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2kg of ice at -20^@C is mixed with 5kg o...

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`

Text Solution

Verified by Experts

Energy with 5 kg of `H_2O` at `20^@C` to become ice at `0^@C`
`E_1=5000xx1xx20=100000cal`
Energy to raise the temperature of 2 kg ice from `-20^@C` to `0^@C`
`E_1=5000xx0.5xx20=20000cal`
`(E_1-E_2)=80000cal` is available to melt ice at `0^@C`.
So only 1000 g or 1 kg of ice would have melt.
So, the amount of water available`1+5=6kg`
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