Questions

# 2 kg of ice at - 20oC is mixed with 5 kg of water at 20oC 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 and ice are 1 kcal/kg per oC and 0.5 kcal kg/oC while the latent heat of fusion of ice is 80 kcal/kg.

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By Expert Faculty of Sri Chaitanya
a
7 kg
b
6 kg
c
4 kg
d
2 kg
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detailed solution

Correct option is B

Initially ice will absorb heat to raise its temperature to 0oC. then its melting takes place.If mi = initial mass of ice, mi' = Mass of ice that melts and mW= Initial mass of waterBy law of mixture, heat gained by ice = heat lost by water⇒ mi×c×(20)+mi′×L=mWCW[20]⇒ 2×0.5(20)+mi′×80=5×1×20⇒mi′=1kgSo final mass of water = Initial mass of water + Mass of ice that melts = 5 + 1 = 6 kg.

Similar Questions

A calorimeter of water equivalent 10 g contains a liquid of mass 50 g at 40oC. When m gram of ice at -10oC is put into the calorimeter and the mixture is allowed to attain equilibrium, the final temperature was found to be 20oC. It is known that specific heat capacity of the liquid changes with temperature as where $\mathrm{\theta }$ is temperature in oC. The specific heat capacity of ice, water and the calorimeter remains constant and values are  and latent heat of fusion of ice is ${\mathrm{L}}_{\mathrm{f}}=80{\mathrm{calg}}^{-1}$. Assume no heat loss to the surrounding and calculate the value of m in grams.

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