`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

Options

A. `(2T)/(rJ)`
B. `(3T)/(rhoJ)(1/r-1/R)`
C. ` (-3T)/(rJ)`
D. `(3T)/(rhoJ)(1/r+1/R)`

Answer

B

Explanation

`("Volume of n drop of water ")=("Volume of 1 drop of water ")`
` :. N xx 4/3 pir^(3) = 4/3 rR^(3) :. N = (R^(3))/(r^(3))`
`"Heat produced " = ("work done ")/J`
` = (S.T xx "decrease in area ")/J`
` m.c d theta = T/j (nxx 4pir^(2) - 4piR^(2))`
`4/3 piR^(3) xx rho xx cd theta = T/J (nxx 4pir^(2) - 4pi R^(2))`
` :. d theta = (3T xx 4 pi )/( rho J 4pi R^(3)c ) [ nr^(2)- R^(2)] `
` = (3T)/(rhojR^(3)c)[(R^(3))/(r^(3))r^(2)-R^(2)] = (3T)/(crhoJ) [ 1/r-1/R]`