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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

AI Generated Solution

To solve the problem of how the rise in temperature \( d\theta \) occurs when \( n \) number of water droplets, each of radius \( r \), coalesce to form a single drop of radius \( R \), we can follow these steps: ### Step 1: Understand the Energy Transfer When the droplets coalesce, the total surface energy decreases, and this lost energy is converted into heat, which raises the temperature of the water. ### Step 2: Calculate the Initial and Final Surface Energy The surface energy \( E \) of a droplet is given by the formula: \[ ...
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