Mis. Wilson leaves her freshly-baked blueberry pie on the windowsill to cool. Th
ID: 1480969 • Letter: M
Question
Mis. Wilson leaves her freshly-baked blueberry pie on the windowsill to cool. The delicious fragrance diffuses through the air with a diffusion coefficient of D = 0.2 cm62 / s . How long does it take for Dennis to smell the pie in his tree house 10 meters away? Is the answer to (a) realistic? Based on your experience, how long does it typically take for a smell to travel this distance (you might have experienced this, e.g., at an outdoor barbeque)? What physical effect is missing from our calculation?Explanation / Answer
a) Distance is given by:
d2 = qiDt
d = 10 m = 1000 cm
D(diffusion coefficinet) = 0.2 cm^2 /sec
qi (numerical constant which depends on dimensionality) = 4
d= sqroot ( qiDt)
1000 = sqroot ( 4 x 0.2 x t)
t = 1250000 seconds
b) That’s a long ! Usually, for a human being to smell something, it takes a lot less time than 1250000 seconds. We must consider the effect of wind that may help in carrying the smell to Dennis’s tree house. And, moreover the concentration difference between the normal air and the air around the pie is big, so the smell travels a lot faster.