Critical radius

  1. 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.
     
  2. jcsd
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