Question

if a number of identical droplets of water each of radius R College to form a single drop of radius R the resulting rise in temperature of water is given by​

Answer 1

Hi

Here is your answer,

Let n be the number of little droplets which coalesce to form single drop. Then,

Volume of n little droplets = Volume of single drop

or n × 4/3 πr³ = 4/3 πR³ or nr³ = R³

Decrease in surface area = n × 4πr² - 4πR²

= 4π [ nr² - R²] = 4π [ nr³/r - R²]

= 4π [ R³/r - R²] = 4πR³ [ 1/r - 1/R]

{ ∴ nr³ = R³ }

The energy released,

E = Surface tension × decrease in surface area

= 4πSR³ [ 1/r - 1/R]

The mass of bigger drop,

M = 4/3 πR³ × 1 = 4/3πR³

E = 4/3 πSR³ × 3 [ 1/r - 1/R]

= 3SM [ 1/r - 1/R] { ∴ M = 4/3 πR³ }

∴ KE of bigger droplets = Energy released

= 1/2 MV² = 3SM [ 1/r - 1/R]

V = √6S(R - r/ Rr)