A calorimeter of mass m contains an equal mass of water in it. The temperature of the water and clorimeter is `t_(2).A` block of ice of mass m and temperature `t_(3)lt0^(@)C` is gently dropped into the calorimeter. Let `C_(1),C_(2) and C_(3)` be the specific heats of calorimeter, water and ice respectively and `L` be the latent heat of ice.
The whole mixture in the calorimeter becomes water if

Options

A. `(C_(1)+C_(2))t_(2)-C_(3)t_(3)+Lgt0`
B. `(C_(1)+C_(2))t_(2)+C_(3)t_(3)+Lgt0`
C. `(C_(1)+C_(2))t_(2)-C_(3)t_(3)-Lgt0`
D. `(C_(1)+C_(2))t_(2)+C_(3)t_(3)-Lgt0`

Answer

D

Explanation

Heat lost `=mC_(1)(t_(2)-0)+mC_(2)(t_(2)-0)`
Heat gained `=mC_(3)(0-t_(3))+mL`
`:. C_(1)t_(2)+C_(2)t_(2)gtC_(3)t_(2)gtC_(3)t_(3)+L`
`:. C_(1)t_(1)+C_(2)t_(2)+C_(3)t_(3)-L gt 0`