A drop's surface to volume ratio changes by what factor when its radius is halved?
Answer: A
The ratio varies inversely with the radius, so halving the radius doubles it. The consequence for evaporation is direct, since the loss rate scales with the exposed surface. Small drops lose a far greater fraction of their mass.
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A bimodal droplet spectrum in a cloud is often taken as evidence of
Answer: B
Uniform condensational growth produces a single narrow mode, so two modes point to parcels that have not grown together. Entrainment and inhomogeneous mixing are the usual explanations offered. A second mode often marks air entrained through the cloud edge.
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Consider the following statements about inhomogeneous mixing.
1. Some droplets evaporate entirely while others are untouched.
2. The surviving droplets then grow in re-moistened air.
3. Mixing always reduces every droplet uniformly in size.
Answer: C
The first two are correct and describe the inhomogeneous limit. The third describes homogeneous mixing, which is the opposite extreme and produces narrowing rather than broadening. Which limit applies depends on the eddy scale involved.
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Match each mixing regime with its effect on the droplet spectrum.
List I
A. Homogeneous mixing
B. Inhomogeneous mixing
C. No mixing
D. Repeated inhomogeneous mixing
List II
1. the spectrum narrows through diffusional growth
2. every droplet shrinks by a similar amount
3. a broadened and often bimodal spectrum
4. some droplets vanish and others survive intact
Answer: D
Which regime applies depends on how the turbulent mixing time compares with the droplet evaporation time. Real clouds sit somewhere between the two idealised extremes. The Damkohler number expresses where a given case falls.
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The Damkohler number in the mixing problem compares
Answer: A
Correct answer: the turbulent mixing time with the droplet evaporation time
The Damkohler number decides what entrainment does to the droplet spectrum. If mixing is fast compared with evaporation, all droplets shrink together and the spectrum stays narrow; if it is slow, some droplets evaporate completely while others are untouched, which broadens the spectrum and helps collection to begin.
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Assertion (A): Whether mixing is homogeneous or inhomogeneous depends on the scale of the eddies involved.
Reason (R): Small eddies mix quickly enough to homogenise before droplets can evaporate.
Answer: B
Both are true and the reason gives the dependence, and large eddies leave pockets of dry air in contact with droplets for longer. The two limits therefore coexist within a single cloud. Eddy size varies continuously through the turbulent cascade.
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The critical radius above which collection dominates over condensation is usually taken as about
Answer: C
Below it collision efficiency is too small for collection to matter, and above it collection accelerates rapidly. Crossing this threshold is the central difficulty of the warm rain problem. Neither mechanism works well on either side of it.
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State whether the following is true or false.
The collision efficiency between two droplets depends on the ratio of their radii as well as their absolute sizes.
Answer: D
Efficiency is low both when the droplets are nearly equal and when the collected droplet is far too small. There is an intermediate ratio at which collection works best for a given collector size. Efficiency is a function of the ratio, not of size alone.
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Three of the following raise the collision efficiency for a given collector. Which is the odd one out?
Answer: A
Correct answer: a collected droplet of almost the same size
Two droplets of nearly equal size fall at nearly equal speeds, so they scarcely approach one another and the efficiency is low. A larger collector, a greater velocity difference and a collected droplet of intermediate size all raise it - the last because very small droplets are swept aside and very large ones do not lag enough.
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Cloud chamber experiments on collection are difficult chiefly because
Answer: B
Reproducing the depth and residence time of a real cloud in the laboratory is the practical obstacle. Levitation techniques and long fall tubes are among the approaches used to work around it. No laboratory can reproduce a kilometre of cloud depth.
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