2kg of ice at `20^@C` is mixed with 5kg of water at `20^@C` in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water & ice are `1kcal//kg//^@C` and `0.5`
`kcal//kg//^@C` while the latent heat of fusion of ice is `80kcal//kg`

Options

A. `7 kg`
B. `6 kg`
C. `4 kg`
D. `2 kg`

Answer

B

Explanation

Initially ice will absorb heat to raise its temperature to `0^(@)C` then its melting takes places if `m_(i)` = initial mass of ice `m_(i)^(')`= mass of ice that melts and `m_(W)`= initial mass of water
By law of mixture Heat gained by ice = Heat lost by water `rArr m_(i) xx c xx (20)+m_(i)^(') xx L = m_(W)c_(W)[20]`
`rArr 2 xx 0.5(20) + m_(i)^(') xx 80 = 5 xx 1 xx 20 rArr m_(i)^(') = 1 kg`.
So final mass of water = Initail mass of water + Mass of ice that melts =`5+1=6kg`.