Discussion
A droplet grows from 1 to 2 micrometres in a certain time by condensation. Roughly how much longer is needed to reach 4 micrometres?
Answer: C
Correct answer: about four times as long
Condensational growth obeys \( r\,\mathrm{d}r/\mathrm{d}t = \) constant, so the square of the radius grows linearly with time. Going from 1 to 2 micrometres costs \( 4-1=3 \) units of \( r^2 \); going from 2 to 4 costs \( 16-4=12 \), four times as much. That slowing is the central fact of the process and the reason condensation alone cannot make rain.
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