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

Maximum heat that can be released by water
`=5xx1xx(20-0)=100kcal`
Heat required to change ice from `-20^@C` to `0^@C`
`=2xx0.5[0-(-20)]=20kcal`
Heat required to melt ice `=2xx80=160cal`
`100kcal lt (20+160)kcal`,
whole ice is not melted.
Equilibrium temperature `=0^@C`
Amount of ice melted `=(100-20)/(80)=1kg`
Amount of water `=5+1=6kg`