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 the heat to raise its temperature at `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_(1) xx c xx (20) + m_(1)^(') xx L = m_(W)c_(W)(20)`
`rArr 2 xx 0.5(20) + m_(1) xx 80 = 5 xx 1 xx 20 rArr m_(i)^(')` = 1kg
So final massof water = Initial mass of water + Mass of ice that melts
= 5+1 =6kg