with the same erroneous figures.
The Flight Management Computer (FMC) measures fuel consumption, allowing the crew to keep track of fuel burned as the flight progresses. It is normally updated automatically by the FQIS, but in the absence of this facility it can be updated manually. Believing he had 22,300 kg of fuel on board, this is the figure the captain entered.
Because the FMC would reset during the stopover in Ottawa, the captain had the fuel tanks measured again with the dripstick while there. In converting the quantity to kilograms, the same incorrect conversion factor was used, leading him to believe he now had 20,400 kg of fuel; in reality, he had less than half that amount.
I believe a few years ago NASA lost a probe on Mars because someone either didn’t convert a speed correctly or forgot to convert the speed.
Remember that lb-mass is not the same as lb-force when it comes to units.
When dealing with american engineering units, mass (e.g., lb-mass) and force (e.g. lb-force) are different units and can not be added/subtracted, so you need to use the g.sub.c constant.
Example: if you have a column of water or mercury in a barometer and you want to determine the atmospheric pressure:
P = P.atm + rhogh
P = Pressure that is measured, which has units of force per area (e.g., psi or lb-force/in^2)
P.atm = atmospheric pressure, force per area
rho = density of the liquid, mass/volume; lb-mass/ft^3
g = acceleration due to gravity, 32.2 ft/s^2
h = height of column of liquid, in or ft.
If you are doing the calculation in american units, you need to include the g.sub.c constant = 32.2 / to get the units to work right - divide the right term in the equation by g.sub.c.
In SI units, the numerical value of g.sub.c is 1.0. Which is why the SI system is totally superior.
Look up two decent freshman chemical engineering texts if you have time. Their introductory chapters spend a lot of time on the subject of units and dimensions, and give lots of example problems.
http://www.austin-books.com/default.asp?pid=6397
http://www4.ncsu.edu/unity/lockers/users/f/felder/public/EPCP.html
"I am trying to make the case that units are important and used all over the place "
Just curious, but is that really a case that needs to be made? It would seem pretty obvious.
Acre-feet of water to gallons of water - commonly used by your municipal water utility
Cubic feet of water to gallons of water at ambient temperature/pressure - commonly used for design
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Electrochemistry problems.
One mole of copper/two moles of electrons
96,500 coulombs/mole of electrons
One amp = one coulomb/second
One mole of copper = 63.55 grams
One kilogram = 1000 grams
One hour = 3600 seconds
One minute = 60 seconds
Solve the following two problems using unit conversions.
“If you use a current of 200 amps, how many hours will it take to deposit 2.5 kg of copper onto an electrode?” (Answer: 10.5 hours)
“If you want to deposit 150 grams of copper onto an electrode in 30 minutes, how much current will you need to use?” (Answer: 253 amps)
Moles to grams to grams/ml when I want to measure liquid reagents.
"I am trying to make the case that units are important and used all over the place "
Just curious, but is that really a case that needs to be made? It would seem pretty obvious.
It is, but it’s pretty standard in academia to set up the rationale for your particular study by explaining how it fits into the larger picture. In my case, finding out what students know about units and how successful they are with units in problems is important because units are important.
ppm (mass) vs ppmv (volume)
In atmospheric chem, the main is converting #/cm^3 to ug/m^3. This is applied primarily to particle chemistry/physics.
Have we had this topic before? I’m having some deja vu.
I had asked when you chemistry and physics types use units (I know a bunch of good examples for physics) when I was writing my thesis. Now I’m turning the thesis into published articles.
The examples I’m using for maths are that integrating velocity → distance; integrating acceleration → velocity. The units of the computation depend on the units of the integrable function. And like I said earlier if you want F = ma and F is in newtons, a is in kgms^-2, if you solve for mass it is in kg not pounds. I’m trying to find a simple example of the same sort of dimensional analysis in chemistry.
PV = nRT
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Post:
PV = nRT
BRILLIANT. Now what does that stand for and what are the units with each of the terms?