In diffusional growth the rate of change of droplet radius is approximately proportional to
Answer: A
The standard result is that r times dr by dt is a constant set by the supersaturation and the thermodynamic conditions. Radius therefore grows as the square root of time, which slows the process markedly as the droplet enlarges.
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Assertion (A): Condensational growth becomes progressively slower as a droplet enlarges.
Reason (R): The radius increases only as the square root of the elapsed time.
Answer: B
Both are true and the reason gives the dependence, and the same vapour flux must be spread over a surface that grows as the square of the radius. Reaching drizzle sizes by condensation alone would take many hours as a result.
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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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The narrowing of a droplet size spectrum during condensational growth arises because
Answer: D
Correct answer: small droplets grow faster in radius than large ones
Because \( \mathrm{d}r/\mathrm{d}t \propto 1/r \), a small droplet gains radius faster than a large one in the same environment, so the population converges and the spectrum narrows with height. That is the difficulty warm rain theory has to overcome: condensation actively works against producing the few large drops that collision and coalescence need.
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Assertion (A): Condensation alone cannot explain the formation of rain in warm clouds.
Reason (R): It narrows the droplet spectrum and slows sharply at the sizes where collision begins.
Answer: A
Both are true and the reason gives both objections together, and warm clouds are observed to rain within tens of minutes rather than hours. Some mechanism beyond diffusion must broaden the spectrum and accelerate growth.
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Consider the following statements about the condensation gap.
1. Condensation is efficient for droplets up to a few micrometres.
2. Collision and coalescence become efficient above about twenty micrometres.
3. Condensation alone readily carries droplets across that range.
Answer: B
The first two are correct and define the gap between the two mechanisms. The third is exactly what does not happen, and bridging that range is one of the classic problems of warm rain microphysics. It is sometimes called the condensation coalescence bottleneck.
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Latent heat released during condensation affects droplet growth by
Answer: C
Correct answer: warming the droplet and reducing the vapour gradient
Condensation releases latent heat into the droplet, raising its temperature and therefore the saturation vapour pressure at its surface. That reduces the difference between the ambient vapour density and the surface value, which is what drives the diffusion, so the droplet grows more slowly than a purely diffusive calculation would predict. The effect is built into the growth equation as a thermodynamic term in the denominator.
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Assertion (A): The growth equation contains a term for heat conduction as well as one for vapour diffusion.
Reason (R): Both the removal of latent heat and the supply of vapour limit how fast a droplet can grow.
Answer: D
Both are true and the reason gives the two limitations, and either can dominate depending on temperature and pressure. At low temperatures the vapour term dominates, while heat conduction matters more in warm conditions.
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Match each quantity with its effect on the diffusional growth rate.
List I
A. Higher supersaturation
B. Larger droplet radius
C. Latent heat release
D. Ventilation by fall motion
List II
1. reduces the effective driving gradient
2. faster growth in radius
3. enhances growth for large drops
4. slower growth in radius
Answer: A
The first two come directly from the growth equation, while the last two are corrections to it. Ventilation is negligible for cloud droplets but matters for falling raindrops considerably. Each correction applies over a different part of the size range.
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The ventilation coefficient in the growth equation accounts for
Answer: B
Correct answer: enhanced vapour transfer to a droplet that is falling
A stationary droplet is surrounded by a diffusive shell that limits the vapour reaching it. A falling droplet continually moves into fresh air, thinning that shell and increasing the transfer, and the ventilation coefficient corrects the growth equation for it. It is negligible for small cloud droplets and becomes important for the larger, faster-falling ones.
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