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

Options

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

Answer

D

Explanation

`4/3piR^(3)nxx4/3pir^(3)` or `R^(3)=nr^(3)`
Energy evolved `=(nx4pir^(2)-4pir^(2))T`
Now `theta=a/(VrhoS)=Q/V=`(In C.G.S system `rho=1` and `S=1)`
`:. theta=([nxx4pir^(2)-4piR^(2)]T)/(4/3piR^(3))`
`(3T[nr^(2)-R^(2)])/R^(3)=3T[(nr^(2))/(nr^(3))-(R^(2))/(R^(3))]=3T[1/r-1/R]`