Originally posted by: dullard
Originally posted by: Reck
how long do you think it'd take to die? i've always wondered...
Damn it, I couldn't stop thinking about this. Math time:
Assume:
[*]Entire head is submerged into lava somehow. You really might not die if just your feet are submerged. I bet you could get your head in temporarily, even though you would float (before you burn up).
[*]Lava is 1800°F.
[*]Head is initially 98°F.
[*]Head has the thermal properties of water.
[*]You die if the center of your brain reaches 110°F. I'm just giving a rough estimate here, but I know if fevers reach 110°F it can be quite deadly.
[*]Your head is a cylinder of r=3.5 inch diameter.
[*]Ignore heat transfer through the top of your head and heat transfer to your neck.
The assumptions give this partial differential equation model:
(1/r)*d/dr [r dT/dr] = (1/A) * dT/dt
Where r=radius, T=temperature as a function of radius and time, t=time, and A=1.45*10^-7 m^2/sec (thermal properties of water).
Boundary conditions: T(r=3.5)=1800°F and dT/dr = 0 at r=0.
Initial condition: T(r,0)=98°F.
Use separation of variables, integration, and knowledge of the Bessel equation to solve. No, I won't type it out. Look it up. Solution is (f-you if you find a goof, I'm just doing it quickly while listening to Tom Waits which is always a distraction):
T(r=0,t)=98°F +1702°F*(1-exp(-t/9400 sec))
Thus after 67 seconds, the temperature in the center of your brain is 110°F. You are fully dead. Sure before that time elapsed, the outer portions of your brain will die. But parts of your brain will still function for 67 seconds.