Santa stands at x = 0 in an infinitely long and narrow corridor (defined by the x-axis). Initially the corridor is devoid of any stink particles. At time t = 0, Santa unleashes a stink bomb (ah political correctness) which releases N stink particles at x = 0. The particles move through the corridor by diffusion only.
Little Timmy’s nose is sensitive enough to smell anything as long as its CONCENTRATION is greater than C. Concentration is defined as the number of particles per unit x distance along the corridor. In terms of N and C, how far away should Timmy stand in order to never smell Santa’s stink bomb?
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FYI: mathematically, diffusion is governed by the following partial differential equation:
∂u/∂t = D* ∂²u/∂x²
-∞ < x < ∞, t > 0
where u = concentration of particles (units: particles / distance)
and D = diffusivity of the particles in the air (units: distance² / time)
10 points for the best answer, plus a load of thumbs ups. Ha ha, load.
2007-12-22
00:08:31
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9 answers
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asked by
Dr D
7
in
Mathematics