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1000 small water drops, each of radius r...

`1000` small water drops, each of radius `r`, combine and form a big drop. In this process, find decrease in surface energy.

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Suppose radius of big drop is `R`. During this process, mass will be conserved, so volume will also be conserved.
`("Volume")_("initial") = ("Volume")_("final")`
`((4)/(3)pir^(3)) xx 1000 = ((4)/(3)piR^(3)) rArr R = 10r`
loss in surface energy
`DeltaU_("loss") = TDeltaA_("loss") = T((4pir^(2)) xx 1000 - 4pi(10r)^(2))`
`DeltaU_("loss") = (T)(900 xx 4pir^(2))`
this energy loss will be converted into heat. So increase in temperature of the drop can be found from `T(900 xx 4pir^(2)) = msDeltaT`, From this get the incerase in temperature `DeltaT`.
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Knowledge Check

  • when n small drops are made to combine to from a big drop then the big drop's

    A
    potential increases to `n^(1//3)` times original potential and the charge density decreases to `n^(1//3)` times original times original charge
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    C
    Potential and charges density decrease to `n^(1//3)` times orgianally values
    D
    potential and charge density increase in `n` times original values

  • One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

    A
    `1000:1`
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