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-   -   Critical radius (http://www.physicsforums.com/showthread.php?t=163183)

wxgirl Mar29-07 04:13 PM

critical radius
 
1. The problem statement, all variables and given/known data

Cloud droplets begin to form on a population of condensation nuclei as the saturation ratio is gradually increased, with temperature held constant. The nuclei have the same chemical composition but a broad range of sizes. Droplets are activated with radii 0.5 μm when the supersaturation reaches 0.15%. Droplets continue to be activated as the supersaturation is raised to 1%. Solve for critical radius corresponding to a supersaturation of 1%. Also solve for the temperature.



2. Relevant equations

S*=critical supersaturation
S=supersaturation
r*= critical radius
r*= (3b/a)^(1/2)
S*=1+((4a^3)/(27b))^(1/2)
S=1+(a/r)-(b/r^3)

3. The attempt at a solution

What ive done:
S*=critical supersaturation
S=supersaturation = .0015
r= .5
I plugged into S=1+(a/r)-(b/r^3)
I solved for a,

then plugged a into S*=1+((4a^3)/27b))^(1/2)
then solved r*=(3b/a)^(1/2)

The right answer .075μm and t+293K- but I cannot get this at all.


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