Questions

2 kg of ice at - 20^{o}C is mixed with 5 kg of water at 20^{o}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 and ice are 1 kcal/kg per ^{o}C and 0.5 kcal kg/^{o}C 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

NEW

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 40^{o}C. When m gram of ice at -10^{o}C is put into the calorimeter and the mixture is allowed to attain equilibrium, the final temperature was found to be 20^{o}C. It is known that specific heat capacity of the liquid changes with temperature as $\mathrm{S}=\left(1+\frac{\mathrm{\theta}}{500}\right)\text{cal}{{\mathrm{g}}^{-1}}^{\circ}{\mathrm{C}}^{-1}$where $\mathrm{\theta}$ is temperature in ^{o}C. The specific heat capacity of ice, water and the calorimeter remains constant and values are ${\mathrm{S}}_{\text{ice}}=0.5\text{cal}{{\mathrm{g}}^{-1}}^{\circ}{\mathrm{C}}^{-1}$; ${\mathrm{S}}_{\text{water}}=1.0\text{cal}{{\mathrm{g}}^{-1}}^{\circ}{\mathrm{C}}^{-1}$ 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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