2 kg of ice at -20^oC is mixed with 5 kg of water at 20^oC in an insulating vessel having a negligible heat capacity. The final mass of water in the container is (The specific heat capacities of water and ice are 1 kcal kg-10C^-1 and 0.5 kcal kg^-1oC^-1 respectively, the latent heat of fusion of ice is 80 kcal kg^-1)

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6 kg

4 kg

7 kg

2 kg

answer is B.

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Detailed Solution

Heat loss by water= $5 \times 10^{3} \times 20 cal$

Heat gained by ice = $2 \times 10^{3} \times 0.5 \times 20 = 20 \times 10^{3} c a l + m \times 80 \times 10^{3}$

m is mass of ice melt.

heat loss =heat gain

$100 \times 10^{3} = 20 \times 10^{3} + m \times 80 \times 10^{3} m = 1 k g$

$s o w a t e r p r e s e n t 5 + 1 = 6 k g$

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