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

Heat released by `5 kg` of water when its temperature falls from `20^(@)C` to `0^(@)C` is
`Q_(1) = cm (DeltaT) = 10^(3) xx 5 xx 20 = 0.2 xx 10^(5)` cals
Heat energy taken by `2 kg` of ice at `-20^(@)C` in coming to `0^(@)C` is
`Q_(2) = Q_(1) - Q_(2) = 0.8 xx 10^(5) cal`
Mass of ice melted `m = (Q)/(L)`
`= (0.8 xx 10^(5))/(80 xx 10^(3)) = 1 kg`
`:.` Temperature of mixture will become `0^(@)C`
Mass of water in it `= 5+1 = 6 kg`
Mass of ice `= 2 - 1 = 1 kg`