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

Answer

B

Explanation

Heat lost by water at `20^(@)C=ms_(W)DeltaT`
`H=5xx1xx20=100 kcal`
At first, ice at `(-20^(@)C)` will take heat to change into ice at `0^(@)C`
`H=ms_(ice)DeltaT=(2kg)xx0.5xx20=20` kcal
`:.` After this, heat available `=(100-20)=20kcal`
This heat will now be gained by ice at `0^(@)C`. Let m kg of ice melt.
`:. mxx80=80:.m=1kg`
Out of `2`kg of ice, `1` kg of ice melts into water and `1`kg of ice remains unmelted in container.
`:.` Amount of water in container. `= 5+1= 6kg`