View Single Post
Old 06-25-2010, 02:21 PM   #36
MagiMaster
 
Join Date: Jan 2007
Location: Your imagination
Default Re: GURPS: Ecosystems and Evolution

Well, rethinking the problem with converting heat to watts, I think I have a first draft of an answer. The Stefan-Boltzmann law says that a hot surface emits energy at a rate of emissivity * constant * (temperature in Kelvin)^4 in watts per sq. meter. The Carnot efficiency is the maximum theoretical efficiency a heat engine can attain, though the endoreversible efficiency gives slightly more reasonable numbers. Multiplying the two gives an answer that's not completely unreasonable, but may be somewhat too big. For a hot temperature of 200 F and a cold of 50 F, I get about 290,000,000 watts per sq. mile, which converts to about 9,500 lbs of biomass per day, which seems high. Either I've got the wrong equation, or there needs to be a conversion efficiency on top of everything else (1% - 5% probably).

Anyway, can someone else play with the equation a bit and see if there are any cases where it gives really obviously wrong results?

Th equation is: 5.67*10^-8 * e * Th^4 * (1 - sqrt(Tc/Th)) * 86
Where: e is emmisivity of the surface (0.9 is an average for rock), Th is the hot temperature in Kelvin and Tc is the cold temperature in Kelvin. (5.67*10^-8 is the Stefan-Boltzmann constant, and the 86 is converting watts per square meter to lbs of biomass per square mile per day.)

Edit: I can't decide if it'd be Th^4 to Tc^4. On one hand, the hot side is what's supplying the energy. On the other hand, if more energy is being transfered than what the cold side is radiating away, it wouldn't stay cold. Also, if you use Tc^4, lowering the cold temperature while keeping the hot the same would lower the power produced. I'm not sure that makes much sense.

Edit again: Oh yeah. My wife also mentioned adding belief to the list of energy sources. I'm not quite sure where to start with that one.

Last edited by MagiMaster; 06-25-2010 at 02:31 PM.
MagiMaster is offline   Reply With Quote