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n number of water droplets, each of radi...

`n` number of water droplets, each of radius `r`, coalese, to form a single drop of radius `R`. The rise in temperature `d theta` is

A

`(2T)/(rJ)`

B

`(3T)/(J)((1)/(r )-(1)/(R ))`

C

`-(3T)/(J)`

D

`(3T)/(J)((1)/(r )+(1)/(R ))`

Text Solution

Verified by Experts

Let `n` drops coalesce to form a big drop. Then
`nxx(4)/(3)pir^(3)=(4)/(3)piR^(3)rArrn=(R^(3))/(r^(3))`
Heat produced `=("work done")/(J)=S.Txx("decrease in area")/(J)=mtheta d theta`
`rArr d theta=(3T)/(J)((1)/(r )-(1)/(R ))`
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Knowledge Check

  • A number of droplets, each of radius r , combine to form a drop of radius R . If T is the surface tension, the rise in temperature will be

    A
    `(2T)/r`
    B
    `(3T)/R`
    C
    `2T[1/r-1/R]`
    D
    `3T[1/r-1/R]`

  • A large number of droplets, each of radius a, coalesce to form a bigger drop of radius b . Assume that the energy released in the process is converted into the kinetic energy of the drop. The velocity of the drop is sigma = surface tension, rho = density)

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    `[(2sigma)/(rho)(1/a-1/b)]^(1/2)`
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