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 output 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.