- Principles of Chemistry I: Honors
Fall 2016, Unique 50015
Extra Credit Assignment 4
Fermi problems are a fantastic way to develop basic problem
solving skills, as well as dazzle your friends at cocktail
parties. To solve a Fermi problem, you don't look up your
facts or the answer on the Google, you guestimate. You solve
the problem using logic, general knowledge of the world,
reasonable approximation of unknowns, back-of-the envelope
calculations, and dimensional analysis. They are named after
the physicist Enrico Fermi, who used to start his freshman physics
class at the University of Chicago every year with the problem
"how many piano tuners are in Chicago?" This is something
that no one really knows (except perhaps the head of the piano
tuners local 101), but the point is that you can come to a
reasonable estimate by guestimating how many pianos are in
Chicago, and then assuming the law of supply-and-demand holds, how
many tuners are necessary to service all of those pianos.
(The Wikipedia page on Fermi problems covers this and other cute
examples if you are interested.) The point is not to get
exactly the correct answer, but to get a reasonable estimate (say
within a factor of 2, 5, or 10), with essentially no work.
Most importantly, the skills necessary to navigate Fermi problems
successfully are absolutely essential to critical problem solving
in the physical sciences.
We have reached a point in this course where Fermi problems about energy can touch on almost every aspect of life, and become extremely important when making personal decisions about where and how to access, store, and expend energy.
Background: This is a Fermi-type problem that has been bothering me for a while. Hopefully you can help me figure it out.
Assignment: A group of engineers at MIT have created a class of nonstick bottle coatings that cause 100% of the material in the bottle to flow out. A particularly important application of this new chemistry is in ketchup bottles, which are almost impossible to completely empty because of ketchup sticking to the side of the bottle. (Google MIT ketchup nonstick if you are interested.) This may seem like a silly problem, but Americans really like ketchup, and throwing away an only partially empty ketchup bottle is a real waste of food. How much ketchup is lost in the US every year because it is stuck inside the ketchup bottle? How many people could be fed with that wasted food?
Your answer will be due at the beginning of class on Tuesday, 22 November, to receive credit.