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 required to convert `5kg` of water at `20^(@)C` to `5kg` of water at `0^(@)C=mC_(omega)DeltaT=5xx1xx20=100Kcal` .
How much ice at `0^(@)C` will convert into water at `0^(@)C` for giving another `80Kcal` of heat `Q=mL`
`implies 80=mxx80 implies m=1kg`
Therefore, the amount of water at `0^(@)C=5kg+1kg=6kg` . Thus, at equilibrium we have
(`6kg` water at `0^(@)C+1kg` ice at `0^(@)C`)