Sunday, March 13, 2011

Chalk Hell

Wright Laboratory of Physics Room 201 at Oberlin College.

"Begone, Ye Accursed Chalk!  I banish thee and thy vile and insufficient yield strength to the depths of Chalk Hell!!!"
Most colleges have at least one big lecture hall with chalk boards that slide up and down.  To make space for the boards to slide underneath, there's usually a small gap behind the wall.  This gap is Chalk Hell: a black hole out of which no chalk ever emerges.1   How long would it take for Chalk Hell to over flow with chalk remnants?

A brief glimpse into the horror that is Chalk Hell.
Chalk Hell is about 1.0 m deep,  10 cm wide, and 3 m long giving a total volume of 0.3 m3.  Much of the chalk in Chalk Hell is about 0.8 cm thick and 6 cm long giving a total volume of about 3.8×10-6 m3.  I drop at least 1 piece per lecture and over the course of a year there might be 300 lectures in a room.  From this we can estimate that there are

0.3 m3 / [ (3.8×10-6 m3 per piece) · (1 piece per lecture) · (300 lecture per year) ]
= 263 years.

It would take over 2.5 centuries to before Chalk Hell flows over.

[1] Unless you duct tape the long erasers together to make a giant set of chop sticks that you can use to pick them out of Chalk Hell.

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