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 required to convert 5 kg of water at `20^(@)C` to 5 kg of water at `0^(@)C=mComegaDeltaT=5xx1xx20=100kcal`.
Heat released by 2 kg ice at `20^(@)C` to convert 2 kg of ice at `0^(@)C=mC_(ice)DeltaT=2xx0.5xx20=20kcal`
How much ice at will convert into water at 0°C for giving another 80 kcal of heat Q = mL
`rArr80=mxx80rArrm=1kg`
Therefore, the amount of water at `0^(@)C=5kg+1kg=6kg`
Thus, at equilibrium we have (6 kg water at `0^(@)C+1kg" ice at"0^(@)C )`