Fun_People Archive
23 Jan
Notes From Nerd Hell

Date: Sun, 23 Jan 94 17:31:29 PST
To: Fun_People
Subject: Notes From Nerd Hell

 From: bostic@vangogh.CS.Berkeley.EDU (Keith Bostic)
 From: /dev/null@gauss.asd.sgi.com
 From: Alan Bawden <Alan@lcs.mit.edu>

I haven't checked this guy's math, but it all seems plausible...

(Some of you may not know that "10-250" is one of MIT's main lecture halls.
And "2.40" is MIT's introductory thermodynamics course.)

 From: Baron Karl <dmark@MIT.EDU>
 Subject: The CP/Donut Heat Engine

Feel free to forward this to any 2.40 types you feel might be interested.  
I'm such a nerd and love it so....

Thursday, there was some conference for campus police officers in 10-250.
I made the mistake of walking by this ill-fated room and discovered (quite
to my surprise, of course) the largest array of donuts I have ever seen in
my life.  They had six full-sized folding tables absolutely FILLED with
donuts.

If we consider 3m^2 of space per table and six tables, that's 18m^2 of
space for donuts.  A donut on its side is approximately 3cm x 15cm or
.0045m^2.  This makes 4000 donuts!  10-250 seats a maximum of 300
people, which gives us an incredible 13.3 cream-filled chocolate-glazed
confectionaries per police officer!

At a conservative 350 calories/donut, that means that each CP consumed
4600  calories at the conference yesterday, which happens to be just
about double the entire reccomended caloric intake of a sedentary
middle-aged male.

Let's model 10-250 as a closed system.  Consider it a triangular prism
formed by cutting a 5m X 30m x 35m rectangular solid across its
diagonal, resulting in an enclosed volume of 2625m^2.  Through PV=mRT
we find that the mass of air enclosed in this room is m=PV/RT (Rair=287,
T=300K, P=10e5 Pa), or 305 kg of air.

If 25% of the donuts' energy is converted to heat by the body (the
remainder going to the production of fat and the recombination of
chemical bonds after digestion), we see that (.25 x 4000 donuts x 350
kcal/donut x 4.16 kJ/kcal) 364000 kJ of energy is released into the
room.

Now, if we use U=mc(T2-T1), we can find the final temperature of the
room.  U=364,000 kJ, m= 305 kJ, T1 = 300 K, c(air)= .716 kJ/kg-K

The final temperature in the room would end up being 1395 K or 1122
degrees C.  This is just about the melting point of copper....

This suggests that 10-250 is NOT an open system or that less than 25%
of the donuts' energy actually gets converted to heat.

Now, what exactly is the implication of 364 MJ?  It may seem like a lot
of energy (and it is) but what exactly is it in terms of power?  As the
egalitarian's credo tells us, power is more important than work, and
the demands of this problem also state that instantaneous output is more
important than the integrated function.

I think the conference was eight hours long.  Instantaneous power
outuput is measured in Kilowatts, which is a J/sec.  Eight hours is (8
hours x 60 min/hr x 60 sec/min) 28800 sec, giving us a power output of
12.64 kW total.  We previously assumed 300 people in the room, or 42
Watts/cop.

Thus, each cop is putting out about 2/3 as much heat as a standard
incandescent light bulb.  This is completely reasonable.

I feel as if I have just hit upon some great truth of humanity here,
but I'm not sure what it is.

In Nerd Hell

Karl

© 1994 Peter Langston