Question

A fix number of spherical drops of a liquid of radius 'r' coalesce to form a large drop of radius 'R' and volume 'V'. If 'T' is the surface tension then energy ______.

Options

• `4"VT"(1/r-1/R)` is released

• `3"VT"(1/r-1/R)` is released

• is neither released nor absorbed

• `3"VT"(1/r-1/R)` is absorbed

Answer 1

A fix number of spherical drops of a liquid of radius 'r' coalesce to form a large drop of radius 'R' and volume 'V'. If 'T' is the surface tension then energy `underline(3"VT"(1/r-1/R)" is released")`.

Explanation:

When a number of drops coalesce, the energy is released, which is the difference of initial surface energy and final surface energy. The volume of liquid remains same.

Initial energy E₁ = 4πnr²T     where n is the number of drops

If V is the volume then

`"V"=4/3pir^3n`

`therefore4pir^2n=(3V)/r`

`thereforeE_1=(3VT)/r`

Final energy E₂ = 4πR²T

`"V"=4/3piR^3`

`therefore4piR^2=(3V)/R`

`thereforeE_2=(3VT)/R`

`thereforeE_1-E_2=3VT(1/r-1/R)`